MikaStars39/nano-eval huggingface dataset:
A continuous-flow reactor is used to carry out a certain liquid-phase decomposition reaction. If the reaction kinetics equation is known to be $(-r_{\mathrm{A}}) = k c_{\mathrm{A}}, k = 0.307\ \mathrm{min}^{-1}$, and the mean residence time is 15 minutes, what is the final conversion rate when using a multi-stage complete mixing model?

Options:
A. 0.96
B. 0.84
C. 0.93
D. 0.90
E. 0.87
F. 0.89
G. 0.88
H. 0.85
I. 0.80
J. 0.92
Answer: A
What is the conversion rate of the second-order reaction $\mathrm{A+B} \to \mathrm{P}$ in a laminar flow tubular reactor? Given: $k = 100 \, \mathrm{cm}^{3} / (\mathrm{mol} \cdot \mathrm{s})$, average residence time $\bar{t} = 10 \, \mathrm{s}$, $c_{\mathrm{A0}} = c_{\mathrm{B0}} = 10^{-3} \, \mathrm{mol} / \mathrm{cm}^{3}$, and molecular diffusion-induced back mixing is neglected.

Options:
A. 0.275
B. 0.485
C. 0.420
D. 0.610
E. 0.530
F. 0.500
G. 0.360
H. 0.390
I. 0.320
J. 0.451
Answer: J
Autocatalytic Reaction
$$
\mathrm{A+P \to P+P}
$$
$k \!=\! 1 \! \mathrm{~ L / (mol ~ \cdot~ min)}$, the reaction takes place in a recycle reactor. Given $F_{\mathrm{A 0}}=1 \ \mathrm{mol} / \mathrm{min}, c_{\mathrm{A 0}}= 1 \ \mathrm{mol} / \mathrm{L}, c_{\mathrm{P_{0}}}=0$, and the conversion rate is 0.99. What is the reactor volume under the optimal recycle ratio?

Options:
A. $$
7.94L
$$
B. $$
9.25L
$$
C. $$
6.59L
$$
D. $$
7.33L
$$
E. $$
9.12L
$$
F. $$
7.46L
$$
G. $$
6.74L
$$
H. $$
8.12L
$$
I. $$
5.87L
$$
J. $$
8.63L
$$
Answer: F
A first-order irreversible reaction at a certain temperature $T$ has a reaction rate constant $k = 2 \, \mathrm{s}^{-1}$ based on the reactor. The catalyst consists of spherical particles with a diameter of 5 mm, and the bed porosity is $\varepsilon = 0.4$. If the internal surface utilization efficiency $\eta_2 = 0.672$ has been calculated, what will the apparent reaction rate constant $k$ be if the catalyst particles are changed to spherical particles with a diameter of 3 mm, assuming $\varepsilon$ remains unchanged?

Options:
A. 1.85
B. 1.58
C. 1.89
D. 1.75
E. 2.01
F. 1.92
G. 2.10
H. 1.67
I. 2.34
J. 1.43
Answer: H
In a closed-loop control system, given
$$
G(s) = \frac{K(s + 9)}{s\big(s^{2} + 4s + 11\big)}, \qquad H(s) = 1
$$
what is the corresponding value of the gain $K$?

Options:
A. 0.5
B. 2
C. 1.5
D. 2.5
E. 0.1
F. 4
G. 0.75
H. 5
I. 1
J. 3
Answer: I
It has been hypothesized that Earth is under continuous bombardment by house-sized minicomets with typical diameters of 10 m, at the rate of some 30,000 per day. Assuming spherical shapes and average densities of $100 kg/m^{3}$, calculate the total mass of material reaching is ().

Options:
A. $$
5. 7 4 \times1 0^{1 1} \mathrm{k g}
$$
B. $$
5. 7 9 \times1 0^{1 1} \mathrm{k g}
$$
C. $$
3. 9 2 \times1 0^{1 1} \mathrm{k g}
$$
D. $$
6. 0 2 \times1 0^{1 1} \mathrm{k g}
$$
E. $$
7. 1 8 \times1 0^{1 1} \mathrm{k g}
$$
F. $$
6. 2 3 \times1 0^{1 1} \mathrm{k g}
$$
G. $$
4. 5 8 \times1 0^{1 1} \mathrm{k g}
$$
H. $$
5. 7 4 \times1 0^{1 2} \mathrm{k g}
$$
I. $$
5. 8 1 \times1 0^{1 1} \mathrm{k g}
$$
J. $$
5. 7 4 \times1 0^{1 0} \mathrm{k g}
$$
Answer: A
Automotive air bags inflate when sodium azide, NaN3, rapidly decomposes to its component elements:
$$
2 \, \mathrm{N a N}_{3} ( s ) \, \longrightarrow\, 2 \, \mathrm{N a} ( s ) \,+\, 3 \, \mathrm{N}_{2} ( g )
$$
How many grams of NaN3 are required to produce 10.0 $\mathrm{f t}^{3}$ of nitrogen gas, about the size of an automotive air bag, if the gas has a density of 1.25 $\mathrm{g / L}?$

Options:
A. $$
4 8 0 \mathrm{g N a N}_{3}
$$
B. $$
5 7 5 \mathrm{g N a N}_{3}
$$
C. $$
6 0 0 \mathrm{g N a N}_{3}
$$
D. $$
5 0 0 \mathrm{g N a N}_{3}
$$
E. $$
5 2 0 \mathrm{g N a N}_{3}
$$
F. $$
4 9 0 \mathrm{g N a N}_{3}
$$
G. $$
5 2 5 \mathrm{g N a N}_{3}
$$
H. $$
5 3 0 \mathrm{g N a N}_{3}
$$
I. $$
5 5 0 \mathrm{g N a N}_{3}
$$
J. $$
5 4 0 \mathrm{g N a N}_{3}
$$
Answer: G
A particular coal contains 2.5% sulfur by mass. When this coal is burned at a power plant, the sulfur is converted into sulfur dioxide gas, which is a pollutant. To reduce sulfur dioxide emissions, calcium oxide (lime) is used. The sulfur dioxide reacts with calcium oxide to form solid calcium sulfite.If the coal is burned in a power plant that uses 2000 tons of coal per day, what mass of calcium oxide is required daily to eliminate the sulfur dioxide?

Options:
A. $$
8. 8 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 8. 8 \times1 0^{7} ~ g ~ C a O}
$$
B. $$
6. 9 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 6. 9 \times1 0^{7} ~ g ~ C a O}
$$
C. $$
7. 3 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 7. 3 \times1 0^{7} ~ g ~ C a O}
$$
D. $$
8. 2 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 8. 2 \times1 0^{7} ~ g ~ C a O}
$$
E. $$
7. 9 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 7. 9 \times1 0^{7} ~ g ~ C a O}
$$
F. $$
7. 1 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 7. 1 \times1 0^{7} ~ g ~ C a O}
$$
G. $$
6. 4 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 6. 4 \times1 0^{7} ~ g ~ C a O}
$$
H. $$
9. 0 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 9. 0 \times1 0^{7} ~ g ~ C a O}
$$
I. $$
8. 5 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 8. 5 \times1 0^{7} ~ g ~ C a O}
$$
J. $$
5. 7 \times1 0^{4} \mathrm{~ k g ~ C a O ~ o r ~ 5. 7 \times1 0^{7} ~ g ~ C a O}
$$
Answer: E
At 298 K and within the range of 0~1000 $p^{\Theta}$, the relationship between the molar volume of water $V_{m}$ and pressure $p$ can be expressed as:
$$
V_{m} - (18.066 - 7.15 \times 10^{-4} p / p^{\Theta} + 4.6 \times 10^{-8} p^{2} / p^{{\Theta}_2}) cm^{3} \cdot mol^{-1}
$$
And
$$
\left( \frac{\partial V_{m}}{\partial T} \right)_{p} = (0.0045 + 1.4 \times 10^{-6} p / p^{\Theta}) cm^{3} \cdot mol^{-1} \cdot K^{-1}.
$$
What is the change in the Gibbs free energy for 1 mol of water compressed from 1 $p^{\Theta}$ to 1000 $p^{\Theta}$ at 298 K?

