Problem 95 - Chemistry The Molecular Science

Question

These amounts of \(\mathrm{HI}, \mathrm{H}_{2},\) and \(\mathrm{I}_{2}\) are introduced into a \(10.00-\mathrm{L}\) flask. The flask is sealed and heated to \(745 \mathrm{~K}\). \begin{tabular}{lccc} \hline & \(n_{\mathrm{HI}}(\mathrm{mol})\) & \(n_{\mathrm{H}_{2}}(\mathrm{~mol})\) & \(\mathrm{n}_{\mathrm{h}_{2}}(\mathrm{~mol})\) \\ \hline Case a & 1.0 & 0.10 & 0.10 \\ Case b & \(10 .\) & 1.0 & 1.0 \\ Case c & \(10 .\) & \(10 .\) & 1.0 \\ Case d & 5.62 & 0.381 & 1.75 \\ \hline \end{tabular} The equilibrium constant for the reaction \(2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g})\) has the value 0.0200 at \(745 \mathrm{~K}\). In which cases does the concentration of HI increase as equilibrium is attained, and in which cases does the concentration of HI decrease?

Step-by-Step Solution

Answer

Cases a and b: HI concentration increases; Cases c and d: HI concentration decreases.

Step 1: Calculate Initial Concentrations

Calculate the initial concentrations of all species using the formula \( C = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume of the flask (10.00 L).

Step 2: Write Expression for Reaction Quotient \( Q_c \)

The reaction quotient \( Q_c \) is given by: \[ Q_c = \frac{[\mathrm{H}_2][\mathrm{I}_2]}{[\mathrm{HI}]^2} \] Calculate \( Q_c \) using the initial concentrations from Step 1.

Step 3: Compare \( Q_c \) with Equilibrium Constant \( K_c \)

Determine the direction of reaction shift by comparing \( Q_c \) to \( K_c = 0.0200 \): - If \( Q_c < K_c \), the reaction will shift to the right to produce more \( \mathrm{HI} \) (increase in \( \mathrm{HI} \) concentration).- If \( Q_c > K_c \), the reaction will shift to the left to consume \( \mathrm{HI} \) (decrease in \( \mathrm{HI} \) concentration).

Step 4: Analyze Each Case

- **Case a:** \([\mathrm{HI}] = 0.1 \, \text{M}, \quad [\mathrm{H}_2] = 0.01 \, \text{M}, \quad [\mathrm{I}_2] = 0.01 \, \text{M} \) \( Q_c = \frac{0.01 \times 0.01}{(0.1)^2} = 0.01 \), which is less than \( K_c \). Increase in \( \mathrm{HI} \).- **Case b:** \([\mathrm{HI}] = 1 \, \text{M}, \quad [\mathrm{H}_2] = 0.1 \, \text{M}, \quad [\mathrm{I}_2] = 0.1 \, \text{M}\) \( Q_c = \frac{0.1 \times 0.1}{(1)^2} = 0.01 \), which is less than \( K_c \). Increase in \( \mathrm{HI} \).- **Case c:** \([\mathrm{HI}] = 1 \, \text{M}, \quad [\mathrm{H}_2] = 1 \, \text{M}, \quad [\mathrm{I}_2] = 0.1 \, \text{M}\) \( Q_c = \frac{1 \times 0.1}{(1)^2} = 0.1 \), which is greater than \( K_c \). Decrease in \( \mathrm{HI} \).- **Case d:** \([\mathrm{HI}] = 0.562 \, \text{M}, \quad [\mathrm{H}_2] = 0.0381 \, \text{M}, \quad [\mathrm{I}_2] = 0.175 \, \text{M}\) \( Q_c = \frac{0.0381 \times 0.175}{(0.562)^2} \approx 0.0215 \), which is greater than \( K_c \). Decrease in \( \mathrm{HI} \).

Key Concepts

Equilibrium Constant

In a chemical reaction, the equilibrium constant (\( K_c \)) is a crucial value that represents the ratio of concentrations of products to reactants at equilibrium. This ratio is specific to a given reaction at a certain temperature. It indicates the extent to which a reaction will proceed before reaching a state of balance where the rates of the forward and reverse reactions are equal. The equilibrium constant helps predict the concentrations of reactants and products once the reaction has reached equilibrium.

For the reaction \(2 \text{HI(g)} \rightleftharpoons \text{H}_2\text{(g)} + \text{I}_2\text{(g)}\), the equilibrium constant expression is given as:\[K_c = \frac{[\text{H}_2][\text{I}_2]}{[\text{HI}]^2} \]This expression means that if you know the equilibrium concentrations of \( \text{H}_2 \), \( \text{I}_2 \), and \( \text{HI} \), you can substitute them into this equation to calculate \( K_c \). However, since \( K_c \) is already known in this example, it is used as a reference to determine how the initial concentrations will change as the reaction approaches equilibrium.

Reaction Quotient

The reaction quotient (\( Q_c \)) is similar to the equilibrium constant but used for non-equilibrium conditions. It is a snapshot of a reaction at any point before it reaches equilibrium. While \( K_c \) is fixed for a reaction at a given temperature, \( Q_c \) can have a range of values depending on the concentrations of the reactants and products at that moment.

To calculate \( Q_c \), you use the same formula as for \( K_c \):\[Q_c = \frac{[\text{H}_2][\text{I}_2]}{[\text{HI}]^2} \]By comparing \( Q_c \) with \( K_c \), you can predict the direction in which the reaction will proceed to reach equilibrium:

• If \( Q_c < K_c \), the reaction will proceed to the right, favoring product formation.
• If \( Q_c > K_c \), the reaction will proceed to the left, favoring reactant formation.
• If \( Q_c = K_c \), the reaction is at equilibrium.

This comparison helps determine whether the concentration of a species will increase or decrease as equilibrium is approached.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in conditions, the system will adjust itself to partially counteract the effect of the change. This principle helps us predict how an equilibrium will respond when subjected to stresses like changes in concentration, pressure, temperature, or volume.

In the context of the equilibrium of the reaction \(2 \text{HI(g)} \rightleftharpoons \text{H}_2\text{(g)} + \text{I}_2\text{(g)}\), we can anticipate changes by examining shifts:

• If the system has an increase in \( \text{HI} \) concentration, according to Le Chatelier's Principle, the equilibrium will shift to partially reduce \( \text{HI} \) by favoring the left side of the reaction, increasing \( \text{H}_2 \) and \( \text{I}_2 \) concentrations.
• If there's a decrease in \( \text{HI} \), the system will compensate by shifting towards the right to produce more \( \text{HI} \) from \( \text{H}_2 \) and \( \text{I}_2 \).

By utilizing Le Chatelier's Principle alongside \( K_c \) and \( Q_c \), we can dynamically understand and predict the behavior of chemical reactions under different conditions.