Question

Consider the reaction

C₂H₄(g) + H₂(g) → C₂H₆(g)

∆H = -137.5 kJ; ∆S = -120.5 J/K

Calculate ∆G at 25 °C and determine whether the reaction is spontaneous. Does ∆G become more negative or more positive as the temperature increases?

a. ∆G = -12,450 J; spontaneous; more negative
b. ∆G = -12,450 J; non-spontaneous; more positive
c. ∆G = 12,450 J; spontaneous; more negative
d. ∆G = 12,450 J; non-spontaneous; more positive

Answer 1

At 25 °C, ΔG for the reaction of ethylene with hydrogen to form ethane is -101,591 J, indicating that the reaction is spontaneous at this temperature. However, as the temperature increases, ΔG will become more positive, potentially making the reaction non-spontaneous at higher temperatures.

Step-by-step explanation:

To calculate the standard free energy change (ΔG) at 25 °C for the reaction C₂H₄(g) + H₂(g) → C₂H₆(g), we use the following formula:

ΔG = ΔH - TΔS

Given that ΔH = -137.5 kJ and ΔS = -120.5 J/K, let's convert ΔH into J by multiplying it by 1000 so that the units match, then plug in the values:

ΔG = (-137.5 kJ × 1000 J/kJ) - (298 K × -120.5 J/K)

ΔG = (-137,500 J) - (298 K × -120.5 J/K)

ΔG = -137,500 J + 35,909 J

ΔG = -101,591 J

Since ΔG is negative, the reaction is spontaneous at 25 °C. However, because ΔS is negative, ΔG will become less negative (more positive) as the temperature increases, making the reaction less likely to be spontaneous at higher temperatures.