Options:
A. $$
- 1 2 2. 0 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
B. $$
- 1 2 8. 4 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
C. $$
- 1 2 7. 8 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
D. $$
- 1 2 6. 7 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
E. $$
- 1 2 1. 9 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
F. $$
- 1 2 4. 2 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
G. $$
- 1 2 5. 1 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
H. $$
- 1 2 3. 6 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
I. $$
- 1 3 0. 3 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
J. $$
- 1 2 0. 4 \, \mathrm{J} \cdot\mathrm{m o l}^{-1}
$$
Answer: H
The following reaction has $\Delta_{\mathrm{r}} G_{\mathrm{m}}^{\Theta}( 630 \, \mathrm{K} )=44.3 \, \mathrm{kJ} \cdot \mathrm{mol}^{-1}$.
$2 \mathrm{HgO} (s)= 2 \mathrm{Hg} (g) + \mathrm{O}_{2} (g)$.
If the container contains $\mathrm{O_{2} (g)}$ at standard pressure $p^{\Theta}$ before the reaction starts, what is the partial pressure of $Hg$ in the gas phase coexisting with $HgO(g)$ at equilibrium at 630 K?

Options:
A. $$
5 4 3 2 \, \mathrm{P a}
$$
B. $$
3 2 1 0 \, \mathrm{P a}
$$
C. $$
8 8 8 8 \, \mathrm{P a}
$$
D. $$
1 2 3 4 \, \mathrm{P a}
$$
E. $$
2 3 4 5 \, \mathrm{P a}
$$
F. $$
9 8 7 6 \, \mathrm{P a}
$$
G. $$
1 4 5 2 \, \mathrm{P a}
$$
H. $$
1 1 1 1 \, \mathrm{P a}
$$
I. $$
4 5 6 7 \, \mathrm{P a}
$$
J. $$
6 7 8 9 \, \mathrm{P a}
$$
Answer: G
At $293 K$, the vapor pressure of pure water is 2.33 kPa. The equilibrium vapor pressure of water above a certain aqueous solution is $2.13 \, \mathrm{kPa}$. Given that at 273 K, the entropy of fusion of ice is $\Delta_{\mathrm{s}}^{l} S - 1.22 \, \mathrm{J} \cdot \mathrm{K}^{-1} \cdot \mathrm{g}^{-1}$. What is the freezing point of this solution? (Reasonable approximations can be made in the calculations).

Options:
A. $$
2. 9 8 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
B. $$
4. 0 7 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
C. $$
3. 6 5 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
D. $$
6. 8 3 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
E. $$
1. 8 4 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
F. $$
4. 5 2 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
G. $$
7. 3 1 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
H. $$
2. 7 4 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
I. $$
3. 7 8 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
J. $$
5. 2 9 \times1 0^{-3} \mathrm{~ K}^{-1}
$$
Answer: I
Elementary reaction $\mathrm{BrH_{2}} \longrightarrow \mathrm{HBr + H}$, the experimentally determined pre-exponential factor is $A = 3.00 \times 10^{13} \ \mathrm{cm^3 \cdot mol^{-1} \cdot s^{-1}}$. What are the reaction cross-section and collision diameter at 400 K?

Options:
A. $$
2. 6 0 \times1 0^{-4} \ \mathrm{m}^{2}, \ 8 9. 7 \ \mathrm{p m}
$$
B. $$
2. 8 0 \times1 0^{-3} \ \mathrm{m}^{2}, \ 8 3. 5 \ \mathrm{p m}
$$
C. $$
4. 0 0 \times1 0^{-3} \ \mathrm{m}^{2}, \ 7 9. 6 \ \mathrm{p m}
$$
D. $$
1. 7 0 \times1 0^{-2} \ \mathrm{m}^{2}, \ 8 8. 8 \ \mathrm{p m}
$$
E. $$
2. 2 0 \times1 0^{-2} \ \mathrm{m}^{2}, \ 9 5. 4 \ \mathrm{p m}
$$
F. $$
1. 1 0 \times1 0^{-3} \ \mathrm{m}^{2}, \ 9 2. 2 \ \mathrm{p m}
$$
G. $$
2. 4 0 \times1 0^{-2} \ \mathrm{m}^{2}, \ 8 7. 4 \ \mathrm{p m}
$$
H. $$
2. 9 0 \times1 0^{-4} \ \mathrm{m}^{2}, \ 9 0. 1 \ \mathrm{p m}
$$
I. $$
3. 5 0 \times1 0^{-2} \ \mathrm{m}^{2}, \ 8 5. 3 \ \mathrm{p m}
$$
J. $$
3. 0 0 \times1 0^{-3} \ \mathrm{m}^{2}, \ 8 6. 1 \ \mathrm{p m}
$$
Answer: G
$298 K, \eta(H_{2} O )=0.900 \times 10^{-3} Pa \cdot s$, the rate constant for the reaction determined by diffusion among neutral molecules is $k_{d}=7.34 \times 10^{9} mol^{-1} \cdot dm^{3} \cdot s^{-1}$.
For the bimolecular collision reaction between $H_{3} O^+$ and $OH^-$, the rate constant is $k_{d}=1.3 \times 10^{11} dm^{3} \cdot mol^{-1} \cdot s^{-1},$ and the diffusion coefficients are known to be $D(H_{3} O^{+} )=9.31 \times 10^{-9} m^{2} \cdot s^{-1}, D( OH^{-} )=5.30 \times 10^{-9} m^{2} \cdot s^{-1} (298 K)$. What is $r \left( H_{3} O^+ \right) + r \left(OH^- \right)$?

Options:
A. $$
5. 6 \times1 0^{-1 0} \mathrm{~ m}
$$
B. $$
7. 2 \times1 0^{-1 0} \mathrm{~ m}
$$
C. $$
5. 3 \times1 0^{-1 0} \mathrm{~ m}
$$
D. $$
6. 5 \times1 0^{-1 0} \mathrm{~ m}
$$
E. $$
6. 2 \times1 0^{-1 0} \mathrm{~ m}
$$
F. $$
6. 9 \times1 0^{-1 0} \mathrm{~ m}
$$
G. $$
7. 5 \times1 0^{-1 0} \mathrm{~ m}
$$
H. $$
7. 0 \times1 0^{-1 0} \mathrm{~ m}
$$
I. $$
5. 8 \times1 0^{-1 0} \mathrm{~ m}
$$
J. $$
6. 8 \times1 0^{-1 0} \mathrm{~ m}
$$
Answer: E
At 298K, a NaCl aqueous solution with a concentration of $5.00 \times 10^{-3} \ mol \cdot kg^{-1}$ is diluted with water to half of its original concentration. The ratio of the mean ionic activity coefficients in the final state to the initial state $\gamma_{\pm,2} / \gamma_{+,1}$ is ().

Options:
A. 0.87
B. 0.76
C. 1.02
D. 0.85
E. 1.00
F. 0.92
G. 1.10
H. 0.99
I. 1.15
J. 1.25
Answer: C
At 298 K, it is known that $\Lambda_{m}^{\infty} (CH_{3}COOK) = 1.144 \times 10^{-2} \Omega^{-1} \cdot m^2 \cdot mol^{-1}$, $\Lambda_{m}^{\infty} (K_2SO_4) = 3.070 \times 10^{-2} \Omega^{-1} \cdot m^2 \cdot mol^{-1}$, and $\Lambda_{m}^{\infty} (H_2SO_4) = 8.596 \times 10^{-2} \Omega^{-1} \cdot m^2 \cdot mol^{-1}$. What is $\Lambda_{m}^{\infty} (CH_3COOH)$?

