Exp. 29 - 3

When the burning is complete, cover the crucible and allow it to cool to room temperature. Weigh and calculate the percent of fixed carbon.

(d) Ash: The remains in the crucible is the ash and represents the mineral matter in the plants from which the coal was originally derived. Determine the percent of ash in your sample.

Questions and Problems:

I. Describe the most important changes in composition which occur as wood is converted to coal.

II. Contrast the bee-hive and by-product coke ovens and explain the advantages of the latter.

Lafayette College
Department of Chemistry

Experiment 30

METALS AND THE EMF SERIES

**Object:** To become familiar with the displacement reactions of metals and with the positions of some metals in the EMF series.

**Discussion:**

You have already learned that certain metals will displace others from solutions of their ions and have understood that any given metal will displace all others which are situated below it in the EMF (Electromotive Force) series. This series serves as a measure of the ease with which the various metals undergo oxidation. Those at the top of the series are oxidized more readily than those near the bottom. This is evident when it is remembered that a displacement reaction is really an oxidation - reduction reaction. Recall that oxidation is a loss of electrons. We may write the equation for the reaction of iron with cupric ion in the following way:

$$Fe + Cu^{++} \longrightarrow Fe^{++} + Cu$$

When a metal is dipped into a solution there exists a certain tendency for the metal ions to go into solution, leaving electrons in excess on the piece of metal. The extent to which this ionization takes place is dependent upon the individual metal in question. The EMF series is a list of elements in order of the ease with which this type of reaction occurs. For the above case of iron displacing cupric ions, we would have the two following reactions which tend to occur when pieces of iron and copper are immersed in solution:

$$Fe \longrightarrow Fe^{++} + 2e$$

$$Cu \longrightarrow Cu^{++} + 2e$$

These are called electrode reactions or half cell reactions. By adding these two half cell reactions together algebraically it is observed that the earlier equation for displacement is obtained.

It is evident that of the above ionization reactions the one which takes place to the greater extent will leave the greater number of electrons on the piece of metal and hence the greater charge. If the two pieces of metal are dipping into solutions of their ions which are in electrical contact (but prevented from diffusing into one another) and if then a metallic conductor is connected between the two strips of metals, electrons can flow through it from the piece of metal having more electrons to the piece having less. This would constitute a simple cell and the strips of metal would be called electrodes. In the case considered above, iron has a greater tendency to go into solution than does copper, therefore, in such an electrolytic cell there will tend to be more electrons on the iron electrode than on the

Exp. 30 - 2

copper electrode, and hence electrons will flow through the conductor from the iron to the copper.

Unfortunately it is common practice to speak of an
electric current flowing in the opposite direction to the flow of
electrons. The electrician thinks of a flow of "positive" elec-
tricity. We will not be perturbed by this when we recall that
an electric current is really a flow of electrons.

If an appropriate instrument is employed, one can measure
the relative tendencies of metals to ionize into solution by deter-
mining the electromotive force (potential) developed between
two half cells of the type we have mentioned. This has been done
for most of the metals and electromotive force values determined
in relation to that of an hydrogen electrode, which has been
assigned quite arbitrarily the potential zero. These single
electrode potentials determine the position of a metal in the
EMF series. The potential which a given cell would produce under
ideal conditions can be calculated by adding the appropriate half
cell potentials algebraically.

Directions:

Obtain in a series of test tubes about 5 ml of each of the following solutions: magnesium chloride, lead nitrate, stannous chloride, copper sulfate, aluminum sulfate, ferrous sulfate, zinc sulfate and mercuric nitrate (or chloride). (1) Dip strips of each of the metals (except mercury, Why?) from which these salts are derived into each of the solutions and determine in which cases displacement takes place. (2) List these metals in their proper order according to displacement, placing the most active at the top of the list.

(3) Determine which of these metals react with dilute hydrochloric acid to produce hydrogen. (4) On the basis of this place hydrogen in its proper position in your list of metals.

(5) Recall from Experiment 25 the action of tin on solu-
tions of arsenic trichloride and antimony trichloride. Locate
as many of the above metals as you can with reference to arsenic
and antimony.

Place a small piece of zinc in dilute sulfuric acid.
Note the action. Now touch the piece of zinc with a platinum
wire and then with a copper wire. (6) Describe and explain the
results. (7) Why is it advantageous to put a few drops of copper
sulfate solution in a hydrogen generator using zinc and dilute
sulfuric acid? Write all necessary equations in your explanation.

