# The Standard Molar Enthalpies of Formation of Nano-ZnO Particles with Different Morphologies

Authors: Ya Li; Xinmin Wu
Journal: Journal of Nanomaterials
 (2015)

---

## Abstract

The thermodynamic properties of nano-ZnO particles with different morphologies were studied. First, based on the measurements of XRD and SEM, the morphologies of the five nano-ZnO products were determined as sheet, block, sieve, column, and rod, and their particle size was about 40 nm. Then, based on a designed thermodynamic cycle, the standard molar enthalpies of formationΔ
f
H
m
Ө of the nano-ZnO particles were determined by the RD496-2000 microcalorimeter, and they are Δ
f
H
m
Ө(sheet) = (
-
337.43
±
0.47
) kJ·mol−1, Δ
f
H
m
Ө(block) = (
-
336.57
±
0.43
) kJ·mol−1, Δ
f
H
m
Ө(sieve) = (
-
337.04
±
0.57
) kJ·mol−1, Δ
f
H
m
Ө(column) = (
-
343.56
±
0.39
) kJ·mol−1, and Δ
f
H
m
Ө(rod) = (
-
341.43
±
0.41
) kJ·mol−1. The results show that the bigger difference of the morphologies of nano-ZnO, the bigger difference of the standard molar enthalpies of formation.


---

## Body

## 1. Introduction

Along with the development of nanotechnology, nano-ZnO becomes an important new species of material in the nanotechnology field [1–3]. Nano-ZnO is a kind of particles whose size is among 1~100 nm. Compared with conventional ZnO, nano-ZnO shows many special properties, such as surface effect and size effect. Because of the small size and large specific surface area, nano-ZnO exhibits unique properties of light, electricity, heat, and magnetic susceptibility. So it is widely used in many fields, such as ultraviolet absorption materials, piezoelectric materials, magnetic materials, pressure sensitive materials, and medicine [4–6]. It has many morphologies, such as rod, sheet, and needle ones. In present work, the preparation of nano-ZnO with different morphologies has been studied. It is the base to research the different functions of nano-ZnO with different morphologies in different fields. The thermodynamic properties are inherent properties of nano material. To find out the change rule of the thermodynamic properties of nano-ZnO with different morphologies and different sizes is helpful for its application in different fields [7, 8]. The “word” nanothermodynamics appeared formally in 2000 [9]. Then Giebultowicz classified nanothermodynamics to thermodynamics [10]. He thought nanothermodynamics is a small-system thermodynamics, which created a new branch of thermodynamics. In 2001, Hill published a series of papers about nanothermodynamics inNano Letters [11–13]. The prospects of nanothermodynamics and the contribution of it to the nanosystem were described in those papers. In 2010, a report about the entropy and enthalpy change of nanoparticle with different sizes was published [14]. But the study on the thermodynamic properties of nano-ZnO with different morphologies is absent.In this work, we determined the standard molar enthalpies of solution of nano-ZnO particles with five different morphologies by RD496-2000 microcalorimeter and calculated the standard molar enthalpies of the nano-ZnO particles.


## 2. Experimental

### 2.1. Reagents and Instruments

Reagents: zinc oxide (ZnO) nanoparticles (J&K Scientific Ltd.), potassium bisulfate (AR, Beijing Jingqiu Chemical Co., Ltd.), potassium sulfate (AR, Beijing Beihua Fine Chemicals Co., Ltd.), potassium chloride (AR, Beijing Chemical Works), and zinc sulfate heptahydrate (AR, Beijing Jingqiu Chemical Co., Ltd.).Instruments: microcalorimeter (RD496-2000, Mianyang Zhongwu Thermal Analysis Instruments Co., Ltd.), X-ray diffractometer (Beijing Purkinje General Instrument Co., Ltd.), and field emission scanning electron microscope (FE-SEM, JEOL JSM-6700F, USA).


### 2.2. Characterization of Nano-ZnO

XRD and SEM analyses were done to determine the particle size and morphology of nano-ZnO products.