Options:
A. $$
3. 7 1 8 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
B. $$
2. 8 0 5 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
C. $$
4. 8 9 6 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
D. $$
3. 5 9 3 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
E. $$
4. 5 8 9 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
F. $$
3. 2 5 4 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
G. $$
4. 0 3 9 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
H. $$
2. 6 7 4 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
I. $$
3. 9 0 7 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
J. $$
4. 1 0 2 \times1 0^{-2} \; \Omega^{-1} \cdot{\mathrm{m}}^{2} \cdot{\mathrm{m o l}}^{-1}
$$
Answer: I
At 298K, the standard electromotive force (EMF) of the following cell is 0.926 V.
$$
Pt, H_{2}(p^{\Theta}) | NaOH(aq)| HgO(s) | Hg(l)
$$
The standard Gibbs free energy of formation for $H_2O(l)$ is $-237.2 kJ \cdot mol^{-1}$.
What is the equilibrium constant for the reaction
$$
HgO(s) = Hg(l) + \frac{1}{2} O_2(g)
$$

Options:
A. $$
2. 7 5 \times1 0^{-1 0}
$$
B. $$
5. 6 1 \times1 0^{-1 1}
$$
C. $$
3. 2 8 \times1 0^{-1 0}
$$
D. $$
8. 2 0 \times1 0^{-1 2}
$$
E. $$
6. 9 4 \times1 0^{-1 1}
$$
F. $$
1. 9 0 \times1 0^{-8}
$$
G. $$
4. 8 2 \times1 0^{-1 3}
$$
H. $$
9. 1 5 \times1 0^{-9}
$$
I. $$
7. 4 8 \times1 0^{-1 2}
$$
J. $$
1. 4 3 \times1 0^{1}
$$
Answer: B
Consider air at a pressure of 0.2 atm. Calculate the values of $\tau_{T}$ and $\tau_{s}$ is (). Express your answer in Sl units.

Options:
A. $$
5. 1 4 \times1 0^{-6} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 6 7 9 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
B. $$
4. 8 7 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 4 9 8 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
C. $$
5. 0 2 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 6 1 0 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
D. $$
4. 9 5 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 3 6 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
E. $$
4. 9 2 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 2 0 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
F. $$
4. 9 7 \times1 0^{-6} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 8 4 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
G. $$
4. 9 1 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 0 8 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
H. $$
5. 0 0 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 3 5 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
I. $$
4. 9 0 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 5 4 5 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
J. $$
4. 7 6 \times1 0^{-5} \frac{{\mathrm{m}}^{2}} {\mathrm{N}}
$$
$$
3. 3 4 4 \times 1 0^{-5} \frac{\mathrm{m}^{2}} {\mathrm{N}}
$$
Answer: D
This problem explores the physics of a centrifuge. A cylinder of fluid of density $\rho_{\text{fuid}}$ and length $L$ is rotated at an angular velocity $\omega$ (rad $s^{-1}$ ) in a horizontal plane about a vertical aris through one end of the tube. Neglect gravity. An object moving in a circle with
constant angular velocity has an acceleration $a=-r \omega^{2}$ toward the center of the circle. Whst the pressure in the fluid as a function of distance from the axis of rotation is____, assuming the pressure is $p_{0}$ at $r=0$ .

Options:
A. $$
p=p_{0}+\rho( \omega / 2 ) r^{2}
$$
B. $$
p=p_{0}-\rho( \omega^{2} / 3 ) r^{2}
$$
C. $$
p=p_{0}+\rho( \omega^{2} / 2 ) r
$$
D. $$
p=p_{0}-\rho( \omega^{2} / 2 ) r^{2}
$$
E. $$
p=p_{0}+\rho( \omega^{2} / 2 ) r^{2}
$$
F. $$
p=p_{0}-\rho( \omega^{2} / 4 ) r^{2}
$$
G. $$
p=p_{0}+\rho( \omega^{2} ) r
$$
H. $$
p=p_{0}+\rho( \omega^{2} ) r^{2}
$$
I. $$
p=p_{0}-\rho( \omega / 2 ) r^{2}
$$
J. $$
p=p_{0}-\rho( \omega^{2} / 2 ) r
$$
Answer: D
A small system $A$ is in contact with a reservoir $A^{\prime}$ and can exchange both heat and particles withthe reservoir. The number of microstates available to system $A$ does not change. That the difference in total entropy when $A$ is in two distinct states is ______.

Options:
A. $$
\Delta S^{*}=+( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}+( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}
$$
B. $$
\Delta S^{*}=+( N_{1}+N_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}-( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}
$$
C. $$
\Delta S^{*}=-( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}+( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}
$$
D. $$
\Delta S^{*}=+( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}-( U_{1}+U_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}
$$
E. $$
\Delta S^{*}=( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}+( U_{1}+U_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}
$$
F. $$
\Delta S^{*}=( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}-( U_{1}+U_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}
$$
G. $$
\Delta S^{*}=-( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}-( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}
$$
H. $$
\Delta S^{*}=-( N_{1}+N_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}+( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}
$$
I. $$
\Delta S^{*}=-( N_{1}+N_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}-( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}
$$
J. $$
\Delta S^{*}=-( N_{1}-N_{2} ) \left( \frac{\partial S} {\partial U} \right)_{N}-( U_{1}-U_{2} ) \left( \frac{\partial S} {\partial N} \right)_{U}
$$
Answer: G
Molecular clouds are routinely studied using spectral lines from all but which of the following?

Options:
A. $$
\mathrm{S u l f u r ~ d i o x i d e}
$$
B. $$
\mathrm{F o r m a l d e h y d e}
$$
C. $$
\mathrm{N i t r o g e n ~ o x i d e s}
$$
D. $$
\mathrm{P r o p y n e ~ r e s o n a n c e}
$$
E. $$
\mathrm{C a r b o n ~ m o n o x i d e}
$$
F. $$
\mathrm{M e t h a n e ~ c o m p o u n d s}
$$
G. $$
\mathrm{A m m o n i a ~ m o l e c u l e s}
$$
H. $$
\mathrm{M o l e c u l a r ~ h y d r o g e n}
$$
I. $$
\mathrm{I o n i z e d ~ o x y g e n}
$$
Answer: H
Let $U=\{ x_{1}, x_{2}, x_{3}, x_{4} \}$ and $f: U \longrightarrow R$. Given:
$$
f(x_{1}) = 0, \quad f(x_{2}) = 3, \quad f(x_{3}) = -1, \quad f(x_{4}) = 1
$$
What is the unconditional $\mathrm{F}$-superior set of $f$?

Options:
A. $$M_{f}=0.25/x_{4}+0.75/x_{3}+0.5/x_{2}$$
B. $$M_{f}=0.25/x_{1}+1/x_{2}+0.5/x_{4}$$
C. $$M_{f}=0.5/x_{3}+0.25/x_{2}+1/x_{4}$$
D. $$M_{f}=0.5/x_{3}+0.75/x_{2}+0.25/x_{4}$$
E. $$M_{f}=1/x_{3}+0.5/x_{2}+0.25/x_{4}$$
F. $$M_{f}=1/x_{1}+0.5/x_{2}+0.25/x_{3}$$
G. $$M_{f}=0.25/x_{1}+0.5/x_{3}+1/x_{4}$$
H. $$M_{f}=0.25/x_{2}+0.75/x_{1}+1/x_{3}$$
I. $$M_{f}=0.5/x_{1}+1/x_{3}+0.25/x_{4}$$
J. $$M_{f}=0.5/x_{4}+0.25/x_{3}+0.75/x_{2}$$
Answer: B
Let $H \,=\, \{( x, y ) \, \in\, \mathbb{R}^{2} \, : \, y \, > \, 0 \}$ be the upper half plane. Let $g$ be the Riemannian metric on $H$ given by
$$
g={\frac{( \mathrm{d} x )^{2}+( \mathrm{d} y )^{2}} {y^{2}}}.
$$
$( H, g )$ is known as the half-plane model of the hyperbolic plane.\
Let $\gamma( \theta)=( \operatorname{c o s} \theta, \operatorname{s i n} \theta)$ and $\eta( \theta)=( \operatorname{c o s} \theta+1, \operatorname{s i n} \theta)$ for $\theta\in( 0, \pi)$ be two paths in $H$ . What is the angle $A$ at their intersection point ? measured by the metric $g$ .