Questions:

I. Why does iron containing traces of impurities such as copper corrode more rapidly than pure iron? Write necessary equations.

II. Theoretically which two of the metals you studied in this experiment should give you the highest potential when coupled in an electrolytic cell?

Experiment 31

ALKALI METAL IONS

**Object:** To study the chemistry of the alkali metal ions and the ammonium ion.

**Discussion:**

The alkali metals all are in Group 1 of the Periodic Table and as such have one electron in their outer (valence) electron shell. These metals lose this electron readily forming positive ions as illustrated by the equation:

$$Na \rightarrow Na^+ + e.$$

The chemical properties of all alkali metals are very similar, but there is a regular gradation in physical properties within the family; physical metallic characteristics being more pronounced in the heavier members of the family. Alkali metals are very active chemically, reacting with water at room temperature to produce bases and hydrogen. This indicates that they occupy positions high in the EMF series.

The ions of these alkali metals are characterized by being relatively unreactive. This indicates first that alkali metal ions are quite stable (also indicated by their position in EMF series) and second that most compounds of the alkali metals are quite soluble and highly ionized. (1) Explain why this latter statement is true.

The ammonium ion ($NH_4^+$) is similar in many of its chemical characteristics to the alkali metal ions. It is monovalent; most of its compounds are soluble and highly ionized. However, this ion is very much less stable than alkali metal ions. It reacts with excess $OH^-$ ion to form ammonia and water; the reaction being aided by high temperature. Thus

$$NH_4^+ + OH^- \rightarrow NH_3 + H_2O$$

(2) Explain why raising the temperature will cause the reaction to proceed further to the right. Most ammonium compounds decompose rather readily when heated, though not all of them produce ammonia.

The student should note carefully the difference between ammonia and ammonium ion. In the proton donor-acceptor sense ammonia is a base which reacts with hydrogen ion (hydronium ion) to produce ammonium ion which is an acid. We can write:

$$NH_3 + H^+ \rightarrow NH_4^+$$

Exp. 31 - 2

Free ammonium is not known. Attempts to produce it electrolytically have failed. However, ammonium amalgam, analogous to sodium amalgam, has been prepared. (An amalgam is an alloy containing mercury.)

### Directions:

Obtain from your Instructor a platinum wire sealed into a short length of glass tubing for use in observing colors which various ions impart to flames. Fill a small test tube nearly full of dilute hydrochloric acid and set it in your test tube rack. Heat the platinum wire to redness in the bunsen flame, being careful not to get the glass handle in the flame. Quickly insert the hot wire in the test tube of hydrochloric acid, but do not wet the handle. Now heat the wire in the flame again. Repeat this procedure until the platinum wire is clean as observed by the fact that practically no coloration is produced by it in the flame after the hydrochloric acid has evaporated. Dip the platinum wire in some sodium chloride solution and then hold it in the bunsen flame. (3) What do you observe? Does the color persist for an appreciable length of time? Clean the wire and then rub it between your fingers and again observe the color imparted to the flame. This color which you see is characteristic of volatile compounds of sodium. It is usually impossible to eliminate it completely from a flame test because it is such an intense coloration. Observe this flame through one or two pieces of cobalt blue glass. (4) Describe and explain.

After cleaning the platinum wire observe the flame color of a potassium salt, such as potassium chloride or nitrate. (5) Describe the color. Can you observe this color through the cobalt blue glass? (6) How could you identify both sodium and potassium if they were present in the same mixture? Test your method. Return the platinum wire to your Instructor.

Sodium and potassium resemble one another so very much that it is difficult to separate them or to identify them in mixtures except by such methods as flame tests or X-ray analysis. However, sodium cobaltinitrite is soluble while the potassium compound is not. Cobaltic ions react with nitrite ions to produce a fairly stable complex ion, cobaltinitrite ions, thusly:

$$ \mathrm{Co}^{+++} + 6 \mathrm{NO}_2 \rightarrow \mathrm{Co(NO}_2)_6^{---} $$

This ion, however, decomposes in both basic and highly acidic solutions, consequently it must be used in a medium of controlled hydrogen ion concentration. To 5 ml of a dilute solution of a potassium salt (which should be nearly a neutral solution) add about 5 drops of dilute acetic acid and then 3 - 5 ml of sodium cobaltinitrite solution. Let the mixture stand for about ten minutes. (7) What do you observe? Write an+ionic equation representing the formation of this compound. Cu+ and Ag+ among other substances interfere with this test.

