Consider the following reaction: C2H4(g) + H2(g) → C2H6(g) with ΔH = -137.5 kJ and ΔS = -120.5 J/K. Calculate ΔG at 25 °C and determine whether the reaction is spontaneous.

• A. ΔG = -137.5 kJ; the reaction is spontaneous.
• B. ΔG = 137.5 kJ; the reaction is non-spontaneous.
• C. ΔG = -101.4 kJ; the reaction is spontaneous.
• D. ΔG = 101.4 kJ; the reaction is non-spontaneous.

Answer: (C)

Verified step by step guidance

1. Identify the given values: ΔH = -137.5 kJ, ΔS = -120.5 J/K, and the temperature T = 25 °C. Convert the temperature to Kelvin by adding 273.15, so T = 298.15 K.
2. Convert ΔS from J/K to kJ/K to match the units of ΔH. Since 1 kJ = 1000 J, divide ΔS by 1000: ΔS = -120.5 J/K ÷ 1000 = -0.1205 kJ/K.
3. Use the Gibbs free energy equation: ΔG = ΔH - TΔS. Substitute the known values into the equation: ΔG = -137.5 kJ - (298.15 K × -0.1205 kJ/K).
4. Calculate the product of T and ΔS: 298.15 K × -0.1205 kJ/K. This will give you the value to subtract from ΔH.
5. Subtract the result from the previous step from ΔH to find ΔG. Determine the sign of ΔG to conclude whether the reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0).