Question

At a certain temperature, only \(50 \% \mathrm{HI}\) is dissociated at equilibrium in the following reaction: $$ 2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) $$ The equilibrium constant for this reaction is : (a) \(0.25\) (b) \(1.0\) (c) \(3.0\) (d) \(0.5\)

Short answer

0.25

Step-by-step solution

Understanding the Dissociation Process

Given that 50% of hydrogen iodide (HI) is dissociated at equilibrium, we can assume that initially there were 100 molecules of HI for simplicity. At equilibrium, 50 molecules of HI have dissociated into an equal number of hydrogen (H2) and iodine (I2) molecules.

Calculating Equilibrium Concentrations

Starting with 100 molecules of HI, at equilibrium there would be 50 molecules of HI left, and 25 molecules of H2 and 25 molecules of I2, since the reaction produces half as many moles of H2 and I2 for every mole of HI that dissociates. These values reflect the changes in concentration, usually denoted as x.

Writing the Equilibrium Constant Expression

The equilibrium constant (Kc) for the reaction is expressed as \[ K_c = \frac{[\mathrm{H}_2][\mathrm{I}_2]}{[\mathrm{HI}]^2} \] where the concentrations of the products and reactants at equilibrium are substituted into the expression.

Substituting Equilibrium Concentrations into Kc Expression

Substituting the equilibrium concentrations (bearing in mind that they should be in molarity, but will cancel out in this case as the stoichiometry is 1:1:1), we get \[ K_c = \frac{(25)(25)}{(50)^2} \]

Calculating the Equilibrium Constant

By performing the calculation provided in the previous step: \[ K_c = \frac{625}{2500} = 0.25 \] The equilibrium constant for the reaction is 0.25.

Key concepts

Understanding Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rates of the forward and backward reactions are equal. This balance results in no net change in the concentration of reactants and products over time, although these substances continue to react with one another.

In the given problem, when 50% of hydrogen iodide (HI) is dissociated at equilibrium, it means that the forward reaction, where HI dissociates into hydrogen (H₂) and iodine (I₂), is occurring at the same rate as the reverse reaction, where H₂ and I₂ combine to form HI. Understanding this concept is key because it helps explain why, even after establishing equilibrium, chemical reactions are still dynamic and not static.

The Reaction Quotient

The reaction quotient (Q) is a measure that compares the relative amounts of products and reactants present during a reaction at any point in time. It is calculated similarly to the equilibrium constant but is used for any moment in the reaction, not just at equilibrium.

The formula is the same, with the concentration of the products raised to the power of their stoichiometric coefficients divided by the concentration of the reactants raised to the power of their coefficients. Therefore, if QK, the reverse reaction is favored to form more reactants. When Q=K, the system is at equilibrium.

Dissociation of HI

The dissociation of hydrogen iodide (HI) into hydrogen (H₂) and iodine (I₂) is an example of a reversible chemical reaction. In this process, a certain percentage of HI decomposes into its constituent elements.

The equilibrium concentrations of H₂, I₂, and remaining HI are crucial for understanding the system's equilibrium state. For instance, in the exercise, because 50% of HI dissociates, we end up with equal amounts of H₂ and I₂ (since the stoichiometry is one to one), and the remaining 50% of the HI is left unreacted. To solve equilibrium constant problems like these, it's essential to comprehend this dissociation process.

Le Chatelier's Principle

Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. This principle predicts how a system at equilibrium will respond to external stresses like changes in concentration, pressure, and temperature.

In the context of the dissociation of HI, if we were to increase the pressure of the system by decreasing the volume, we would expect the equilibrium to shift towards the side with fewer gas molecules, which in this case would be the production of more HI. Understanding Le Chatelier's principle helps us predict the direction in which a reaction will proceed when it is subjected to different environmental changes.