Ammonium ion is very similar to the alkali metal ions in its chemistry. It gives, however, no flame test. Most of its

Exp. 31 - 3

compounds are soluble. Repeat the above cobaltinitrite test with
a solution of ammonium chloride in place of the potassium salt.
(8) Record your observations and write ionic equations for any
reactions.

The fact that ammonium hydroxide is a weak base which
decomposes readily into water and ammonia contributes to compli-
cating the chemistry of ammonium compounds. A more modern state-
ment would be that there is a great tendency for ammonium ions to
react with hydroxyl ions to produce ammonia and water. This
reaction is aided by heating. (9) Give two reasons why this is
true. Note the odor of a bottle of ammonium hydroxide (ammonia
water). Add 2 ml of sodium hydroxide solution to 4 - 5 ml of a
solution of ammonium chloride and heat. Note the odor. Hold a
piece of moistened red litmus paper at the mouth of the test tube,
taking care that none of the contents of the test tube comes in
contact with the litmus paper. (10) Describe the results which
you obtain and interpret them with aid of ionic equilibria equa-
tions. Is this test dependent upon which ammonium compound is
used? If another base were substituted for sodium hydroxide in
this test, what particular conditions would it have to meet in
order for the test to be successful? Explain.

Heat in your porcelain dish under the hood about one
quarter of a gram of ammonium chloride until fumes are no longer
obtained. (11) Is there a residue remaining in the dish? Explain
what has happened. Repeat with about a quarter of a gram of sodium
chloride. (12) How could you obtain pure sodium chloride from a
mixture known to contain sodium chloride and ammonium chloride only

Heat about half a gram of each of the following ammonium
salts separately in clean dry test tubes: chloride, sulfate,
nitrate, nitrite. (13) Describe and explain the behavior in each
case, indicating clearly the products obtained. Write equations
for all reactions. If a gas is evolved test it with a glowing
solvent to see whether it will support combustion. Recall that
nitrous oxide supports combustion, though less vigorously than
oxygen.

Questions and Problems:

I. What volume of ammonia, measured dry at 750 mm and 23°C,
could be obtained from the number of grams of ammonium sulfate
corresponding to your de sk number if it were treated with excess
sodium hydroxide and heated?

II. Explain clearly the acid-base relationships of ammonia and ammonium ion on the basis of the proton donor-acceptor theory of acids and bases.

Experiment 32

COPPER AND COMPLEX IONS

**Object:** To study the typical reactions of the compounds of copper and to become familiar with the chemistry of the complex ions.

**Discussion:**

As stated above, the two major points to be covered in this experiment are the reactions of the cupric ion, with particular emphasis on those which may be used to identify it, and the formation of complexes by this ion. The first of these points needs no discussion here since the only principles involved have been met previously in this course. The formation of complex ions and their influence on the behavior of the metallic ions which form them is a new principle to you and will need some explanation. The part which these complexes play in the chemistry of the metallic ions is closely tied up with the principle of solubility product and the effect of concentration on an equilibrium. It would be well to review Experiment 24, page 4, at this point.

Certain metallic ions, such as the cupric ion, combine with neutral molecules or negative ions to form larger, more complex ions which are usually very stable, and are soluble. Although you will use the cupric ion to study these complexes in this experiment, you should remember that this same principle applies to many other metallic ions. The way in which the cupric ion forms such a complex with the ammonia molecule is indicated by the following equation:

$$ \mathrm{Cu}^{\mathrm{++}} + 4 \mathrm{NH}_{3} \rightleftharpoons \mathrm{Cu}(\mathrm{NH}_{3})_{4}^{\mathrm{++}} $$

Notice that the charge on the complex ion is the same as that on the cupric ion. Explain. What does the above equation indicate regarding the stability of the copper ammonia complex? The concentration of the cupric ion in such a solution?

The formation of this complex accounts for the dissolving of copper hydroxide in ammonia water. The equilibria which are represented below make this action clear. Study them carefully so that you may apply this same principle to other reactions.

Exp. 32 - 2

When copper hydroxide is mixed with pure water a very small quantity of it dissolves. (1) Explain in terms of the solubility product when this process will stop. Explain how the ammonia molecule affects the equilibrium represented by the top line of the above equations.

