Question

Consider the following reaction:

2NO(g) + O₂(g) → 2NO₂(g)
Estimate ΔG° for this reaction at each of the following temperatures and predict whether or not the reaction will be spontaneous. (Assume ΔH°/ΔS° do not change too much)
a. 298 K
b. 724 K
c. 845 K

Answer 1

To estimate ΔG° for the reaction 2NO(g) + O₂(g) → 2NO₂(g) at different temperatures and predict spontaneity, we can use the equation ΔG° = -RTlnK. By substituting the given equilibrium constants and calculating the result, we can estimate ΔG° at each temperature.

Step-by-step explanation:

For the reaction 2NO(g) + O₂(g) → 2NO₂(g), the standard free energy change (ΔG°) can be estimated using the equation ΔG° = -RTlnK, where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and K is the equilibrium constant.

To predict whether or not the reaction will be spontaneous, we determine the sign of ΔG°. If ΔG° is negative, the reaction is spontaneous; if ΔG° is positive, the reaction is non-spontaneous.

a. At 298 K:

• ΔG° = -RTlnK = -(8.314 J/(mol·K) * 298 K) * ln(K)
• Substitute the given equilibrium constant into the equation, ln(5.9 × 10^-3)
• Calculate the result to estimate ΔG°

b. At 724 K:

• ΔG° = -RTlnK = -(8.314 J/(mol·K) * 724 K) * ln(K)
• Substitute the given equilibrium constant into the equation, ln(1.3 × 10^-6)
• Calculate the result to estimate ΔG°

c. At 845 K:

• ΔG° = -RTlnK = -(8.314 J/(mol·K) * 845 K) * ln(K)
• Substitute the given equilibrium constant into the equation, ln(K)
• Calculate the result to estimate ΔG°