Options:
A. $$
3\pi/4
$$
B. $$
\pi/4
$$
C. $$
\pi/6
$$
D. $$
2\pi/3
$$
E. $$
\pi/5
$$
F. $$
\pi/2
$$
G. $$
\pi
$$
H. $$
\pi/3
$$
I. $$
7\pi/8
$$
J. $$
5\pi/6
$$
Answer: D
The angular momentum of the sun (assuming uniform rotation) is $J=1. 6 3 \times1 0^{4 8} \mathrm{~ g ~ c m^{2} ~ s^{-1} ~}.$ What is $a / M$ for the sun?

Options:
A. $$
1. 5 6 8
$$
B. $$
0. 8 4 1
$$
C. $$
3. 9 8 2
$$
D. $$
1. 7 5 9
$$
E. $$
2. 1 0 6
$$
F. $$
4. 2 7 9
$$
G. $$
0. 1 8 5
$$
H. $$
0. 2 9 3
$$
I. $$
0. 9 7 4
$$
J. $$
5. 2 3 4
$$
Answer: G
The fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater is() .

Options:
A. $$
3. 8 \times1 0^{-2}
$$
B. $$
5. 7 \times1 0^{-2}
$$
C. $$
7. 1 \times1 0^{-2}
$$
D. $$
9. 0 \times1 0^{-2}
$$
E. $$
1. 5 \times1 0^{-2}
$$
F. $$
4. 9 \times1 0^{-2}
$$
G. $$
2. 3 \times1 0^{-2}
$$
H. $$
8. 4 \times1 0^{-2}
$$
I. $$
6. 2 \times1 0^{-2}
$$
J. $$
0. 6 \times1 0^{-2}
$$
Answer: F
Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits $8 \times1 0^{-1 3}$ of energy and if the average person weighs 75 kg, the number of rads and rems of radiation in 1 yr from such a level of plutonium is().

Options:
A. $$
5.4 \, \times\, 1 0^{-5} \mathrm{~ r e m / y r}
$$
B. $$
6.1 \, \times\, 1 0^{-5} \mathrm{~ r e m / y r}
$$
C. $$
2.0\, \times\, 1 0^{-5} \mathrm{~ r e m / y r}
$$
D. $$
5.1\, \times\, 1 0^{-6} \mathrm{~ r e m / y r}
$$
E. $$
4.5 \, \times\, 1 0^{-4} \mathrm{~ r e m / y r}
$$
F. $$
8.5\, \times\, 1 0^{-6} \mathrm{~ r e m / y r}
$$
G. $$
2.2 \, \times\, 1 0^{-6} \mathrm{~ r e m / y r}
$$
H. $$
3.5 \, \times\, 1 0^{-4} \mathrm{~ r e m / y r}
$$
I. $$
1.5 \, \times\, 1 0^{-4} \mathrm{~ r e m / y r}
$$
J. $$
2.1 \, \times\, 1 0^{-5} \mathrm{~ r e m / y r}
$$
Answer: C
The concentration of $\mathrm{C a^{2+}} \operatorname{i n}$ a particular water supply is $5. 7 \times1 0^{-3} \, M$ . The concentration of bicarbonate ion, $HCO_{3}$$^{-}$, in the same water is $1. 7 \times1 0^{-3} \, M$ . What masses of $\mathrm{C a ( O H )_{2}}$ and $Na_{2}CO_{3}$ must be added to $5.0\times1 0^{7} \mathrm{L}$ of this water to reduce the level of $Ca^{2+}$ to 20% of its original level?

Options:
A. $$
3. 1 \, \times\, 1 0^{5} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
2. 1 \times1 0^{8} \mathrm{g N a_{2} C O_{3}}
$$
B. $$
3. 1 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
2. 0 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
C. $$
5. 5 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
3. 0 \times1 0^{6} \mathrm{g N a_{2} C O_{3}}
$$
D. $$
6. 5 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
2. 4 \times1 0^{6} \mathrm{g N a_{2} C O_{3}}
$$
E. $$
2. 5 \, \times\, 1 0^{7} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
2. 2 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
F. $$
3. 9 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
1. 6 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
G. $$
1. 9 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
1. 8 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
H. $$
7. 2 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
2. 3 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
I. $$
2. 2 \, \times\, 1 0^{5} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
1. 5 \times1 0^{6} \mathrm{g N a_{2} C O_{3}}
$$
J. $$
4. 0 \, \times\, 1 0^{6} \mathrm{~ g ~ C a ( O H )_{2} ~}
$$
$$
3. 2 \times1 0^{7} \mathrm{g N a_{2} C O_{3}}
$$
Answer: B
A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the de- vice for 2.00 min, 12.3 mL of water-saturated $H_{2} ( g )$ is collected. The temperature of the system is $25.5^ \circ C,$ and the atmospheric pressure is 768 torr. What is the magnitude of the current in amperes?

Options:
A. 1.300amp
B. 0.610amp
C. 0.530amp
D. 0.920amp
E. 0.790amp
F. 1.200amp
G. 0.880amp
H. 0.450amp
I. 1.050amp
J. 0.670amp
Answer: E
Estimate the vapour pressure of sea water at 20°C given that the vapour pressure of pure water is 2.338 kPa at that temperature and the solute is largely Nat and CF ions, each present at about 0.50 mol dm$^{-3}$.

Options:
A. $$
2. 2 9 k P a
$$
B. $$
2. 2 8 k P a
$$
C. $$
2. 3 1 k P a
$$
D. $$
2. 2 7 k P a
$$
E. $$
2. 3 2 k P a
$$
F. $$
2. 3 0 k P a
$$
G. $$
2. 3 4 k P a
$$
H. $$
2. 2 6 k P a
$$
I. $$
2. 3 5 k P a
$$
J. $$
2. 3 3 k P a
$$
Answer: F
One reaction has a standard Gibbs energy of -320 kJ mol- and a second reaction has a standard Gibbs energy of -55 kJ moll. What is the ratio of their equilibrium constants at 300 K?

Options:
A. $$
7. 9 1 \times1 0^{5 0}
$$
B. $$
4. 5 5 \times1 0^{3 8}
$$
C. $$
2. 6 9 \times1 0^{4 2}
$$
D. $$
5. 8 1 \times1 0^{4 5}
$$
E. $$
1. 2 1 \times1 0^{4 4}
$$
F. $$
9. 4 7 \times1 0^{3 9}
$$
G. $$
1. 3 8 \times1 0^{4 6}
$$
H. $$
8. 3 3 \times1 0^{3 7}
$$
I. $$
6. 0 8 \times1 0^{4 8}
$$
J. $$
3. 2 4 \times1 0^{4 9}
$$
Answer: G
The equilibrium constant $K=0$ .36 for the reaction PCl,(g) $\rightleftharpoons\mathrm{P C l}_{3} ( \mathrm{g} )+\mathrm{C l}_{2} ( \mathrm{g} )$ at 400 K. Given that 1.5 $g$ of $\mathrm{P C l}_{5}$ was initially placed in a reaction vessel of volume 250 cm$^{3}$, determine the molar concentrations in the mixture at equilibrium.