### 2.3. Determination of Standard Molar Enthalpy

The determination of enthalpy of formation was carried out with the RD496-2000 microcalorimeter [15]. To verify the reliability of the microcalorimeter, the molar enthalpy of solution of KCl in water was measured at 298.15 K, and the experimental data were shown in Table 1. The calculated molar enthalpy of solution of KCl was determined to be 17.57
±
0.02 kJ·mol−1, which was within ±0.5% of literature values (17.56
±
0.21 kJ·mol−1) [16].Table 1
The enthalpy of solution of KCl in water at 298.15 K.
Reaction system
Number
m
KCl (g)
V
H
2
O (mL)
Q
1 (mJ)
Δ
r
H
m1
Ө (kJ⋅mol−1)
1
0.0112
3.0
2640.34
17.56
2
0.0112
3.0
2643.35
17.58
KCl→H2O
3
0.0112
3.0
2642.60
17.58
4
0.0112
3.0
2639.89
17.56
5
0.0112
3.0
2641.10
17.57
6
0.0112
3.0
2640.80
17.57
Average value
2641.35
17.57 ± 0.02The standard enthalpies of formation of nano-ZnO particles were determined according to a designed chemical cycle shown in Figure1.Figure 1
Designed thermochemical cycle of ZnO reaction system.In the experiment of calorimetry, 15 mL steel reservoir with two separable glass sleeves in it is used as sample cells, and the solid and liquid substances were put into the glass sleeves, respectively. Then the cells were put into calorimeter chamber at 298.15 K; when the baseline kept going steadily (the fluctuation is less than ±0.00001 mV) the firing pin was triggered to break the glass sleeve and to make the sample mix with the solution. Then the chamber was kept to be at 298.15 K until the thermodynamic curve kept going parallel to the baseline with very small fluctuation which shows the completion of reaction. In this experiment, the solids were products (0.0141 g ZnSO4·7H2O and 0.0086 g K2SO4) and reactants (0.0040 g ZnO and 0.0134 g KHSO4) (there were 5 kinds of reactant systems by choosing different morphologies of nano-ZnO) showed in Figure 1. The liquid was 0.3000 g HCl solution (0.26 mol·L−1). The products and reactants were mixed with the HCl solution separately. Then the heat of the reaction (Q
1 and Q
2) in the process was determined.


## 2.1. Reagents and Instruments

Reagents: zinc oxide (ZnO) nanoparticles (J&K Scientific Ltd.), potassium bisulfate (AR, Beijing Jingqiu Chemical Co., Ltd.), potassium sulfate (AR, Beijing Beihua Fine Chemicals Co., Ltd.), potassium chloride (AR, Beijing Chemical Works), and zinc sulfate heptahydrate (AR, Beijing Jingqiu Chemical Co., Ltd.).Instruments: microcalorimeter (RD496-2000, Mianyang Zhongwu Thermal Analysis Instruments Co., Ltd.), X-ray diffractometer (Beijing Purkinje General Instrument Co., Ltd.), and field emission scanning electron microscope (FE-SEM, JEOL JSM-6700F, USA).


## 2.2. Characterization of Nano-ZnO

XRD and SEM analyses were done to determine the particle size and morphology of nano-ZnO products.


