Lecture 23. Chemical equilibrium

Thursday 18 April 2023

Le Châtelier's Principle and its applications. Shifting a chemical equilibrium: Changing concentrations, volume or pressure, temperature.

Reading: Tro NJ. Chemistry: Structure and Properties (3rd ed.) - Ch.15 §15.7, §15.9 (pp.679b-682t, 691-699).

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Summary

A qualitative principle, known as Le Châtelier's Principle, allows us to predict the direction of change in equilibrium when conditions of concentration, temperature, and other system variables change. The principle can be summarized by saying that when equilibrium is perturbed (changed, disturbed), the system will respond by a spontaneous re-establishment of a new equilibrium in the direction that counteracts the perturbation. Analysis of a physicochemical system according to Le Châtelier's Principle corresponds quantitatively to comparison of the reaction quotient Q to K_eq. When the perturbation induces a change in temperature, K_eq itself changes, in accordance with the enthalpy change. If a chemical reaction is endothermic (ΔH_rxn > 0), K_eq increases with temperature; for an exothermic (ΔH_rxn < 0) reaction, K_eq decreases with increasing temperature.

Applying Le Châtelier's Principle to different types of changes imposed on a system at equilibrium

Effect of addition of reactants or products to a system at equilibrium. The addition of reactants to a system at equilibrium changes the conditions from Q = K_eq to Q < K_eq, since the concentration terms for reactants are in the denominator of the reaction quotient expression. In order for equilibrium to be re-established (which means that Q must increase to match K_eq once again), some of the added reactants must be converted to products (increasing the value of Q). Thus, Le Châtelier's Principle is fulfilled in this scenario because when the system is perturbed (addition of reactants), it responds in a way that counteracts the perturbation (reactants are consumed as system moves back toward equilibrium). If products are added to a system at equilibrium, then it goes from Q = K_eq to Q > K_eq. For equilibrium to be re-established, some of the added products must be converted to reactants (lowering the value of Q). Le Châtelier's Principle is fulfilled in that the perturbation of the system (addition of products), is counteracted by the reversion of products to reactants as the system moves to re-establish equilibrium.

Effect of removal of reactants or products from a system at equilibrium. We can analyze the the effect of removal of reactants or products in essentially the same fashion as above - that is by looking at the effect of the removal in terms of its effect on Q vs. K_eq. As an exercise, you may want to go through the reasoning that leads to the conclusion that removal of reactants causes some of products to be converted to reactants, and that removal of products leads the reaction to shift toward generation of products. In both cases, be sure to also explicitly explain how theses conclusions are consistent with Le Châtelier's Principle.

Effect of changing volume of a system at equilibrium. We must use the balanced chemical equation for the reaction, complete with all phase designations, to determine whether, in the stoichiometry of reaction, the number of moles of gas increases, decreases, or stays the same. In other words, the balanced equation determines a quantity Δn_g, which is computed as

Δn_g  =  n_{g, products}  −  n_{g, reactants}

which we can state as "the moles of gas-phase products minus the moles of gas-phase reactants in the reaction equation". The quantity Δn_g is also useful in relating the two forms of Q and K_eq, namely (for equilibrium constants) K_P and K_c, and (for the variable reaction quotient expression) Q_P and Q_c. Now if the volume of the system were to decrease, the total pressure of the system is increased, and the partial pressures of all gas phase components of the system change proportionately. The value of Δn_g determines the response in this case as follows. If Δn_g = 0, then a change in volume cannot affect the value of Q_P. If Δn_g > 0, then a decrease in volume must increase Q_P and the system then responds by shifting toward the reactant side, reducing the total moles of gas. If Δn_g < 0, then a decrease in volume will decrease Q_P. The system then responds by shifting toward the product side, again reducing the total moles of gas. In all cases, decreasing the volume of a reaction involving gases, which increases the total pressure of the system, will shift the reaction toward the side with fewer molecules in the gas phase, if a difference exists, and Le Châtelier's Principle holds as an increase in total pressure is counteracted - where possible - by the pressure decrease resulting from the decrease in total moles of gas.

Effect of changing the temperature of a system at equilibrium. When the temperature changes, the value of K_eq changes. Of all the perturbations we discuss in this context, this the only case where this occurs. In order to analyze this situation, we need some additional information about the reaction, namely whether the reaction is exothermic or endothermic. Then we regard heat as a product (the exothermic case) or a reactant (the endothermic case). If, for example, the reaction under consideration is endothermic, then raising the temperature will result in a shift in composition toward products, since by converting some reactants to products some of the heat added to the system to raise its temperature is consumed.

Example

For the homogeneous gas phase reaction introduced previously,

N₂(g)  +  3 H₂(g)  =  2 NH₃(g)       ΔH_rxn  =  − 92 kJ mol_rxn

write the reaction quotient expression. Predict the response of a closed system in which this reaction occurs to each of the following perturbations of an equilibrium state: (i) removal of NH₃ (ii) addition of H₂ (iii) increasing temperature (iv) decreasing volume of the system.

Solution: The reaction quotient expression for the reaction is

Q  =  [NH₃]² / [N₂] [H₂]³

The effects of the perturbations can be predicted as follows. (i) Perturbation of the system at equilibrium by the removal of some NH₃ should result in the shift of the reaction to the right, which generates more NH₃ to counteract the imposed change. (ii) Addition of H₂ should also drive the reaction toward more products as the system responds by consuming some of the added reactant. (iii) Since ΔH_rxn < 0, the reaction is exothermic, meaning heat can be viewed as a product of the forward reaction, and conversely is consumed by the reverse reaction. If heat is added to the system to raise its temperature, the system will respond to counter this perturbation by using up some of the added energy in shifting its composition toward reactants. (iv) The number of moles of gas decreases as reactants are changed to products. Since Δn_g < 0, then a decrease in volume will decrease Q, hence the reaction will shift toward products to reduce the total number of molecules - this counteracts the increased pressure imposed on the system by decreasing its volume - and increases Q to match the value of K_eq once again.