Options:
A. $$
0. 0 2 5 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 3 9 \bmod\mathrm{d m}^{-3}
$$
B. $$
0. 0 3 0 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 4 5 \bmod\mathrm{d m}^{-3}
$$
C. $$
0. 0 2 7 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 4 2 \bmod\mathrm{d m}^{-3}
$$
D. $$
0. 0 2 9 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 3 5 \bmod\mathrm{d m}^{-3}
$$
E. $$
0. 0 1 8 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 6 0 \bmod\mathrm{d m}^{-3}
$$
F. $$
0. 0 1 9 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 2 2 \bmod\mathrm{d m}^{-3}
$$
G. $$
0. 0 1 3 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 1 6 \bmod\mathrm{d m}^{-3}
$$
H. $$
0. 0 1 5 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 1 2 \bmod\mathrm{d m}^{-3}
$$
I. $$
0. 0 3 3 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 5 3 \bmod\mathrm{d m}^{-3}
$$
J. $$
0. 0 2 1 \bmod\mathrm{d m}^{-3}
$$
$$
0. 0 1 0 \bmod\mathrm{d m}^{-3}
$$
Answer: G
Calculate the pH at the stoichiometric point of the titration of 25.00 cm$^{3}$ of 0.150 M lactic acid with 0.188 M NaOH(aq).

Options:
A. $$
9.00
$$
B. $$
6.25
$$
C. $$
6.50
$$
D. $$
7.50
$$
E. $$
5.75
$$
F. $$
8.00
$$
G. $$
9.50
$$
H. $$
8.25
$$
I. $$
8.50
$$
J. $$
7.00
$$
Answer: F
Estimate the mean ionic activity coefficient and activity of a solution that is 0.015 mol kg$^{-1}$ Mg$F_{\mathrm{2}}$(ac) and 0.025 mol kg$^{-1}$ NaCI(aq).

Options:
A. $$
{0. 0 5 5}
$$
$$
{0. 50}
$$
$$
{0. 0031}
$$
$$
{0. 011}
$$
$$
{0. 68}
$$
$$
{0. 013}
$$
$$
{0. 013}
$$
B. $$
{0. 0 8 5}
$$
$$
{0. 49}
$$
$$
{0. 0021}
$$
$$
{0. 010}
$$
$$
{0. 67}
$$
$$
{0. 012}
$$
$$
{0. 012}
$$
C. $$
{0. 0 6 5}
$$
$$
{0. 51}
$$
$$
{0. 0051}
$$
$$
{0. 013}
$$
$$
{0. 70}
$$
$$
{0. 015}
$$
$$
{0. 015}
$$
D. $$
{0. 0 7 5}
$$
$$
{0. 57}
$$
$$
{0. 0111}
$$
$$
{0. 019}
$$
$$
{0. 76}
$$
$$
{0. 021}
$$
$$
{0. 021}
$$
E. $$
{0. 0 9 0}
$$
$$
{0. 52}
$$
$$
{0. 0061}
$$
$$
{0. 014}
$$
$$
{0. 71}
$$
$$
{0. 016}
$$
$$
{0. 016}
$$
F. $$
{0. 0 6 0}
$$
$$
{0. 53}
$$
$$
{0. 0071}
$$
$$
{0. 015}
$$
$$
{0. 72}
$$
$$
{0. 017}
$$
$$
{0. 017}
$$
G. $$
{0. 0 9 5}
$$
$$
{0. 50}
$$
$$
{0. 0041}
$$
$$
{0. 012}
$$
$$
{0. 69}
$$
$$
{0. 014}
$$
$$
{0. 014}
$$
H. $$
{0. 0 7 0}
$$
$$
{0. 54}
$$
$$
{0. 0081}
$$
$$
{0. 016}
$$
$$
{0. 73}
$$
$$
{0. 018}
$$
$$
{0. 018}
$$
I. $$
{0. 0 8 0}
$$
$$
{0. 55}
$$
$$
{0. 0091}
$$
$$
{0. 017}
$$
$$
{0. 74}
$$
$$
{0. 019}
$$
$$
{0. 019}
$$
J. $$
{0. 0 5 0}
$$
$$
{0. 56}
$$
$$
{0. 0101}
$$
$$
{0. 018}
$$
$$
{0. 75}
$$
$$
{0. 020}
$$
$$
{0. 020}
$$
Answer: H
Zinc has five naturally occurring isotopes: $48.63\%$of$^{64}Zn$ with an atomic weight of 63.929 amu;
$27.90\%$ of $^{66}Zn$ with an atomic weight of 65.926 amu; $4.10\%$ of $^{67}Zn$ with an atomic weight of 66.927 amu; 18.75% of $^{68}Zn$ with an atomic weight of 67.925 amu; and $0.62\%$ of $^{70}Zn$ with an atomic weight of 69.925 amu. The average atomic weight of $Zn$ is().

Options:
A. $$
6 5. 2 0 0 amu
$$
B. $$
6 5. 7 0 0 amu
$$
C. $$
6 5. 4 0 0 amu
$$
D. $$
6 5. 3 8 0 amu
$$
E. $$
6 5. 3 2 0 amu
$$
F. $$
6 5. 4 6 0 amu
$$
G. $$
6 4. 9 0 0 amu
$$
H. $$
6 5. 5 0 0 amu
$$
I. $$
6 5. 6 5 0 amu
$$
J. $$
6 4. 8 5 0 amu
$$
Answer: C
Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants n and $k$ have values of 2.0 and $5 \times1 0^{-4}$, respectively, for time expressed in seconds.

Options:
A. $$
6. 7 3 × 1 0^{-5} \mathrm{~ s^{-1} ~}
$$
B. $$
7. 5 4 × 1 0^{-6} \mathrm{~ s^{-1} ~}
$$
C. $$
1. 5 8 × 1 0^{-4} \mathrm{~ s^{-1} ~}
$$
D. $$
3. 6 8 × 1 0^{-2} \mathrm{~ s^{-1} ~}
$$
E. $$
2. 0 5 × 1 0^{-2} \mathrm{~ s^{-1} ~}
$$
F. $$
3. 2 7 × 1 0^{-3} \mathrm{~ s^{-1} ~}
$$
G. $$
5. 4 6 × 1 0^{-3} \mathrm{~ s^{-1} ~}
$$
H. $$
4. 1 9 × 1 0^{-1} \mathrm{~ s^{-1} ~}
$$
I. $$
2. 6 9 \times1 0^{-2} \mathrm{~ s^{-1} ~}
$$
J. $$
9. 0 1 × 1 0^{-7} \mathrm{~ s^{-1} ~}
$$
Answer: I
Consider a region of the atmosphere of volume 25 dm, which at 20°C contains about 1.0 mol of molecules. Take the average molar mass of the molecules as 29 g mol$^{-1}$ and their average speed as about 400 m $\mathrm{s^{-1}}$ . Estimate the energy stored as molecular kinetic energy in this volume of air.

Options:
A. $$
1. 9 ~ \mathrm{k J}
$$
B. $$
3. 5 ~ \mathrm{k J}
$$
C. $$
2. 9 ~ \mathrm{k J}
$$
D. $$
2. 3 ~ \mathrm{k J}
$$
E. $$
2. 0 ~ \mathrm{k J}
$$
F. $$
3. 7 ~ \mathrm{k J}
$$
G. $$
3. 0 ~ \mathrm{k J}
$$
H. $$
1. 2 ~ \mathrm{k J}
$$
I. $$
1. 8 ~ \mathrm{k J}
$$
J. $$
4. 6 ~ \mathrm{k J}
$$
Answer: D
In the following exercises you will explore the Maxwell distribution of speeds in more detail.Find an expression for the most probable speed of molecules of molar mass $M$ at a temperature $T$ Hint: Look for a maximum in the Maxwell distribution (the maximum occurs as $\mathrm{d} F / \mathrm{d} s=0$ .

