How to determine whether a reaction is feasible

A spontaneous or feasible process must be accompanied by a positive change in total entropy (entropy of the universe). Whether this is the case is almost always down to the temperature – hence ice melts at 23°C but not at -14°C.

Before we go any further, I’m assuming that you are confident in your understanding of the concept of entropy and that these equations look familiar:

ΔS_sys = ∑ S_products – ∑ S_reactants

ΔS_total = ΔS_surr + ΔS_sys

ΔS_surr = -ΔH / T

ΔS_total = (-ΔH / T) + ΔS_sys

NOTE: not all exam specifications require you to be able to determine the feasibility of a reaction by calculating total change in entropy – some jump straight from the concept of entropy change of system to Gibbs free energy, ΔG, hence I’m going to show you both methods of determining feasibility.

ΔG = ΔH – TΔS_sys

Personally, I’m not sure how you can genuinely understand Gibbs free energy without an understanding of entropy change of surroundings and total entropy change, so I strongly recommend you read up on it all 🧐.

Calculating the temperature at which a reaction becomes feasible

The decomposition of calcium carbonate into calcium oxide and carbon dioxide is an endothermic reaction, however if we know ΔS_sys and Δ_rH for the reaction, we can figure out the temperature at which this reaction becomes feasible or spontaneous.

CaCO_3(s) ⇾ CaO_(s) + CO_2(g) ΔS_sys = +161 JK^-1mol^-1 Δ_rH = +178 kJ mol^-1

1. ΔS_total = (-ΔH / T) + ΔS_sys and a reaction is feasible when ΔS_total = 0 since this is when the reaction is at equilibrium (K_c = 1).

0 = (-178000 / T) + 161 (remembering to convert Δ_rH into J mol^-1)

-161 = -178000 / T

T = 1106K

2. ΔG = ΔH – TΔS_sys and ΔG = 0 at the minimum temperature required for the reaction to occur

0 = ΔH – TΔS_sys

TΔS_sys = ΔH

T = ΔH / ΔS_sys = +178 / + 0.161 = 1106K remembering to convert ΔS_sys into kJ K^-1 mol^-1

Practice question

You will need standard molar entropy data from the table below:

Substance	S⦵  / JK-1mol-1
CH4 (g)	186.2
H2O (g)	189.0
CO (g)	197.6
H2 (g)	130.6

 CH_4(g)  +   H₂O_(g)  ⇾  CO_(g)   +   3H_2(g)       Δ_rH = +206 kJ mol^-1

(a) Calculate ΔS_sys for the reaction above.

(b) Explain how the sign of your answer to part (a) is predicted by the equation.

(c) Calculate the minimum temperature required for the forward reaction to be feasible.

Answer

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