Question

Write the equilibrium expression for each of the following reactions. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) b. \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) c. \(2 \mathrm{NO}_{2}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{O}_{2}(g)\)

Short answer

The equilibrium expressions for each reaction are: a. \(K_a = \frac{[SO_{3}]^2}{[SO_{2}]^2[O_{2}]}\) b. \(K_b = \frac{[HF]^2}{[H_{2}][F_{2}]}\) c. \(K_c = \frac{[N_{2}O_{5}][O_{2}]}{[NO_{2}]^2[O_{3}]}\)

Step-by-step solution

Identify the balanced chemical equation

The balanced chemical equation for reaction (a) is: \[2SO_{2}(g) + O_{2}(g) \rightleftharpoons 2SO_{3}(g)\]

Write the equilibrium expression

The equilibrium expression for reaction (a) is: \[K_a = \frac{[SO_{3}]^2}{[SO_{2}]^2[O_{2}]}\] Reaction (b)

Identify the balanced chemical equation

The balanced chemical equation for reaction (b) is: \[H_{2}(g) + F_{2}(g) \rightleftharpoons 2HF(g)\]

Write the equilibrium expression

The equilibrium expression for reaction (b) is: \[K_b = \frac{[HF]^2}{[H_{2}][F_{2}]}\] Reaction (c)

Identify the balanced chemical equation

The balanced chemical equation for reaction (c) is: \[2NO_{2}(g) + O_{3}(g) \rightleftharpoons N_{2}O_{5}(g) + O_{2}(g)\]

Write the equilibrium expression

The equilibrium expression for reaction (c) is: \[K_c = \frac{[N_{2}O_{5}][O_{2}]}{[NO_{2}]^2[O_{3}]}\]

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This means that the concentrations of the reactants and products remain constant over time, but not necessarily equal.

When writing equilibrium expressions, such as those for the reactions provided in the exercise, the products are placed in the numerator and the reactants in the denominator. These expressions are derived from the balanced chemical equations and are shown as ratios of the molar concentrations raised to the power of their coefficients in the balanced equation.

The equilibrium constant, represented as 'K', quantifies the equilibrium state. For instance, in the equilibrium expression for reaction (a), \(K_a = \frac{[SO_{3}]^2}{[SO_{2}]^2[O_{2}]}\), the subscript ‘a’ can denote that this is the constant for this specific reaction involving sulfur dioxide and oxygen. Understanding and calculating the equilibrium constant is vital for predicting the position of equilibrium and the concentrations of reactants and products at equilibrium.

Reaction Quotient

The reaction quotient, designated as 'Q', is a number that represents the ratio of product concentrations to reactant concentrations at any point during a reaction, not just at equilibrium.

The formula for 'Q' is the same as that of the equilibrium constant 'K', but 'Q' is calculated using the concentrations of the reactants and products at any moment in time. For example, if you were considering the reaction in part (b) of the exercise at a particular instant, you would calculate the reaction quotient as \(Q_b = \frac{[HF]^2}{[H_{2}][F_{2}]}\), which uses the current concentrations of hydrogen, fluorine, and hydrogen fluoride.

The comparison between 'Q' and 'K' is a tool for predicting the direction in which a reaction will proceed to reach equilibrium. If 'Q' is less than 'K', the forward reaction is favored to produce more products. Conversely, if 'Q' is greater than 'K', the reaction will proceed in the reverse direction to produce more reactants. When 'Q' equals 'K', the system is at equilibrium, and no net change occurs.

Le Chatelier's Principle

Le Chatelier's Principle provides a qualitative way of predicting the effect of a change in conditions on a chemical equilibrium. This principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to counteract that change and a new equilibrium position will be established.

For example, consider reaction (c) given in the exercise. If the concentration of one of the reactants, say \(NO_{2}(g)\), is increased, the principle predicts that the equilibrium will shift to the right, favoring the production of more \(N_{2}O_{5}(g)\) and \(O_{2}(g)\) to reduce the stress of the added \(NO_{2}(g)\). Alternatively, an increase in temperature for an exothermic reaction will cause the equilibrium to shift towards the reactants because the system wants to absorb the extra heat.

This shifting of equilibrium in response to changes in concentration, temperature, or pressure can be harnessed in industrial chemical processes to maximize the desired product yield. Understanding how these shifts occur and their implications on the equilibrium constant is crucial for anyone studying chemical reactions.