## 2.3. Determination of Standard Molar Enthalpy

The determination of enthalpy of formation was carried out with the RD496-2000 microcalorimeter [15]. To verify the reliability of the microcalorimeter, the molar enthalpy of solution of KCl in water was measured at 298.15 K, and the experimental data were shown in Table 1. The calculated molar enthalpy of solution of KCl was determined to be 17.57
±
0.02 kJ·mol−1, which was within ±0.5% of literature values (17.56
±
0.21 kJ·mol−1) [16].Table 1
The enthalpy of solution of KCl in water at 298.15 K.
Reaction system
Number
m
KCl (g)
V
H
2
O (mL)
Q
1 (mJ)
Δ
r
H
m1
Ө (kJ⋅mol−1)
1
0.0112
3.0
2640.34
17.56
2
0.0112
3.0
2643.35
17.58
KCl→H2O
3
0.0112
3.0
2642.60
17.58
4
0.0112
3.0
2639.89
17.56
5
0.0112
3.0
2641.10
17.57
6
0.0112
3.0
2640.80
17.57
Average value
2641.35
17.57 ± 0.02The standard enthalpies of formation of nano-ZnO particles were determined according to a designed chemical cycle shown in Figure1.Figure 1
Designed thermochemical cycle of ZnO reaction system.In the experiment of calorimetry, 15 mL steel reservoir with two separable glass sleeves in it is used as sample cells, and the solid and liquid substances were put into the glass sleeves, respectively. Then the cells were put into calorimeter chamber at 298.15 K; when the baseline kept going steadily (the fluctuation is less than ±0.00001 mV) the firing pin was triggered to break the glass sleeve and to make the sample mix with the solution. Then the chamber was kept to be at 298.15 K until the thermodynamic curve kept going parallel to the baseline with very small fluctuation which shows the completion of reaction. In this experiment, the solids were products (0.0141 g ZnSO4·7H2O and 0.0086 g K2SO4) and reactants (0.0040 g ZnO and 0.0134 g KHSO4) (there were 5 kinds of reactant systems by choosing different morphologies of nano-ZnO) showed in Figure 1. The liquid was 0.3000 g HCl solution (0.26 mol·L−1). The products and reactants were mixed with the HCl solution separately. Then the heat of the reaction (Q
1 and Q
2) in the process was determined.


## 3. Result Analysis and Discussion

### 3.1. Particle Size and Morphology of Nano-ZnO

The XRD and SEM results of 5 kinds of nano-ZnO particles with different morphologies were shown in Figures2 and 3. The sharp XRD peaks suggest that the products are highly crystallized and the morphology of each nanoparticle is uniform, and the morphologies of the nano-ZnO can be seen clearly in the SEM pictures.Figure 2
XRD spectra of 5 nano-ZnO particles with different morphologies (the serial numbers 1~5 were denoted by the ones of sheet, sieve, block, column, and rod morphology).SEM pictures of 5 nano-ZnO particles.
(a)
Sheet
(b)
Sieve
(c)
Block
(d)
Column
(e)
Rod


