The equilibrium constant, [tex]$K _{ p }$[/tex], for the following reaction

[tex]\[H_2(g) + Cl_2(g) \leftrightarrow 2 HCl(g)\][/tex]

at [tex]$25^{\circ} C$[/tex] is 13.75. Which of the following conditions are NOT at equilibrium?



Answer :

To determine if the conditions are at equilibrium for the reaction [tex]\(H_2(g) + Cl_2(g) \rightleftharpoons 2 HCl(g)\)[/tex], where the equilibrium constant [tex]\(K_p\)[/tex] is 13.75 at 25°C, we can compare the reaction quotient [tex]\(Q\)[/tex] for each set of initial conditions to the equilibrium constant [tex]\(K_p\)[/tex]. The reaction quotient [tex]\(Q\)[/tex] is calculated using the same formula used for the equilibrium constant but with the current concentrations (or partial pressures if we were dealing with gases).

The reaction quotient [tex]\(Q\)[/tex] for this reaction is given by:

[tex]\[ Q = \frac{[HCl]^2}{[H_2] \cdot [Cl_2]} \][/tex]

Now, let's calculate [tex]\(Q\)[/tex] for each set of initial conditions and compare it with [tex]\(K_p = 13.75\)[/tex].

### Initial Conditions and Calculations

1. Condition 1:
- [tex]\( [H_2] = 0.1 \)[/tex]
- [tex]\( [Cl_2] = 0.2 \)[/tex]
- [tex]\( [HCl] = 1.5 \)[/tex]

[tex]\[ Q = \frac{(1.5)^2}{(0.1) \cdot (0.2)} = \frac{2.25}{0.02} = 112.50 \][/tex]

2. Condition 2:
- [tex]\( [H_2] = 0.5 \)[/tex]
- [tex]\( [Cl_2] = 0.5 \)[/tex]
- [tex]\( [HCl] = 2 \)[/tex]

[tex]\[ Q = \frac{(2)^2}{(0.5) \cdot (0.5)} = \frac{4}{0.25} = 16.00 \][/tex]

3. Condition 3:
- [tex]\( [H_2] = 0.3 \)[/tex]
- [tex]\( [Cl_2] = 0.2 \)[/tex]
- [tex]\( [HCl] = 1 \)[/tex]

[tex]\[ Q = \frac{(1)^2}{(0.3) \cdot (0.2)} = \frac{1}{0.06} = 16.67 \][/tex]

4. Condition 4:
- [tex]\( [H_2] = 0.4 \)[/tex]
- [tex]\( [Cl_2] = 0.4 \)[/tex]
- [tex]\( [HCl] = 4 \)[/tex]

[tex]\[ Q = \frac{(4)^2}{(0.4) \cdot (0.4)} = \frac{16}{0.16} = 100.00 \][/tex]

### Comparison with [tex]\(K_p = 13.75\)[/tex]

Now we compare [tex]\(Q\)[/tex] to [tex]\(K_p\)[/tex] for each condition:
- Condition 1: [tex]\(Q = 112.50\)[/tex]; [tex]\(Q \neq K_p\)[/tex]
- Condition 2: [tex]\(Q = 16.00\)[/tex]; [tex]\(Q \neq K_p\)[/tex]
- Condition 3: [tex]\(Q = 16.67\)[/tex]; [tex]\(Q \neq K_p\)[/tex]
- Condition 4: [tex]\(Q = 100.00\)[/tex]; [tex]\(Q \neq K_p\)[/tex]

### Conclusion
Since [tex]\(Q\)[/tex] is not equal to [tex]\(K_p\)[/tex] (13.75) for any of the conditions, none of them are at equilibrium.

Thus, the conditions that are NOT at equilibrium are:

1. Condition 1
2. Condition 2
3. Condition 3
4. Condition 4