Question

Write the equilibrium constant expression for each of the following reactions: (a) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) (b) \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\)

Short answer

The equilibrium constants are given by: (a) \(K=\frac{{[\mathrm{HF}]^{2}}}{{[\mathrm{H}_{2}][\mathrm{F}_{2}]}}\), (b) \(K=\frac{{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^{4}}}{{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^{2}}}\), and (c) \(K=\frac{{[\mathrm{NO}_{2}]^{2}}}{{[\mathrm{N}_{2}\mathrm{O}_{4}]}}\).

Step-by-step solution

Write Expression for Reaction (a)

The equilibrium constant expression for the reaction \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) is given as \[K=\frac{{[\mathrm{HF}]^{2}}}{{[\mathrm{H}_{2}][\mathrm{F}_{2}]}}\]

Write Expression for Reaction (b)

The equilibrium constant expression for the reaction \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) is given as \[K=\frac{{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^{4}}}{{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^{2}}}\]

Write Expression for Reaction (c)

The equilibrium constant expression for the reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\) is given as \[K=\frac{{[\mathrm{NO}_{2}]^{2}}}{{[\mathrm{N}_{2}\mathrm{O}_{4}]}}\]

Key concepts

Chemical Equilibrium

Understanding chemical equilibrium is essential for explaining how reactions occur and why they sometimes don't proceed to completion. In a chemical reaction, reactants convert into products, but under certain conditions, the products can also revert back into reactants. When the rate of the forward reaction (reactants to products) equals the rate of the reverse reaction (products to reactants), a state of dynamic balance is established; this is known as chemical equilibrium.

At this point, the concentrations of the reactants and products remain constant over time, not because the reactions have stopped, but because they are occuring at the same rate in both directions. The equilibrium constant expression for a reaction quantifies this balance and is derived from the concentrations of the reactants and products when the reaction is at equilibrium. For instance, given the reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant expression (K) is written as:\[K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]where the concentration of each species is raised to the power of its stoichiometric coefficient in the balanced equation. It's important for students to recognize that solid and liquid concentrations are omitted from the expression, as their concentrations change negligibly in a reaction.

Reaction Quotient

When first learning about the reaction quotient (Q), it's easy to confuse it with the equilibrium constant (K). However, while K describes the ratio of concentrations at equilibrium, Q can be calculated at any point during a reaction. The reaction quotient uses the same formula as the equilibrium constant expression, but with the current concentrations of the reactants and products, regardless of whether the system is at equilibrium.

For a general reaction: \(aA + bB \rightleftharpoons cC + dD\), the reaction quotient (Q) is given by:\[Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]

Comparing Q to K provides valuable information about the direction in which the reaction will proceed to reach equilibrium. If \(Q < K\), the forward reaction is favored to form more products. If \(Q > K\), the reaction will proceed in the reverse direction to produce more reactants. When \(Q = K\), the reaction is at equilibrium.

Le Chatelier's Principle

When a system at equilibrium is disturbed, it responds in a way that tends to counteract the disturbance and re-establish equilibrium. This is known as Le Chatelier's Principle, a fundamental concept in chemical equilibrium. The principle provides a qualitative prediction of how changes in concentration, temperature, or pressure will shift the position of equilibrium.

For example, if the concentration of a reactant is increased, the system will respond by consuming some of the added reactant to form more products, thereby shifting the equilibrium to the right. Conversely, decreasing the concentration of a product will cause the reaction to shift to the left, forming more of that product.

Temperature changes can also affect equilibrium; raising the temperature favors the endothermic direction of a reaction, while lowering the temperature favors the exothermic direction. Pressure changes will influence systems where gases are involved; increasing the pressure shifts the equilibrium towards the side of the reaction with fewer gas molecules.

It's essential to keep in mind that Le Chatelier's Principle is a qualitative tool, so while it indicates the direction of the shift, it doesn't quantify the extent of the change in concentrations of reactants and products.