For the reaction:
`CH_4(g)+2H_2S(g) hArr CS_2(g) + 4H_2(g)` at 1173 K, `K_c`=3.6 .For each of the followng compositions predict whether the reaction mixture is at equilibrium or not. If it is not, decide to which direction, the reaction should go :
(i)`[CH_4]`=1.07 M,`[H_2S` =1.20 M , `[CS_2]` 0.90 M, `[H_2]` = 1.78 M
(ii)`[CH_4]`=1.45 M , `[H_2S]`=1.29 M, `[CS_2]` = 1.25 M , `[H_2]` =1.75 M

Explanation

To determine whether the reaction is at equilibrium for the given compositions, we will calculate the reaction quotient \( Q_c \) and compare it with the equilibrium constant \( K_c \).

### Given Reaction:
\[ \text{CH}_4(g) + 2\text{H}_2\text{S}(g) \rightleftharpoons \text{CS}_2(g) + 4\text{H}_2(g) \]

### Given Equilibrium Constant:
\[ K_c = 3.6 \quad \text{at } 1173 \text{ K} \]

### General Formula for \( Q_c \):
\[ Q_c = \frac{[\text{CS}_2][\text{H}_2]^4}{[\text{CH}_4][\text{H}_2\text{S}]^2} \]

### Step 1: Calculate \( Q_c \) for the first composition
#### (i) Given concentrations:
- \([CH_4] = 1.07 \, \text{M}\)
- \([H_2S] = 1.20 \, \text{M}\)
- \([CS_2] = 0.90 \, \text{M}\)
- \([H_2] = 1.78 \, \text{M}\)

#### Calculation:
\[ Q_c = \frac{(0.90)(1.78)^4}{(1.07)(1.20)^2} \]

Calculating \( (1.78)^4 \):
\[ (1.78)^4 \approx 10.56 \]

Now substituting back into the \( Q_c \) formula:
\[ Q_c = \frac{(0.90)(10.56)}{(1.07)(1.44)} \approx \frac{9.504}{1.5408} \approx 6.17 \]

### Step 2: Compare \( Q_c \) with \( K_c \)
- \( Q_c = 6.17 \)
- \( K_c = 3.6 \)

Since \( Q_c > K_c \), the reaction will shift to the left (towards the reactants).

### Conclusion for (i):
The reaction is **not at equilibrium** and will shift to the **left**.

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### Step 3: Calculate \( Q_c \) for the second composition
#### (ii) Given concentrations:
- \([CH_4] = 1.45 \, \text{M}\)
- \([H_2S] = 1.29 \, \text{M}\)
- \([CS_2] = 1.25 \, \text{M}\)
- \([H_2] = 1.75 \, \text{M}\)

#### Calculation:
\[ Q_c = \frac{(1.25)(1.75)^4}{(1.45)(1.29)^2} \]

Calculating \( (1.75)^4 \):
\[ (1.75)^4 \approx 9.3789 \]

Now substituting back into the \( Q_c \) formula:
\[ Q_c = \frac{(1.25)(9.3789)}{(1.45)(1.6641)} \approx \frac{11.7236}{2.41445} \approx 4.86 \]

### Step 4: Compare \( Q_c \) with \( K_c \)
- \( Q_c = 4.86 \)
- \( K_c = 3.6 \)

Since \( Q_c > K_c \), the reaction will again shift to the left (towards the reactants).

### Conclusion for (ii):
The reaction is **not at equilibrium** and will shift to the **left**.

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### Summary of Results:
1. For (i), the reaction is not at equilibrium and shifts to the left.
2. For (ii), the reaction is not at equilibrium and shifts to the left.

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