### 3.2. Standard Molar Enthalpy of Formation of Nano-ZnO

Standard molar enthalpy of formation of nano-ZnO can be obtained according to the designed thermodynamic cycle shown in Figure1 and Hess law, and the detailed calculation was performed as formula (1). The experimental and calculated data were shown in Tables 2, 3, and 4
(1)
Δ
f
H
m
Ө
ZnO
=
Δ
f
H
m
Ө
K
2
SO
4
+
Δ
f
H
m
Ө
ZnSO
4
·
7
H
2
O
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
-
6
Δ
f
H
m
Ө
(
H
2
O
)
-
2
Δ
f
H
m
Ө
(
KHSO
4
)
=
(
-
1414
)
kJ
·
mol
-
1
+
(
-
3077.75
)
kJ
·
mol
-
1
-
6
×
(
-
285.83
±
0.04
)
kJ
·
mol
-
1
-
2
×
(
-
285.83
±
0.04
)
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
.Table 2
Thermochemical data of reactant system of sheet nano-ZnO with particle size of 45 nm.
Reaction system
Number
m
ZnO (g)
m
KHSO
4 (g)
Q
1 (mJ)
Δ
r
H
m1
Ө (kJ⋅mol−1)
ZnO + KHSO4 + HCl
1
0.0040
0.0134
−1720.67
−35.01
2
0.0040
0.0134
−1734.42
−35.29
3
0.0040
0.0134
−1739.00
−35.38
4
0.0040
0.0134
−1766.67
−35.94
5
0.0040
0.0134
−1722.82
−35.05
6
0.0040
0.0134
−1745.87
−35.52
Average value
−1738.24
-
35.37
±
0.34Table 3
TheΔ
r
H
m1
Ө of reactants system of nano-ZnO with the morphology of sieve, block, column, and rod.
Reaction system
Number
Sieve (45 nm)
Block (45 nm)
Column (37 nm)
Rod (36 nm)
ZnO + KHSO4 + HCl
Δ
r
H
m1
Ө (kJ⋅mol−1)
1
−35.69
−36.05
−29.66
−31.45
2
−35.01
−36.44
−29.36
−31.03
3
−35.90
−36.05
−29.12
−31.59
4
−36.39
−36.12
−29.11
−31.18
5
−35.52
−36.74
−29.02
−31.25
6
−36.04
−36.01
−29.17
−31.70
Average value
Δ
r
H
m1
Ө (kJ⋅mol−1)
-
35.76
±
0.47
-
36.23
±
0.29
-
29.24
±
0.24
-
31.37
±
0.26Table 4
Thermochemical data of system products.
Reaction system
Number
m
ZnSO
4
⋅
7
H
2
O (g)
m
K
2
SO
4 (g)
Q
2 (mJ)
Δ
r
H
m2
Ө (kJ⋅mol−1)
ZnSO4⋅7H2O + K2SO4 + HCl
1
0.0141
0.0086
4044.12
82.48
2
0.0141
0.0086
4065.86
82.93
3
0.0141
0.0086
4060.14
82.81
4
0.0141
0.0086
4068.27
82.98
5
0.0141
0.0086
4064.98
82.91
6
0.0141
0.0086
4046.63
82.53
Average value
4058.33
82.77
±
0.21According to (1) and the data in Table 2 to Table 4, the standard molar enthalpies of formation of the five kinds of nano-ZnO with different morphologies were calculated as follows:
(2)
Δ
f
H
m
Ө
ZnO
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
(
88.77
±
0.21
)
kJ
·
mol
-
1
-
Δ
r
H
m
1
Ө
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
Δ
r
H
m
1
Ө
Δ
f
H
m
Ө
Sheet
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
35.37
±
0.34
kJ
·
mol
-
1
=
(
-
337.43
±
0.47
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Block
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
36.23
±
0.29
kJ
·
mol
-
1
=
(
-
336.57
±
0.43
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Sieve
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
35.76
±
0.47
kJ
·
mol
-
1
=
(
-
337.04
±
0.57
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Cloumn
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
29.24
±
0.24
kJ
·
mol
-
1
=
(
-
343.56
±
0.39
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Rob
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
31.37
±
0.26
kJ
·
mol
-
1
=
(
-
341.43
±
0.41
)
kJ
·
mol
-
1
.


### 3.3. Discussions

The experimental data show that the value of standard molar enthalpy of formation of nano-ZnO is larger than that of bulk ZnO [-
350.46
±
0.27 kJ·mol−1] [17]. The morphologies of the sheet, sieve, and block nanoparticles are similar to each other by the observation of SEM figure and their particle sizes are all 45 nm. Their enthalpy values are -
337.43
±
0.47 kJ·mol−1 (sheet), -
336.56
±
0.43 kJ·mol−1 (block), and -
337.04
±
0.57 kJ·mol−1 (sieve), which are close to each other. So the influence of the morphology and particle size on the standard molar enthalpy of formation is smaller for the three particles. According to literature 17 and literature 18, the standard molar enthalpy of formation of the same morphology of nano-ZnO decreases with the increase of the particle size. The particle sizes of nano-ZnO with morphologies of column and rod are 37 nm and 36 nm, which are smaller than the sheet, sieve, and block (45 nm) ones, so without considering the influence of the morphology of zinc oxide, the molar enthalpy values of nano-ZnO with morphology of column and rod should be bigger than the ones with morphologies of sheet, sieve, and block. But the experimental results are opposite [Δ
f
H
m
Ө
column
=
-
343.56
±
0.39 kJ·mol−1, Δ
f
H
m
Ө
rod
=
-
341.43
±
0.41 kJ·mol−1]. The reason is that their particle sizes are smaller than the sheet, sieve, and block nano-ZnO particles; the surface area of the nanoparticles with morphologies of column and rod is bigger, so they are more instable than the other ones. The more instable the nano-ZnO is, the bigger the Gibbs free energy is. According to the thermodynamic formula, Δ
f
H
m
Ө
=
Δ
f
G
m
Ө
+
T
Δ
f
S
m
Ө, the entropy of nano-ZnO must be considered. The irregularity of nano-ZnO with morphologies of column and rod is smaller, which determines its smaller entropy. So their entropy change (
Δ
S
) becomes smaller in the generative process of nano-ZnO. In conclusion, the standard molar enthalpy of formation is associated with Gibbs free energy and entropy [18, 19]. This agrees well with the experimental results. According to the discussions above, it is concluded that the enthalpy values are influenced by the morphology and particle size. More experiments must be taken to obtain more influencing factors about the standard molar formation enthalpy of nano-ZnO.