Options:
A. $$
\left( \frac{8 R T} {M} \right)^{1 / 2}
$$
B. $$
\left( \frac{6 RT} {3M} \right)^{1 / 2}
$$
C. $$
\left( \frac{RT} {2M} \right)^{1 / 2}
$$
D. $$
\left( \frac{4 R T} {M} \right)^{1 / 2}
$$
E. $$
\left( \frac{9 R T} {M} \right)^{1 / 2}
$$
F. $$
\left( \frac{5 R T} {2M} \right)^{1 / 2}
$$
G. $$
\left( \frac{2 R T} {M} \right)^{1 / 2}
$$
H. $$
\left( \frac{R T} {M} \right)^{1 / 2}
$$
I. $$
\left( \frac{7 R T} {4M} \right)^{1 / 2}
$$
J. $$
\left( \frac{3 R T} {M} \right)^{1 / 2}
$$
Answer: G
The heat capacity of air is much smaller than that of water, and relatively modest amounts of heat are needed to change its temperature. This is one of the reasons why desert regions, though very hot during the day, are bitterly cold at night. The heat capacity of air at room temperature and pressure is approximately $21 \operatorname{J} \operatorname{K}^{-1} \operatorname{m o l}^{-1}$ . How much energy is required to raise the temperature of a room of dimensions 5.5 m x 6.5 m x 3.0 m by 10°C? If losses are neglected, how long will it take a heater rated at 1.5 kW to achieve that increase given that 1 $\mathrm{W}=1 \mathrm{J s}^{-1}?$

Options:
A. $$
9. 2 \times1 0^{2} \mathrm{~ k J}
$$
$$
6. 1 \times1 0^{2} \mathrm{s}
$$
B. $$
8. 9 \times1 0^{2} \mathrm{~ k J}
$$
$$
7. 5 \times1 0^{2} \mathrm{s}
$$
C. $$
1. 2 \times1 0^{3} \mathrm{~ k J}
$$
$$
7. 0 \times1 0^{2} \mathrm{s}
$$
D. $$
1. 0 \times1 0^{3} \mathrm{~ k J}
$$
$$
6. 8 \times1 0^{2} \mathrm{s}
$$
E. $$
7. 1 \times1 0^{2} \mathrm{~ k J}
$$
$$
8. 2 \times1 0^{2} \mathrm{s}
$$
F. $$
6. 5 \times1 0^{2} \mathrm{~ k J}
$$
$$
9. 5 \times1 0^{2} \mathrm{s}
$$
G. $$
8. 4 \times1 0^{2} \mathrm{~ k J}
$$
$$
6. 4 \times1 0^{2} \mathrm{s}
$$
H. $$
9. 0 \times1 0^{2} \mathrm{~ k J}
$$
$$
8. 8 \times1 0^{2} \mathrm{s}
$$
I. $$
9. 8 \times1 0^{2} \mathrm{~ k J}
$$
$$
5. 0 \times1 0^{2} \mathrm{s}
$$
J. $$
7. 4 \times1 0^{2} \mathrm{~ k J}
$$
$$
5. 9 \times1 0^{2} \mathrm{s}
$$
Answer: A
Combustion reactions are relatively easy to carry out and study, and their data can be combined to give enthalpies of other types of reaction. As an illustration, calculate the standard enthalpy of hydrogenation of cyclohexene to cyclohexane given that the standard enthalpies of combustion of the two compounds are -3752 kJ mol$^{-1}$ (cyclohexene) and -3953 kJ mol$^{-1}$ (cyclohexane).

Options:
A. $$
-258km \ mol
$$
B. $$
-603km \ mol
$$
C. $$
-832km \ mol
$$
D. $$
-911km \ mol
$$
E. $$
-121km \ mol
$$
F. $$
-479km \ mol
$$
G. $$
-567km \ mol
$$
H. $$
-192km \ mol
$$
I. $$
-745km \ mol
$$
J. $$
-334km \ mol
$$
Answer: E
Acetylene gas, $\mathrm{C_{2} H_{2}} ( g ),$ can be prepared by the reaction of calcium carbide with water.
$$
\mathrm{C a C}_{2} ( s ) \,+\, 2 \ \mathrm{H}_{2} \mathrm{O} ( l ) \, \longrightarrow\, \mathrm{C a} ( \mathrm{O H} )_{2} ( s ) \,+\, C_{2} \mathrm{H}_{2} ( g )
$$
The volume of $C_{2}H_{2}$, that is collected over water at 23°C by reaction of 0.752 $g$ of $\mathsf{C a C}_{2}$ if the total pressure of the gas is 745 torr is____.

Options:
A. $0. 3 0 8 \mathrm{L C}_{2} \mathrm{H}_{2}$
B. $0. 2 6 7 \mathrm{L C}_{2} \mathrm{H}_{2}$
C. $0. 3 1 5 \mathrm{L C}_{2} \mathrm{H}_{2}$
D. $0. 2 8 5 \mathrm{L C}_{2} \mathrm{H}_{2}$
E. $0. 3 1 0 \mathrm{L C}_{2} \mathrm{H}_{2}$
F. $0. 2 9 9 \mathrm{L C}_{2} \mathrm{H}_{2}$
G. $0. 3 0 2 \mathrm{L C}_{2} \mathrm{H}_{2}$
H. $0. 2 9 0 \mathrm{L C}_{2} \mathrm{H}_{2}$
I. $0. 2 7 3 \mathrm{L C}_{2} \mathrm{H}_{2}$
J. $0. 3 2 4 \mathrm{L C}_{2} \mathrm{H}_{2}$
Answer: F
A 6.53-g sample of a mixture of magnesium carbonate and calcium carbonate is treated with excess hydrochloric acid. The resulting reaction produces $1. 7 2 \, \mathrm{L}$ of carbon dioxide gas at 28°C and 743 torr pressure. Assuming that the reactions are complete, The percentage by mass of magnesium carbonate in the mixture is().

Options:
A. 20.8%
B. 23.3%
C. 18.5%
D. 27.0%
E. 24.1%
F. 21.7%
G. 25.6%
H. 26.5%
I. 19.4%
J. 22.9%
Answer: B
Let $$R_1 = \begin{pmatrix}
0.5 & 0.4 & 0.2 & 0.1 \\
0.2 & 0.6 & 0.4 & 0.5 \\
0.1 & 0.9 & 1 & 0.7
\end{pmatrix},$$
$$
R_2 = \begin{pmatrix}
0.4 & 0.1 & 0.1 & 0.6 \\
0.5 & 0.9 & 0.7 & 0.5 \\
0.6 & 0.8 & 0.7 & 0.6 \\
\end{pmatrix},
$$
$$
R_3 = \begin{pmatrix}
0.6 & 0.5 \\
0.7 & 0.8\\
1&0.9\\0.2&0.3
\end{pmatrix},
$$
$$
R_4 = \begin{pmatrix}
0.7 & 0.3 \\
0.6 & 0.4\\0.5&0.5\\0.4&0.6
\end{pmatrix},
$$
$$
R_5 = \begin{pmatrix}
0.2 & 0.3&0.7\\
0.6 & 0.4&0.8
\end{pmatrix},
$$
$$
R_6 = \begin{pmatrix}
0.2 & 0.6 & 0.9 \\
0.3 & 0.2 & 0.1
\end{pmatrix}
$$
What is the value of $(R_1 \cup R_2) \cdot (R_3 \cdot R_5)$?