In addition to the ammonia complex, the cupric ion behaves in this same manner with certain negative ions. One of the most useful of these is the tartrate complex which is formed as represented below:

$$ \mathrm{Cu}^{2+} + \mathrm{C}_{4}\mathrm{H}_{4}\mathrm{O}_{6}^{-} \rightleftharpoons \mathrm{Cu}(\mathrm{C}_{4}\mathrm{H}_{2}\mathrm{O}_{6})^{-} $$

In Fehlings solution this complex is used as a source of cupric ions in an alkaline solution. The above equilibrium is shifted so far to the right that the concentration of the cupric ion in solution is exceedingly small. Because of this it is possible to have a relatively large concentration of hydroxyl ions and still not exceed the solubility product of copper hydroxide. If the cupric ions in such a solution are used, additional ions are supplied by the dissociation of the cupric tartrate complex.

If a solution containing cyanide ions is added to one containing cupric ions, a cuprocyanide complex is formed but the formation takes place in two steps. The first step involved the formation of cuprous cyanide and cyanogen according to the following equation:

$$ 2 \mathrm{Cu}^{2+} + \mathrm{CN}^{-} \rightarrow 2 \mathrm{CuCN} + (\mathrm{CN})_{2} $$

When additional cyanide ion is added the cuprous cyanide dissolves to form the cuprocyanide complex:

$$ \mathrm{CuCN} + \mathrm{CN}^{-} \rightleftharpoons \mathrm{Cu}(\mathrm{CN})_{2}^{-} $$

This cuprocyanide complex is even more slightly ionized than are the ammonia and tartrate complexes and thus supplies a much smaller concentration of cupric ions. Such a solution is often used as the source of cupric ions in electroplating with copper.

### Directions:

Obtain 5 ml of cupric sulphate solution and add sodium hydroxide drop by drop until no more precipitate is formed. Save the resulting mixture for a later test. Repeat the above test using copper nitrate in place of the sulphate. (2) Write an ionic equation using only the ions which were actually involved in the above changes. (3) Explain in terms of solubility product why precipitates were formed. (4) Are there still some cupric ions in the solution? Explain.

Add an iron nail to 3 ml of copper sulphate solution and allow to stand for ten or fifteen minutes. (5) List at least two indications that a chemical change has occurred. Write

Exp. 32 - 3

an equation using only the ions involved. Add about 1 ml of potassium ferrocyanide to a solution containing cupric ions. The ferrocyanide ion which reacts with the cupric ions is $(Fe(CN)_6)^{-4}$. (6) Write an ionic equation for the formation of the precipitate. Record the color.

Make a solution of cupric ions acidic with hydrochloric acid and pass hydrogen sulphide into the solution. In the presence of a strong acid like HCl, the weak acid, hydrogen sulphide, is very slightly ionized and thus furnishes only very small concentrations of sulphide ions:

$$H_2S \rightleftharpoons H^+ + HS^- \rightarrow H^+ + S^=$$

(7) What does the fact that a precipitate of cupric sulphide is obtained under these conditions indicate about the solubility product of cupric sulphide? (8) Write an ionic equation for the formation of the precipitate.

Warm the cupric hydroxide suspension which you retained from the first test in this exercise. Notice the change in color. (9) Account for the formation of the oxide. Write an equation. What does this indicate with regard to the stability of the hydroxide.

**CAUTION:** Potassium cyanide will be used in this section of the experiment. In using any cyanide observe closely the following rules: (a) Perform all experiments under a hood whose fans are operating. (b) Avoid spilling any of the substance on your hands. (c) Unless otherwise directed discard cyanide solution in a container provided under the hood. (d) Wash your hands after performing the experiment. Cyanides are extremely poisonous. Make a suspension of cupric hydroxide by adding sodium hydroxide to about 15 ml of a solution of cupric ions. Allow the precipitate to settle, decant the liquid, and add about 20 ml of water. Stir the mixture and divide into four equal portions in test tubes. (10) Assuming that all the excess sodium hydroxide was decanted, what equilibria exist in the suspensions? Indicate by means of equations. Add ammonia water (ammonium hydroxide) to the first tube, sodium potassium tartrate to the second and potassium cyanide to the third. (11) What action accounts for the results in each case? Explain in terms of solubility product. (12) How would the stability of the complex ions affect the results? Pass hydrogen sulphide into each of the three test tubes. (13) Which complex ions furnish sufficient cupric ions to exceed the solubility product of cupric sulphide? Which does not? Add ammonium hydroxide to the fourth tube until the precipitate dissolves. Now add dilute hydrochloric acid drop by drop until definite results are obtained. (14) Study the equilibria in the discussion and explain the results obtained here.

