# Finding atomic weight from vapor density of metal chloride

1. Aug 7, 2011

### Quantum Mind

1. The problem statement, all variables and given/known data

Vapor density of a metal chloride is 66. Its oxide contains 53% metal. The atomic weight of the metal is ?

2. Relevant equations

vapor density = 0.5 * molar mass

3. The attempt at a solution

Using the above formula, I found the molar mass of the metal chloride as 132. I am stuck here, as the problem talks about the oxide containing 53% metal.

In 100 g of Metal oxide, 47% is oxygen, i.e. roughly the weight of three oxygen atoms which is 48. The Formula is therefore M2O3 ? Does this mean that this metal is hexa valent? This doesn't seem right, because the mol wt of chlorine is 35.5 and six chlorine atoms would weigh 213 g whereas the sample is only 132 g.

The choices for answer are 21, 54, 27.06 and 2.7.

Logically I think the answer should be 54, as this would correspond to cobalt while the rest are not metals.

Can anybody please explain how the answer is to be arrived at?

2. Aug 7, 2011

### Dickfore

density is a physical quantity with units. you had presented a unitless quantity for it.

3. Aug 8, 2011

### Quantum Mind

Vapor density is a ratio, being a proportion of mass. Therefore no unit.

Now, how do I go about solving the problem?

4. Aug 8, 2011

### Dickfore

Proportion between what masses?

5. Aug 9, 2011

### Quantum Mind

Source: http://en.wikipedia.org/wiki/Vapour_density" [Broken]

Last edited by a moderator: May 5, 2017
6. Aug 10, 2011

### Dickfore

Is the content of metal in the oxide given by mass or by number?

7. Aug 11, 2011

### Quantum Mind

I have reproduced the question exactly. It has to be 53% by mass since molar mass is involved.

Sorry if I sound rude, but the discussion doesn't seem to be going anywhere.

8. Aug 11, 2011

### Dickfore

Suppose the valency of the metal is v and its atomic mass is x. Then the ratio of the masses of the metal and oxygen in the oxide is:

$$\frac{2 \, x}{16 \times v} = \frac{53}{47} \Rightarrow 94 \, x = 848 \, v \Rightarrow 47 \, x = 424 \, v$$

Next, the molar mass of the chloride is:
$$1 \times x + v \times 35 = 66 \Rightarrow x + 35 \, v = 66$$
where I had used the definition of vapour density.

Now, you have 2 linear equations in 2 unknowns (x and v). Solve them

9. Aug 11, 2011

### Dickfore

or, if the vapour density is defined with respect to H2, then you should substitute the 66 in the second equation with a 132.

10. Aug 11, 2011

### Quantum Mind

Thanks for the reply, but I still don't understand. The ratio of the masses of the metal and the oxide is 53:47 as per the question. How do I relate it to valency and atomic mass and form an equation with v and x?

Can you make it a bit clearer?

11. Aug 11, 2011

### Dickfore

No, this is enough hints. If you cannot solve it, that's your problem.