Options:
A. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 5}}} & {{{0. 4}}} & {{{0. 5}}} \\ {{{0. 5}}} & {{{0. 4}}} & {{{0. 8}}} \\ {{{0. 5}}} & {{{0. 4}}} & {{{0. 8}}} \\ \end{matrix} \right\}
$$
B. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 3}}} & {{{0. 1}}} & {{{0. 3}}} \\ {{{0. 3}}} & {{{0. 3}}} & {{{0. 3}}} \\ {{{0. 3}}} & {{{0. 6}}} & {{{0. 7}}} \\ \end{matrix} \right\}
$$
C. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 6}}} & {{{0. 3}}} & {{{0. 7}}} \\ {{{0. 6}}} & {{{0. 1}}} & {{{0. 9}}} \\ {{{0. 6}}} & {{{0. 3}}} & {{{0. 9}}} \\ \end{matrix} \right\}
$$
D. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 4}}} & {{{0. 6}}} & {{{0. 4}}} \\ {{{0. 4}}} & {{{0. 2}}} & {{{0. 5}}} \\ {{{0. 4}}} & {{{0. 4}}} & {{{0. 6}}} \\ \end{matrix} \right\}
$$
E. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 9}}} & {{{0. 7}}} & {{{0. 8}}} \\ {{{0. 9}}} & {{{0. 5}}} & {{{0. 8}}} \\ {{{0. 9}}} & {{{0. 5}}} & {{{0. 6}}} \\ \end{matrix} \right\}
$$
F. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{1. 0}}} & {{{0. 9}}} & {{{0. 9}}} \\ {{{1. 0}}} & {{{0. 7}}} & {{{0. 6}}} \\ {{{1. 0}}} & {{{0. 2}}} & {{{0. 5}}} \\ \end{matrix} \right\}
$$
G. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 8}}} & {{{0. 2}}} & {{{0. 8}}} \\ {{{0. 8}}} & {{{0. 3}}} & {{{0. 2}}} \\ {{{0. 8}}} & {{{0. 5}}} & {{{0. 3}}} \\ \end{matrix} \right\}
$$
H. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 7}}} & {{{0. 5}}} & {{{0. 6}}} \\ {{{0. 7}}} & {{{0. 5}}} & {{{0. 7}}} \\ {{{0. 7}}} & {{{0. 1}}} & {{{0. 5}}} \\ \end{matrix} \right\}
$$
I. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 1}}} & {{{0. 5}}} & {{{0. 1}}} \\ {{{0. 1}}} & {{{0. 8}}} & {{{0. 1}}} \\ {{{0. 1}}} & {{{0. 7}}} & {{{0. 3}}} \\ \end{matrix} \right\}
$$
J. $$
(R_1 \cup R_2) \cdot (R_3 \cdot R_5)=\left\{\begin{matrix} {{{0. 2}}} & {{{0. 8}}} & {{{0. 2}}} \\ {{{0. 2}}} & {{{0. 6}}} & {{{0. 2}}} \\ {{{0. 2}}} & {{{0. 9}}} & {{{0. 2}}} \\ \end{matrix} \right\}
$$
Answer: A
The most fundamental change in Chinese society after the Opium War was ().

Options:
A. The Qing Dynasty successfully maintained its territorial integrity
B. The Chinese Emperor initiated a campaign of isolationism
C. The Chinese people shoulder the dual task of fighting against feudalism and aggression
D. China adopted a system of direct democratic governance
E. All foreign influence was expelled from Chinese ports
F. The new idea of "learning from the West" has emerged
G. China began to fall into a semi colonial and semi feudal society
H. Buddhism was reestablished as the dominant ideology in China
I. The contradiction between foreign capitalism and the Chinese nation has become the main contradiction
J. The Chinese economy transitioned to a strictly agrarian model
Answer: G
Over the past few years, the proportion of entertainment spending in household expenditure has risen sharply, while the income of movie theaters has been declining. This is largely due to the growth of the video rental industry, which has taken business away from movie theaters, according to the theater industry. All of the following answer choices are true, which of them weakens the above argument most strongly?

Options:
A. The video rental industry has seen a significant decline in revenue in recent years.
B. The cost of renting videotapes is much higher than going to the movies.
C. Business at movie theaters was on the decline even before the video rental industry boomed.
D. Movie theaters have diversified their offerings to include live events and concerts.
E. The majority of consumers have switched to streaming services instead of video rentals.
F. Among consumers, there are still some who prefer watching movies.
G. The quality of films available for rent is often lower than that of films shown in theaters.
H. Many consumers enjoy the social experience of watching movies in theaters.
I. Many movie studios earn large sums of money by selling the video rights to their films.
J. Movie theaters have started offering lower ticket prices to attract more customers.
Answer: C
The most effective method currently adopted by countries worldwide to avoid international double taxation is ( ).

Options:
A. withholding method
B. allocation method
C. deduction method
D. credit method
E. deferral method
F. low tax method
G. exemption method
H. consolidation method
I. repatriation method
J. treaty method
Answer: D
In China's international trade business, the most commonly used and relatively fair and reasonable commodity inspection method is ( ).

Options:
A. Inspection in the exporting country
B. Random sampling inspection
C. Inspection in the importing country
D. Weight inspection at the port of shipment and quality inspection at the port of destination
E. Inspection at the manufacturing site
F. Inspection by a third-party agency
G. Pre-shipment inspection by the exporting company
H. Comprehensive inspection before customs clearance
I. Joint inspection by import and export authorities
J. Inspection in the exporting country and re-inspection in the importing country
Answer: J
When examining the consumption functions by age groups, we find that the marginal propensity to consume varies across different age segments. Therefore, what is the most appropriate econometric model approach?

Options:
A. Model separately by age groups
B. Incorporate dummy variables in the age segments
C. Adjust the constant term without dummy variables
D. Add a dummy variable to the constant term
E. Adjust the variable coefficients for each age group
F. Add dummy variables to both the constant term and variable coefficients
G. Incorporate dummy coefficients in the constant terms
H. Increase the constant terms in the coefficients
I. Model separately the variable coefficients
J. Increase the dummy variables in the variable coefficients
Answer: J
Which of the following crimes committed by a Chinese citizen, A, in Country A can be exempted from prosecution regardless of whether the law of the place where the crime was committed imposes a penalty?

Options:
A. Theft
B. Bribery
C. Kidnapping
D. Bigamy
E. Tax evasion
F. Rape
G. Drug trafficking
H. Fraud
I. Murder
J. Assault
Answer: D
From the development of children's color vision, can correctly identify the basic color, but can not be correctly named, when is it?

Options:
A. About 18 months old
B. About 3 years old
C. About 4 years old
D. About 6 months old
E. About 1 year old
F. About 4.5 years old
G. About 2 years old
H. About 5 years old
Answer: B
For infants aged 3-6 months, apart from the provision of auditory devices such as rattles or music boxes with sound, what should be added?

Options:
A. Climbing toys
B. Operate game materials
C. Interactive storybooks
D. Image toys
E. Develop tactile toys
F. Educational mobile apps
G. Shape-sorting toys
H. Visual tracking cards
Answer: E
Preschool teachers should refrain from using technical terms when talking with parents. What does this require kindergartens to do in carrying out parental work?

Options:
A. Understand the mentality of parents and carry out targeted parental work
B. Focus solely on child-centered activities
C. Treat different types of parents differently
D. Provide parenting guidance to parents
E. Develop a standardized communication procedure
F. Maintain a professional distance from parents
G. The art of conversation and communication
H. Limit interactions to written communications only
Answer: G
In what year did the appointment system of kindergarten teachers begin in China?

Options:
A. 1999
B. 1996
C. 1998
D. 2001
E. 2000
F. 1992
G. 1994
H. 1995
I. 1997
J. 1993
Answer: B
What age are toys suitable for children that move the whole body, develop intelligence and practice hand skills?

Options:
A. 9 to 10 years old
B. 1 to 2 years old
C. 3 years old
D. 4 to 6 months old
E. 5 to 6 years old
F. 11 to 12 years old
G. 7 to 8 years old
H. 4 and 5 years old
I. Before 1 year of age
Answer: C
individual development is carried out from the head to the feet, from the middle to the periphery, which indicates the characteristics of individual development?

Options:
A. Stages
B. Uniformity
C. Consistency
D. Regularity
E. Sociality
F. Individual differences
G. Predictability
H. Continuity
I. Symmetry
J. Sequentiality
Answer: D
Montessori believes that there are three main teaching tasks of teachers, which are respectively ().

Options:
A. Set educational goals, prepare teaching AIDS, and demonstrate
B. Organize activities, monitor attendance, and enforce policies
C. Plan lessons, evaluate progress, and provide feedback
D. Facilitate discussions, promote collaboration, and encourage creativity
E. Develop resources, maintain discipline, and assess students
F. Observe and guide, demonstration and preparation
G. Set educational goals, create environment, and demonstrate
H. Design curriculum, set rules, and manage classroom
I. Observe and guide, prepare teaching AIDS, and create the environment
J. Create schedules, assign homework, and grade tests
Answer: F
What should be the evaluation of children's games?

