Question

For the reaction NH4Cl (s)→NH3 (g)  + HCl (g) at 25°C, ΔH = 176 kJ/mol and ΔS = 0.285 kJ/(mol - K).

What is the ΔG, and will this reaction be spontaneous in the forward direction?

Responses

91 kJ/mol; yes

91 kJ/mol; yes

261 kJ/mol; yes

261 kJ/mol; yes

91 kJ/mol; no

91 kJ/mol; no

261 kJ/mol; no

Answer 1

To calculate the Gibbs free energy change (ΔG) for the reaction, you use the equation:

\[
\Delta G = \Delta H - T \Delta S
\]

where:
- \(\Delta H = 176 \text{ kJ/mol}\)
- \(\Delta S = 0.285 \text{ kJ/(mol K)}\)
- \(T = 25°C = 298 \text{ K}\) (convert Celsius to Kelvin by adding 273)

Now, let's calculate \(T \Delta S\):

\[
T \Delta S = 298 \text{ K} \times 0.285 \text{ kJ/(mol K)} = 84.93 \text{ kJ/mol}
\]

Now we can substitute \(\Delta H\) and \(T \Delta S\) into the ΔG equation:

\[
\Delta G = 176 \text{ kJ/mol} - 84.93 \text{ kJ/mol} = 91.07 \text{ kJ/mol}
\]

Rounding this to two decimal places gives:

\[
\Delta G \approx 91 \text{ kJ/mol}
\]

To determine whether the reaction is spontaneous, we look at the sign of ΔG:

- If \(\Delta G < 0\), the reaction is spontaneous in the forward direction.
- If \(\Delta G > 0\), the reaction is non-spontaneous in the forward direction.

Since \(\Delta G = 91 \text{ kJ/mol}\) (> 0), the reaction is not spontaneous.

Therefore, the correct answer is:

**91 kJ/mol; no**