Question

In a study of the formation of HI from its elements, $$ \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) $$ equal amounts of \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) were placed in a container, which was then sealed and heated. (a) On one set of axes, sketch concentration vs. time curves for \(\mathrm{H}_{2}\) and HI, and explain how \(Q\) changes as a function of time. (b) Is the value of \(Q\) different if \(\left[\mathrm{I}_{2}\right]\) is plotted instead of \(\left[\mathrm{H}_{2}\right] ?\)

Short answer

In the reaction \(\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g)\), the value of \(Q\) increases over time until it equals the equilibrium constant \(K\). The value of \(Q\) is the same when \([I_2]\) is plotted instead of \([H_2]\).

Step-by-step solution

Understanding the Reaction

The given reaction is \ \[ \mathrm{H}_{2}(g) + \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) \]. \ It indicates that hydrogen gas and iodine gas react to form hydrogen iodide gas.

Sketching the Concentration vs. Time Curves

On a set of axes, plot concentration (vertical axis) against time (horizontal axis). \[ \text{For } \mathrm{H}_{2}: \text{Start at } [H_2]_0 \text{ and decrease over time until equilibrium is reached, forming a curve.} \] \[ \text{For } \mathrm{HI}: \text{Start at 0 and increase as } HI \text{ is formed, then level off at equilibrium.} \]

Explaining the Changes in Q

The reaction quotient (\(Q\)) is defined as \(Q = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\). Initially, \(Q\) is zero because \( \left[ \mathrm{HI} \right] = 0 \). \ As the reaction proceeds, \(Q\) increases as the concentration of \( \mathrm{HI} \) increases and the concentrations of \( \mathrm{H}_2 \) and \( \mathrm{I}_2 \) decrease until equilibrium is reached. At equilibrium, \(Q = K \), where \(K\) is the equilibrium constant.

Analyzing the Plot of [I2]

If the concentration of \( \mathrm{I}_2 \) is plotted instead of \( \mathrm{H}_2 \), the value of \(Q\) remains the same because \( \left[ \mathrm{I}_2 \right] \) is directly proportional to \( \left[ \mathrm{H}_2 \right] \) due to the stoichiometry of the reaction.\

Key concepts

reaction quotient

The reaction quotient, or \(Q\), is a measure used to determine the direction in which a reaction will proceed to reach equilibrium. For the reaction involving \(\text{H}_2\) and \(\text{I}_2\) to form \(2 \text{HI}\), \(Q\) is calculated using the formula: \( Q = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \). The values of concentrations are taken from the instant you are interested in.
For example, at the start of the reaction, when no product has formed, \([ \text{HI} ] = 0\), making \(Q = 0\). As the reaction progresses, the concentration of \(\text{HI}\) increases while that of \(\text{H}_2\) and \(\text{I}_2\) decreases. This makes \(Q\) increase over time until it matches the equilibrium constant \(K\), indicating that the equilibrium has been reached.

equilibrium constant

The equilibrium constant, represented as \(K\), is a fixed value that describes the ratio of product concentrations to reactant concentrations at equilibrium for a reversible reaction. For our reaction \(\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g)\), \(K\) is given by \(K = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]}\).
It's crucial to note that \(K\) remains constant for a given reaction at a specific temperature. It does not change even if the initial concentrations of the reactants or products are altered. At equilibrium, the reaction quotient \(Q\) reaches this constant value \(K\), indicating that the reaction mixtures are in a state of balance where the rate of the forward reaction equals the rate of the reverse reaction.

concentration vs. time curves

Concentration vs. time curves offer a visual representation of how the concentrations of reactants and products change over time. For the reaction involving \(\text{H}_2\) and \(\text{I}_2\) to form \(2 \text{HI}\), these curves can be plotted on a graph with concentration on the vertical axis and time on the horizontal axis.
Initially, the concentration of \(\text{H}_2\) and \(\text{I}_2\) starts at their initial values, while the concentration of \(\text{HI}\) starts at zero. As the reaction proceeds:

• The concentrations of \(\text{H}_2\) and \(\text{I}_2\) decrease as they are consumed.
• The concentration of \(\text{HI}\) increases as it forms, eventually flattening out as equilibrium is approached.

These curves provide insight into how quickly a reaction progresses and when equilibrium is reached.

stoichiometry

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction, based on their balanced chemical equation. For the reaction \(\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g)\), the stoichiometric coefficients are 1:1:2, meaning one molecule of \(\text{H}_2\) reacts with one molecule of \(\text{I}_2\) to produce two molecules of \(\text{HI}\).
This stoichiometric relationship helps determine how the concentrations of the reactants and product will change over time. For example:

• If 1 mole of \(\text{H}_2\) reacts fully, it would need 1 mole of \(\text{I}_2\), and together they would produce 2 moles of \(\text{HI}\).
• The stoichiometry also ensures that the decrease in the concentrations of \(\text{H}_2\) and \(\text{I}_2\) is proportional to their coefficients, maintaining balance in the reaction.