Exp. 32 - 4

Add 2 ml of sodium potassium tartrate solution to 2 ml of copper sulphate solution. Add potassium hydroxide solution until the solution is strongly basic. (15) Why do you not obtain a precipitate of copper hydroxide? Are there any cupric ions in the solution? Add about 2 ml of glucose solution and warm gently. The precipitate is cuprous oxide and is formed as the result of the reduction of cupric ions in an alkaline solution by an aldehyde (glucose).

Soak a small wad of cotton in 10 ml of sodium hydroxide for at least 10 minutes. While this is soaking, slowly add ammonium hydroxide to 5 ml of copper sulphate solution until the precipitate which is formed redissolves and then add about 2 ml in excess. Squeeze the cotton with a stirring rod, add it to the copper solution which you have prepared, and stir with a glass rod. What happens to the cotton? Pour the solution slowly into about 25 ml of dilute sulphuric acid made by adding 10 ml of the acid from your reagent shelf to 15 ml of water. Notice that the cellulose (cotton) is reprecipitated. These changes represent essentially those used in the manufacture of one type of rayon, cuproammonia or Bemberg.

Questions:

I. Explain why most compounds containing copper can be dissolved in a solution of a cyanide.

II. What weight of copper can be obtained from a ton of copper ore which is 7.5% cuprous sulphide?

III. Explain by means of horizontal-vertical-ionic equations why silver chloride dissolves in ammonium hydroxide. Why will silver iodide not dissolve?

IV. Strips of copper and zinc are placed in contact with a solution of their ions. The solutions are connected by a salt bridge. What will happen if the metals are connected by a wire?

-5-

9. Given the equation for the reaction,

$$3 \text{ Cu} + 8 \text{ HNO}_3 \longrightarrow 3 \text{ Cu(NO}_3)_2 + 2 \text{ NO} + 4 \text{ H}_2\text{O},$$

what weight of copper will be required to produce 5 liters of nitric oxide (NO) gas measured at 15°C and 740 mm pressure? At. wt. of Cu = 63.57.

$$\frac{63.57}{19.071} \times 190.01 = \frac{5}{44.8} \times \frac{190.75}{953.55} = \frac{44.8 \sqrt{953.55}}{896} = \frac{575}{448} = \frac{21.12}{1275} \quad (3)$$

IX. (a) All pure substances can be divided into two classes. These classes are ______ and ______. Give an example of each class.

(b) State two characteristics of a chemical change. Give an example of a chemical change.

1. The weight of carbon will remain the same.

2. Heat must be taken on it to complete the reaction or battery is given off in the reaction.

3. Example: Burned wood.

(3)

(c) Name the four most important types of chemical change and illustrate one of them with a balanced equation. Indicate the type illustrated.

1. Decomposition

3. Analysis

2. Double Decomposition

4. Combining.

$$\text{Example: } \ce{2 CaO + 2 NO} \ce{3 PO4} \ce{3 Ca(OH)2} + 6 NaCl \text{ (Example of NO2)} \quad (3)$$

(3)

X. (a) Write a balanced equation for the common laboratory preparation of oxygen gas. $2H_2O \xrightarrow{O_2} H_2 + O_2$

(1)

2. Name two factors which influence the rate of a chemical reaction which were employed in the preparation of oxygen gas in (a).

(2)

(c) What is the most outstanding chemical property of oxygen?

(1)

(d) Complete and balance: Name the product formed in each case:

$$(1) 2Ca + O_2 \longrightarrow 2CaO \xrightarrow{\Delta} \Delta$$

$$(3) CaO + H_2O \longrightarrow Ca(OH)_2 \quad \text{Calcium Hydroxide}$$

$$(2) C + O_2 \longrightarrow CO_2 \xrightarrow{\Delta} \Delta$$

$$(4) SO_2 + H_2O \xrightarrow{\Delta} SO_3 + H_2O \quad (2)$$

(e) State 2 important commercial uses of oxygen.

(1)

(f) What is an exothermic reaction? Give an example.