Options:
A. Combine positive evaluation with negative evaluation
B. Positive comments
C. Set unrealistic expectations
D. Focus only on mistakes
E. Emphasize competition over fun
F. Ignore their efforts
G. Compare them to other children
H. Negative comments
I. Avoid giving any feedback
J. Offer only praise without critique
Answer: B
What is the most direct factor affecting the personality development of elementary school students?

Options:
A. Family cultural background
B. Family income situation
C. Availability of extracurricular activities
D. Teacher-student relationships
E. Peer influence in school
F. Community support and involvement
G. Media exposure and consumption
H. Family education methods
I. Socioeconomic status of the neighborhood
Answer: H
Athlete's foot is usually due to a lack of______.

Options:
A. Vitamin K
B. Calcium
C. Zinc
D. Iron
E. Vitamin C
F. Vitamin B1
G. Vitamin B2
H. Vitamin D
I. Magnesium
J. Protein
Answer: F
Who is the author of "The Head Teacher"?

Options:
A. Wang Anyi.
B. Han Han.
C. Lu Yao.
D. Ma Jian.
E. Yu Hua.
F. Liu Xinwu.
G. Cao Wenxuan.
H. Wang Shuo.
I. Jiang Rong.
J. Mo Yan.
Answer: F
Since the Wanli period of the Ming Dynasty, nianhua (New Year picture) workshops began to appear in Yangliuqing, Tianjin. Which were the earliest two known workshops?

Options:
A. The earliest two known workshops were Liu Zhen and Tang Wei.
B. The earliest two known workshops were Zhang Yuxin and Li Minghao.
C. The earliest two known workshops were Chen Guozhong and Sun Yifan.
D. The earliest two known workshops were Lin Yutang and Feng Zhi.
E. The earliest two known workshops were Dai Lianzeng and Qi Jianlong.
F. The earliest two known workshops were Zhao Qiang and Xu Wei.
G. The earliest two known workshops were Yang Shouyi and Wu Jian.
H. The earliest two known workshops were He Jian and Guo Xiaoping.
I. The earliest two known workshops were Wang Shizhen and Liu Feng.
J. The earliest two known workshops were Qian Lian and Zhou Ming.
Answer: E
What is the academic term for a character in literature who possesses unique and charming traits?

Options:
A. Character motif.
B. Imaginative construct.
C. Literary archetype.
D. Dramatic embodiment.
E. Trait exemplar.
F. Literary figurehead.
G. Fictional persona.
H. Thematic figure.
I. Protagonist model.
J. Narrative trope.
Answer: C
Who is Mo Jiren from the Neapolitan opera school during the Baroque period?

Options:
A. Lotti
B. Handel
C. Pergolesi
D. Vivaldi
E. Corelli
F. Albinoni
G. Scarlatti
H. Galuppi
I. Vinci
J. Provenzal
Answer: J
The author of the song 'Unity is Strength' is ( ).

Options:
A. Li Zhafu
B. Lu Zhao
C. Luo Ming
D. Li Xun
E. Lin Zhou
F. Lu Su
G. Liao Zhu
H. Li Yiming
I. Lei Song
J. Lu Xin
Answer: F
Which film was recognized as the Best Picture at the 2023 Golden Horse Awards?

Options:
A. The Jade Oath
B. The Silken Road
C. The Shadow Play
D. The Scarlet Harmony
E. The Lantern's Glow
F. The Whispering Veil
G. The Searing Passage
Answer: C
Who is the author of 'Victory Celebration Article'?

Options:
A. Zhang Xu
B. Zhong Yao
C. Zhao Mengfu
D. Cai Yong
E. Huai Su
F. Wang Xianzhi
G. Liu Gongquan
H. Suo Jing
I. Mi Fu
J. Huang Xiang
Answer: B
Based on the equation
$$
y^{\prime\prime}-6 y^{\prime}+5 y=-3 e^{\prime}+x+1.
$$
the solution of this equation is ().

Options:
A. $$
f(x) = \left(4 + \frac{1}{2} x^2\right) e^x
$$
B. $$
f(x) = \left(3 + \frac{1}{2} x^2\right) e^{3x}
$$
C. $$
f(x) = \left(1 + \frac{1}{2} x^2\right) e^{2x}
$$
D. $$
f(x) = \left(1 + \frac{1}{2} x^2\right) e^{3x}
$$
E. $$
f(x) = \left(2+ \frac{1}{2} x^2\right) e^x
$$
F. $$
f(x) = \left(3 + \frac{1}{2} x^2\right) e^x
$$
G. $$
f(x) = \left(2 + \frac{1}{2} x^2\right) e^{3x}
$$
H. $$
f(x) = \left(1 + \frac{1}{2} x^2\right) e^x
$$
I. $$
f(x) = \left(5 + \frac{1}{2} x^2\right) e^{3x}
$$
J. $$
f(x) = \left(5 + \frac{1}{2} x^2\right) e^x
$$
Answer: H
A cylinder with a radius of $R$ and a length of $l$ is placed flat in a pool of water with a depth of $2R$ (the side of the cylinder is tangent to the water surface). Let the density of the cylinder be $\rho\left(\rho> 1 \right)$, and the work required to pull the cylinder out of the water surface is ().

Options:
A. $$ ( \rho+2 ) \, \pi g^{2} l R^{2} $$
B. $$ ( 3\rho-2 ) \, \pi g l R^{3} $$
C. $$ ( 2 \rho-1 ) \, \pi g l R^{3} $$
D. $$ ( \rho - 1 ) \, \pi^{3} g^{3} l R^{3} $$
E. $$ ( \rho^2 - 1 ) \, \pi g l R^{3} $$
F. $$ ( 2 \rho+1 ) \, \pi g l R^{3} $$
G. $$ ( \rho-2 ) \, \pi g l R^{3} $$
H. $$ ( 2 \rho-3 ) \, \pi g^{3} l R^{3} $$
I. $$ ( \rho+2 ) \, \pi g l R^{3} $$
J. $$ ( \rho-1 ) \, \pi g^{3} l R^{3} $$
Answer: C
Someone wants to invest 10,000 yuan to buy a stock. The current price of this stock is 2 yuan per share. Suppose that the price of this stock may be 1 yuan per share or 4 yuan per share in one year. Is the financial advisor's advice correct? What is the market value E(X) of the stock purchased in one year, and what is the number of stocks purchased in one year, E(Y)?

Options:
A. incorrect,E(X)=5000,E(Y)=2500
B. correct,E(X)=12500,E(Y)=6250
C. incorrect,E(X)=13000,E(Y)=9000
D. incorrect,E(X)=10000,E(Y)=5000
E. incorrect,E(X)=12500,E(Y)=6250
F. incorrect,E(X)=14000,E(Y)=7000
G. incorrect,E(X)=7500,E(Y)=3750
H. incorrect,E(X)=15000,E(Y)=3860
I. incorrect,E(X)=15000,E(Y)=3760
J. incorrect,E(X)=12000,E(Y)=6000
Answer: B
A spherical surface with radius R is uniformly charged, and the surface charge density is $\sigma$. What is the magnitude of the electric field strength at a distance R from the surface?

Options:
A. $\frac{\sigma}{9 \varepsilon_0}$
B. $\frac{\sigma}{10 \varepsilon_0}$
C. $\frac{\sigma}{5 \varepsilon_0}$
D. $\frac{\sigma}{3 \varepsilon_0}$
E. $\frac{\sigma}{7 \varepsilon_0}$
F. $\frac{\sigma}{4 \varepsilon_0}$
G. $\frac{\sigma}{8 \varepsilon_0}$
H. $\frac{\sigma}{6 \varepsilon_0}$
I. $\frac{\sigma}{2 \varepsilon_0}$
J. $\frac{\sigma}{\varepsilon_0}$
Answer: F