# Equilibrium problem - right method, wrong answer

1. Jul 18, 2009

### ghostanime2001

1. The problem statement, all variables and given/known data
Keq = 100 at a certain temperature for the reaction

CH4(g) + 2 H2S(g) $$\rightleftharpoons$$ CS2(g) + 4 H2(g)

Some CH4 and H2S were introduced into a 1.0 L bulb and at equilibrium 0.10 mol of CH4 and 0.30 mol of H2S were found. What was [CS2] at equilibrium?
2. Relevant equations

$$K_{eq} = \frac{[CS_{2(g)}][H_{2(g)}]^{4}}{[CH_{4(g)}][H_{2}S_{(g)}]^{2}}$$

3. The attempt at a solution
I know that I'm not given any information about starting or changing amounts so therefore an ICE table would not work. I think to calculate the [CS2]:

$$100 = \frac{^{4}}{[0.1][0.3]^{2}}$$

$$100 = \frac{s^{5}}{0.009}$$

$$s^{5} = 0.9$$

$$s = 0.9791$$

But, the answer from the worksheet is 0.323 M. What am I doing wrong. I've arrived at the answer using the right method but the answer is wrong!! can you please help point out my mistake. Thanks

2. Jul 18, 2009

### Ygggdrasil

for every mole of CS2 produced, how many moles of hydrogen gas must be produced?

3. Jul 18, 2009

### ghostanime2001

I don't understand. CS2 reacts with hydrogen gas. It doesn't produce hydrogen gas.

4. Jul 18, 2009

### ghostanime2001

4 moles of hydrogen gas is produced for every mol of CS2 produced

5. Jul 18, 2009

### ghostanime2001

btw, do i have to find the limiting reactant is this question?

6. Jul 18, 2009

### Ygggdrasil

Correct. But, your expressions for [CS2] and [H2] do not reflect this fact. (e.g. if [CS2] = s, then [H2] is not also s)

7. Jul 19, 2009

### ghostanime2001

4s then?

8. Jul 19, 2009

### Ygggdrasil

Yes.

9. Jul 21, 2009

### ghostanime2001

A reaction mixture is at equilibrium according to the equation: LaCl3(s) + H2O(g) $$\rightleftharpoons$$ LaClO(s) + 2HCl(g). Some more HCl(g) is then added such that when equilibrium is re-established the amount of HCl(g) in the mixture is found to have doubled. By what factor will the amount of H2O in the system have been multiplied?

$$\left[ \mbox{Hint: Write an expression for Keq in terms of unknown concentrations, before and after adding HCl. Then: K_{eq}\mbox{(before)} = K_{eq}\mbox{(after)}} \right]$$

$$\begin{tabular}{|c|c|c|c|c|} \hline & LaCl_{3} & H_{2}O & LaClO & 2HCl \\ \hline S & & & & Y \\ \hline \Delta & -2X & -2X & +2X & +2X \\ \hline E & & & +2X & Y+2X \\ \hline \end{tabular}$$

10. Jul 22, 2009

### Ygggdrasil

Start by writing out the expression for Keq in terms of the concentrations of each reactant and product.

11. Jul 22, 2009

### ghostanime2001

$$K_{eq} = \frac{[HCl]^{2}}{[H_{2}O]}$$

I am not given any information of starting, changing amounts. I could have X moles of both LaCl3 and H2O or neither and have moles of products only OR I can have concentrations of one only. I do not know which. I can also have either products increasing concentration or reactants increasing concentrations. I do not know any information of the "how" of initial amounts will progress as time goes on. There must be some other way of doing this problem. Some way which i am misinterpreting. Please help. Let's take this step by step.

Last edited: Jul 22, 2009
12. Jul 22, 2009

### Ygggdrasil

You have all the information you need to solve the problem. Follow the hint and write an expression for Keq before and after the reaction.

13. Jul 22, 2009

### ghostanime2001

$$K_{eq(before)} = \frac{[2x]^2}{x}$$
$$K_{eq(after)} = \frac{[2(2x +s)]^2}{4x} = \frac{16x+4s}{4x)$$

?????? I Really do no understand.

14. Jul 22, 2009

### Ygggdrasil

Let's start with a very basic equation before we start plugging in variables and making things complicated:
$$\frac{[HCl]_i^2}{[H_2O]_i} = \frac{[HCl]_f^2}{[H_2O]_f}$$

Now let's consider what the problem tells us about these values and what relationships the problem asks us to derive. The problem statement says that [HCl]f = 2[HCl]i and asks you to derive a relationship between [H2O]i and [H2O]f.

15. Jul 22, 2009

### ghostanime2001

okay....

$$\frac{[HCl]_i^2}{[H_2O]_i} = \frac{[4HCl]_i^2}{[H_2O]_f}$$

now what ?

Last edited: Jul 22, 2009
16. Jul 22, 2009

### Ygggdrasil

....

17. Jul 22, 2009

### ghostanime2001

errr..... ????

18. Jul 22, 2009

### Ygggdrasil

Let's say [HCl]i = x and [H2O]i = y. Solve for [H2O]f in terms of x and y (you should see that x will cancel).

19. Jul 22, 2009

### ghostanime2001

Why not just create an ICE table?

20. Jul 22, 2009

### Ygggdrasil

You could create an ICE table, but because none of the initial concentrations are known, it will not be so helpful. This question is less of a question about stoichiometry and using ICE tables and more of a question testing basic understanding of the equilibrium constant.