E11 Applications of the equilibrium law : temperature change

Aim: To show what influence the temperature has on the equilibrium mixture.

In general changes in concentrations of one or more components are the only changes, which can be exerted upon an equilibrium reaction. A change in temperature should not be seen as bringing about a change in the equilibrium, rather as changing the value of the equilibrium constant itself. The equilibrium constant always changes if the reaction temperature is changed.

It is sufficient to remember that : “In the case of an exothermic reaction, the Kc-value decreases with increasing temperatue and in the case of an endothermic reaction, the Kc-value increases with increasing temperature”.


The so-called van ‘t Hoff equation relates Kc to the temperature in K :


where K1 is the equilibrium constant at temperature T1,
K2 is the equilibrium constant at temperature T2;
is the increase in molar enthalpy of the equilibrium reaction under normal temperature and pressure, and R is the molar gas constant: 8,314 J mol-1K-1.
is negative for an exothermic reaction and positive for an endothermic reaction. Fortunately does not appear to be strongly dependent upon temperature.
Considering the influence of temperature on as equilibrium mixture we will first explain the evolution in terms of equilibrium laws: one which supplies at the first equilibrium temperature and the second which is valid at the final temperature. After this, we will repeat the reasoning but this time on this basis of the qualitative principle of le Chatelier.

The influence of temperature on an equilibrium reaction is illustrated for the NO2-dimerization in illustration E11a. Again the starting point is the equilibrium mixture resulting from experiment A. In a reaction equation any molar enthalpy increase is included on the left side of the equation and any molar enthalpy reduction on the right side. In the reaction equation for the NO2-dimerization reaction at the top of illustration
E11a :


+ 58 kJ is written on the right hand side indicating that 58 kJ is released during dimerization and hence that the
reaction is exothermic.

At time t1 the equilibrium mixture resulting from experiment A is subjected to a temperature jump from 25 to 70 C, i.e. heat is supplied to the system. A new equilibrium constant will apply at this higher temperature, which will be lower than that at 25 C due to the exothermic nature of the reaction.

The changes in concentration of N2O4 and NO2 in response to this temperature jump at time t1, are shown in illustration E11a as a function of time. The new equilibrium condition is attained at time t2, with a considerably increased NO2 concentration (0.037 mol/L vs 0.011 mol/L) and a considerably reduced N2O4 -concentration (0.014 mol/L vs 0.027 mol/L).

In the first instance, it may seem strange that the concentration curves cross or that the NO2-concentration increases above the initial N2O4 -concentration.


 

However, this is readily explained in terms of the equilibrium law, as can be seen from illustration E11b. The influence of the jump in temperature on Kc shows an immediate decrease from 222 to 10 as a result of the increase in reaction temperature. As is known, the new Kc -value can be calculated using the van 't Hoff equation. Kc at 70 C is calculated to be 10.2 compared with a value of 222 at 25 C.

Immediately the temperature increases from 25 to 70 C, a new Kc value of 10.2 applies, but the equilibrium concentrations at 25 C no longer satisfy the new equilibrium conditions

In the time interval t1 to t2, Qc will change from 222 (equal to Kc at 25 C) to 10.2 (equal to Kc at 70 C). To obtain the required reduction in Qc the numerator has to decrease by x and the denominator has to increase correspondingly by 2x, in line with the stoichiometry of the dimerization reaction. x can be calculated from the following equation, with the equilibrium concentrations applying at the new equilibrium condition being represented by [ ]’e :

which on solving yields values for x of - 0.049 mol/L, which can be rejected as not being chemically realistic because it gives a negative NO2-concentration at equilibrium, and + 0.013 mol/L, which is chemically realistic.

Due to the stoichiometry of the reaction, the increase in NO2-concentration, 0.026 mol/L, is double that of the decrease in N2O4-concentration, 0.013 mol/L and equilibrium concentrations for NO2 and N2O4 are 0.037 mol/L and 0.014 mol/L respectively.

The temperature jump has thus clearly shifted the reaction to the left of the reaction equation, the new equilibrium concentration for NO2 being higher than that for N2O4.

Le Chatelier’s principle also yields the same conclusion, as an increase in temperature means that heat has been pumped into the system and the system will try to counter act this by reducing the heat content of the system. In other words reactions will be favoured in which heat is absorbed, as is the case with the dissociation of N2O4 into NO2.

For the sake of interest, Kc-values are given below for the NO2-dimerization reaction for four different temperatures :



With these values the influence of temperature on the equilibrium concentrations of NO2 and N2O4 can be further elucidated.