## 3.1. Particle Size and Morphology of Nano-ZnO

The XRD and SEM results of 5 kinds of nano-ZnO particles with different morphologies were shown in Figures2 and 3. The sharp XRD peaks suggest that the products are highly crystallized and the morphology of each nanoparticle is uniform, and the morphologies of the nano-ZnO can be seen clearly in the SEM pictures.Figure 2
XRD spectra of 5 nano-ZnO particles with different morphologies (the serial numbers 1~5 were denoted by the ones of sheet, sieve, block, column, and rod morphology).SEM pictures of 5 nano-ZnO particles.
(a)
Sheet
(b)
Sieve
(c)
Block
(d)
Column
(e)
Rod


## 3.2. Standard Molar Enthalpy of Formation of Nano-ZnO

Standard molar enthalpy of formation of nano-ZnO can be obtained according to the designed thermodynamic cycle shown in Figure1 and Hess law, and the detailed calculation was performed as formula (1). The experimental and calculated data were shown in Tables 2, 3, and 4
(1)
Δ
f
H
m
Ө
ZnO
=
Δ
f
H
m
Ө
K
2
SO
4
+
Δ
f
H
m
Ө
ZnSO
4
·
7
H
2
O
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
-
6
Δ
f
H
m
Ө
(
H
2
O
)
-
2
Δ
f
H
m
Ө
(
KHSO
4
)
=
(
-
1414
)
kJ
·
mol
-
1
+
(
-
3077.75
)
kJ
·
mol
-
1
-
6
×
(
-
285.83
±
0.04
)
kJ
·
mol
-
1
-
2
×
(
-
285.83
±
0.04
)
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
.Table 2
Thermochemical data of reactant system of sheet nano-ZnO with particle size of 45 nm.
Reaction system
Number
m
ZnO (g)
m
KHSO
4 (g)
Q
1 (mJ)
Δ
r
H
m1
Ө (kJ⋅mol−1)
ZnO + KHSO4 + HCl
1
0.0040
0.0134
−1720.67
−35.01
2
0.0040
0.0134
−1734.42
−35.29
3
0.0040
0.0134
−1739.00
−35.38
4
0.0040
0.0134
−1766.67
−35.94
5
0.0040
0.0134
−1722.82
−35.05
6
0.0040
0.0134
−1745.87
−35.52
Average value
−1738.24
-
35.37
±
0.34Table 3
TheΔ
r
H
m1
Ө of reactants system of nano-ZnO with the morphology of sieve, block, column, and rod.
Reaction system
Number
Sieve (45 nm)
Block (45 nm)
Column (37 nm)
Rod (36 nm)
ZnO + KHSO4 + HCl
Δ
r
H
m1
Ө (kJ⋅mol−1)
1
−35.69
−36.05
−29.66
−31.45
2
−35.01
−36.44
−29.36
−31.03
3
−35.90
−36.05
−29.12
−31.59
4
−36.39
−36.12
−29.11
−31.18
5
−35.52
−36.74
−29.02
−31.25
6
−36.04
−36.01
−29.17
−31.70
Average value
Δ
r
H
m1
Ө (kJ⋅mol−1)
-
35.76
±
0.47
-
36.23
±
0.29
-
29.24
±
0.24
-
31.37
±
0.26Table 4
Thermochemical data of system products.
Reaction system
Number
m
ZnSO
4
⋅
7
H
2
O (g)
m
K
2
SO
4 (g)
Q
2 (mJ)
Δ
r
H
m2
Ө (kJ⋅mol−1)
ZnSO4⋅7H2O + K2SO4 + HCl
1
0.0141
0.0086
4044.12
82.48
2
0.0141
0.0086
4065.86
82.93
3
0.0141
0.0086
4060.14
82.81
4
0.0141
0.0086
4068.27
82.98
5
0.0141
0.0086
4064.98
82.91
6
0.0141
0.0086
4046.63
82.53
Average value
4058.33
82.77
±
0.21According to (1) and the data in Table 2 to Table 4, the standard molar enthalpies of formation of the five kinds of nano-ZnO with different morphologies were calculated as follows:
(2)
Δ
f
H
m
Ө
ZnO
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
Δ
r
H
m
2
Ө
-
Δ
r
H
m
1
Ө
=
-
455.57
±
0.24
kJ
·
mol
-
1
+
(
88.77
±
0.21
)
kJ
·
mol
-
1
-
Δ
r
H
m
1
Ө
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
Δ
r
H
m
1
Ө
Δ
f
H
m
Ө
Sheet
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
35.37
±
0.34
kJ
·
mol
-
1
=
(
-
337.43
±
0.47
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Block
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
36.23
±
0.29
kJ
·
mol
-
1
=
(
-
336.57
±
0.43
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Sieve
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
35.76
±
0.47
kJ
·
mol
-
1
=
(
-
337.04
±
0.57
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Cloumn
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
29.24
±
0.24
kJ
·
mol
-
1
=
(
-
343.56
±
0.39
)
kJ
·
mol
-
1
Δ
f
H
m
Ө
Rob
=
-
372.80
±
0.32
kJ
·
mol
-
1
-
-
31.37
±
0.26
kJ
·
mol
-
1
=
(
-
341.43
±
0.41
)
kJ
·
mol
-
1
.