(2)

XI. (a) Write an equation for a suitable laboratory preparation of hydrogen gas.

(1)

(b) Name and give the symbols of two metals that will liberate H₂ from cold water. Potassium K and Sodium Na

(1)

(c) Give the name and symbol of a metal that never liberates hydrogen from water or acids.

(1)

$$(d) \text{ Complete and balance: } \text{CuO} + \text{H}_2 \xrightarrow{\text{heat}} \text{Cu} + \text{H}_2O \quad (1)$$

-6-

[y]

(e) What chemical property of H₂ is illustrated by the reaction in (d)? (1)

(f) Complete and balance: ²H₂ + O₂ $\xrightarrow[\text{Spark}]{\text{Electric}}$ 2H₂O

If 60 cc of H₂ and 40 cc of O₂ are exploded in a closed tube, which of the initial gases would remain unreacted? [Oxygen] . How many cc of it would remain? 10 cc . (3)

(g) What is the most abundant naturally occurring source of combined hydrogen? __________. Describe one commercial method for preparing H₂ from this source. (1)

A.S.T. MATHEMATICS 407

Test 6.2

1. What is the diameter of the circle which has its center at the point (-6, 4) and which is tangent to the line $5x=12y$? (1) 13; (2) $5\sqrt{6}$; (3) $2\sqrt{39}$; (4) 12; (5) 6.

2. Which one of the following values of x yields the largest algebraic value of the ordinate of the curve represented by the equation $y=2\sin x\cos 2x+\sin 2x$?
(1) $x=\pi$; (2) $\frac{\pi}{6}$; (3) $\frac{\pi}{2}$; (4) $\frac{3\pi}{4}$; (5) $\frac{2\pi}{3}$.

3. What is the relationship between the lines $\frac{y-x=3}{x-3=y}$? (1) They are perpendicular; (2) they intersect at the point (0, -3); (3) they intersect at the point (-3, 0); (4) they intersect at the origin; (5) they are parallel.

4. The vertices of triangle ABC are (1, 1), (2, -3), (-2, 4) respectively. The equation of the altitude from C to side AB is (1) $y=x+6$; (2) $y=4x+12$; (3) $2y=x+3$; (4) $4y=x+18$.

5. The equation $PV^T=C$, where r and C are positive constants, gives the relation of pressure to volume of a gas. The particular equation $PV=2$ is that of (1) an equilateral hyperbola; (2) a parabola; (3) an ellipse; (4) two straight lines,

6. What is the equation of the locus of a point which moves so that its distance from the point (1, 2) is always equal to its distance from the line $y=-1$?
(1) $y^2-2y+x+3=0$; (2) $x^2-y^2-2x+y=0$; (3) $2x^2+y^2+3x+y=3$; (4) $x^2-2x-6y+4=0$.

7. The period of the curve $y=4 \sin x$ is (1) $4\pi$; (2) $2\pi$; (3) $\frac{\pi}{2}$; (4) $\frac{3\pi}{4}$; (5) $2\pi$.

8. Which of the following pairs of points are farthest from each other?
(1) (4, -1); (1, -1); (2) (4, 0); (2, -2); (3) (1, -1); (-2, -2); (4) (3, -1); (1, -3); (5) (-4, 1); (-1, 1).

9. Which one of the following points does NOT lie on at least one of the lines represented by the equation $y=ax+b$ where $\begin{cases} a < 0 \\ b < 0 \end{cases}$?
(1) (2, 0); (2) (3, 1); (3) (-2, -1); (4) (-2, 0).

10. The length of the latus rectum of the parabola $y^2=8x$ is: (1) 32; (2) 2; (3) 4; (4) 16; (5) 8.

11. The distance between the parallel lines $\begin{cases} 3x-4y+7=0 \\ 3x-4y-3=0 \end{cases}$ is (1) $1\frac{4}{7}$; (2) $2\frac{3}{4}$; (3) $\frac{10}{\sqrt{5}}$; (4) $3\frac{1}{7}$; (5) 2.

12. What is the equation in intercept form of the line passing through the points $(\frac{2}{3}, -2)$ and $(-2, -6)$? (1) $2y=3x-6$; (2) $\frac{3x}{\sqrt{13}} + \frac{2y}{\sqrt{13}} - \frac{6}{\sqrt{13}} = 0$; (3) $\frac{x}{2} - \frac{y}{2} = 1$; (4) $\frac{x}{2} + \frac{y}{3} = 1$.