The quantum casino: tutorials

# ∆G and temperature

We can see from the expression

G =  ∆HTSsystem

that the value of ∆G depends on temperature. Sometimes, changing the temperature can change the sign of ∆G. This explains why some reactions go in one direction at one temperature and in the opposite direction at a different temperature.

Let us look at the reaction

CaO(s) + CO2(g)  CaCO3(s)

that we considered above.

H is  –178 kJ mol-1 (–178 000 J mol-1) and  ∆Ssystem is –161 J K-1 mol-1

 Note ∆Ssystem is calculated from the difference between the total entropy of the product(s) and the total entropy of the reactants. The data can be obtained from Table 1. S (CaCO3) = 93 J K-1 mol-1 S (CaO) = 40 J K-1 mol-1 S (CO2) = 214 J K-1 mol-1 So ∆Ssystem = 92 – (40 + 214) = –161 J K-1 mol-1

If ∆G is negative, the reaction ‘goes’ from left to right. If it is positive, the reaction goes in the opposite direction.

Let us put in some figures.

## At 298 K (room temperature)

G =  ∆HT∆Ssystem

G = –178 – (298 x –0.161)    (remember to convert entropy in  J K-1 mol-1 to kJ K-1 mol-1)

G = –178 + 48

G = –130 kJ mol-1

G is negative and the reaction is feasible at this temperature. It is the reaction that happens in an absorption tube.

## At 1500 K  (the sort of temperature in a lime kiln)

G =  ∆H TSsystem

∆G = –178 – (1500 x –0.161)  (remember to convert entropy in  J K-1 mol-1 to kJ K-1 mol-1)

G = –178 + 242

G = +64 kJ mol-1

G is positive and the reaction is not feasible at this temperature. In fact the reverse reaction, which will have ∆G = –64 kJ mol-1 is feasible and this is the reaction that occurs in a lime kiln

The ‘crossover point ‘is when ∆G is zero. At this point, 0 = ∆HTSsystem

ie ∆H = TSsystem

Putting in the figures

–178 000 = T x –161

So T = 178 000 / 161 = 1105 K

So this temperature is a sort of ‘tipping point’ between the reaction being feasible or not.

Note. In this calculation we have assumed that ∆H does not change with temperature. This is an approximation only, but for most reactions the change with temperature is small. ∆Ssystem may change with temperature. For example if one of the reactants or products changes state (melts or boils) this will affect ∆Ssystem. In fact the reaction does not simply ‘flip’ between feasibility and non–feasibility (or going in one direction or the other).  If the reaction were to take place in a closed system, an equilibrium would be set up. As a rule of thumb, reactions with ∆G more negative than –60 kJ mol-1 are considered to go to completion while those with  ∆G more positive than +60 kJ mol-1 are considered not to occur at all. Between these temperatures, the reaction is considered to be reversible and in a closed system an equilibrium would be set up containing some of all the reactants and products concerned.

 ∆G and temperature

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