## 3.3. Discussions

The experimental data show that the value of standard molar enthalpy of formation of nano-ZnO is larger than that of bulk ZnO [-
350.46
±
0.27 kJ·mol−1] [17]. The morphologies of the sheet, sieve, and block nanoparticles are similar to each other by the observation of SEM figure and their particle sizes are all 45 nm. Their enthalpy values are -
337.43
±
0.47 kJ·mol−1 (sheet), -
336.56
±
0.43 kJ·mol−1 (block), and -
337.04
±
0.57 kJ·mol−1 (sieve), which are close to each other. So the influence of the morphology and particle size on the standard molar enthalpy of formation is smaller for the three particles. According to literature 17 and literature 18, the standard molar enthalpy of formation of the same morphology of nano-ZnO decreases with the increase of the particle size. The particle sizes of nano-ZnO with morphologies of column and rod are 37 nm and 36 nm, which are smaller than the sheet, sieve, and block (45 nm) ones, so without considering the influence of the morphology of zinc oxide, the molar enthalpy values of nano-ZnO with morphology of column and rod should be bigger than the ones with morphologies of sheet, sieve, and block. But the experimental results are opposite [Δ
f
H
m
Ө
column
=
-
343.56
±
0.39 kJ·mol−1, Δ
f
H
m
Ө
rod
=
-
341.43
±
0.41 kJ·mol−1]. The reason is that their particle sizes are smaller than the sheet, sieve, and block nano-ZnO particles; the surface area of the nanoparticles with morphologies of column and rod is bigger, so they are more instable than the other ones. The more instable the nano-ZnO is, the bigger the Gibbs free energy is. According to the thermodynamic formula, Δ
f
H
m
Ө
=
Δ
f
G
m
Ө
+
T
Δ
f
S
m
Ө, the entropy of nano-ZnO must be considered. The irregularity of nano-ZnO with morphologies of column and rod is smaller, which determines its smaller entropy. So their entropy change (
Δ
S
) becomes smaller in the generative process of nano-ZnO. In conclusion, the standard molar enthalpy of formation is associated with Gibbs free energy and entropy [18, 19]. This agrees well with the experimental results. According to the discussions above, it is concluded that the enthalpy values are influenced by the morphology and particle size. More experiments must be taken to obtain more influencing factors about the standard molar formation enthalpy of nano-ZnO.



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*Source: 738909-2015-02-04.xml*