E10 Applications of the equilibrium law : concentration changes of all components by a volume change

Equilibria in the gas phase can be shifted by changing the volume of the closed system. The concentrations of all the components are thereby changed in the same way. Illustration E10a shows the evolution of the concentrations of NO₂ and N₂O₄ as a function of time, after decreasing the volume of the closed system. As with the external addition of NO₂, the starting point is the equilibrium mixture resulting from Experiment A. At time t₁ the reaction volume is halved, for example by pushing in a piston in a closed cylinder. This doubles the concentrations of NO₂ and N₂O₄ (resulting in concentrations of 0.022 mol/L and 0.054 mol/L respectively), which no longer comply with the equilibrium conditions at 25 °C.

This abrupt doubling in N₂O₄- and NO₂-concentrations is counteracted by concentration changes in the reaction mixture, the N₂O₄-concentration increasing slowly to 0.057 mol/L and the NO₂-concentration slowly decreasing from 0.022 mol/L to 0.016 mol/L. This is, of course, consistent with the 2:1 stoichiometry of the reaction.

The fact that the N₂O₄-concentration further increases, poses the question: how is this to be explained? Has the reaction stoichiometry changed or is it simply because the N₂O₄-concentration was the greater? The actual explanation is contained in the equilibrium law.

The green band in illustration E10b shows the variation in Q_c as a function of time. The doubling of the concentrations reduces Q_c from 222 to 111, which is half the K_c-value of 222. The equilibrium law is relentless, the disturbance has to be counteracted by changing the concentrations rapidly or slowly to the new values dictated by the K_c-value. These changes must result in an increase in the numerator and hence a corresponding decrease in the denominator, as dictated by the stoichiometry of the reaction. The new equilibrium concentration of N₂O₄ is, at 0.057 mol/L slightly higher than the concentration resulting from the volume decrease. The new equilibrium concentration of NO₂ is, at 0.016 mol/L slightly lower than the concentration resulting from the volume decrease.

A calculation and a table such as in illustration E09b can be useful in understanding the relationship between the change in Q_c (the green band) and the changes in
N₂O₄ (white band)-and NO₂ (brown band)-concentrations as a function of time.

If the equilibrium concentrations after the volume decrease, are compared with those before the volume decrease, the concentrations of both components have increased. This is solely due to the volume decrease. In the case of N₂O₄, with the lower stoichiometric number, the change in concentration becomes even greater, whereas in the case of NO₂ the change has been counteracted as much as possible. This is again in accordance with the general principle of the smallest change, the final concentration of NO₂ not being able to dip below the previous equilibrium concentration.

Conclusion

In the case of simultaneous and uniform concentration change of reactants and products, the equilibrium law can again be relied upon to predict the composition of the new equilibrium mixture. It is a simple rule of thumb that if the concentrations of the components are simultaneously and uniformly increased, then according to the Chatelier’s principle, the equilibrium will shift to the side of the reaction equation with the fewer molecules to keep the number of molecules per unit volume in the system as constant as possible. In the event of simultaneous and uniform concentration decrease, on the other hand, the equilibrium will shift to the side of the reaction equation with more molecules, again to keep the number of molecules per unit volume in the system as constant as possible. In general in the event of volume change, its effects must be predicted in terms of concentration changes.