At `1400 K, K_( c) = 2.5 xx 10^(-3)` for the reaction
`CH_(4)(g)+2H_(2)S(g)hArrCS_(2)(g)+4H_(2)(g)`
A ` 10 L` reaction vessel at `1400 K` contains `2.0 mol` of `CH_(4)`, `4.0 mol` of `H_(2)S` ,`3.0 mol` of `CS_(2)`, `3.0 mol` of `H_(2)`. In which direction does the reaction proceed to reach equilibrium?

Options

A. Forward
B. Backward
C. May be forward or backward
D. Reaction is in equilibrium

Explanation

To determine the direction in which the reaction will proceed to reach equilibrium, we need to calculate the reaction quotient (Q) and compare it with the equilibrium constant (Kc).

### Step-by-Step Solution:

1. **Write the balanced chemical equation:**
\[ \text{CH}_4(g) + 2\text{H}_2\text{S}(g) \rightleftharpoons \text{CS}_2(g) + 4\text{H}_2(g) \]

2. **Identify the given quantities:**
- Moles of CH₄ = 2.0 mol
- Moles of H₂S = 4.0 mol
- Moles of CS₂ = 3.0 mol
- Moles of H₂ = 3.0 mol
- Volume of the reaction vessel = 10 L

3. **Calculate the molar concentrations:**
\[ \text{Concentration} = \frac{\text{Number of moles}}{\text{Volume (L)}} \]
- Concentration of CH₄ = \(\frac{2.0 \, \text{mol}}{10 \, \text{L}} = 0.2 \, \text{M}\)
- Concentration of H₂S = \(\frac{4.0 \, \text{mol}}{10 \, \text{L}} = 0.4 \, \text{M}\)
- Concentration of CS₂ = \(\frac{3.0 \, \text{mol}}{10 \, \text{L}} = 0.3 \, \text{M}\)
- Concentration of H₂ = \(\frac{3.0 \, \text{mol}}{10 \, \text{L}} = 0.3 \, \text{M}\)

4. **Write the expression for the reaction quotient (Q):**
\[ Q = \frac{[\text{CS}_2][\text{H}_2]^4}{[\text{CH}_4][\text{H}_2\text{S}]^2} \]

5. **Substitute the concentrations into the Q expression:**
\[ Q = \frac{(0.3)(0.3)^4}{(0.2)(0.4)^2} \]

6. **Calculate Q:**
\[ Q = \frac{(0.3)(0.0081)}{(0.2)(0.16)} = \frac{0.00243}{0.032} = 0.0759 \]

7. **Compare Q with Kc:**
- Given \(K_c = 2.5 \times 10^{-3} = 0.0025\)
- Since \(Q = 0.0759\) and \(K_c = 0.0025\), we find that \(Q > K_c\).

8. **Determine the direction of the reaction:**
- If \(Q > K_c\), the reaction will proceed in the backward direction (to the left) to reach equilibrium.

### Conclusion:
The reaction will proceed in the backward direction to reach equilibrium.

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