Question

For the reaction, \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\) the equilibrium concentration of \(\mathrm{H}_{2}, \mathrm{I}_{2}\) and \(\mathrm{HI}\) are \(8.0,3.0\) and \(28.0\) mole/litre, respectively, the equilibrium constant is: (a) \(28.34\) (b) \(32.66\) (c) \(34.78\) (d) \(38.88\)

Short answer

The equilibrium constant is 32.66.

Step-by-step solution

Understand the Reaction and Equilibrium Constant

We are given a chemical reaction: \( \mathrm{H}_2 + \mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI} \). For this reaction, the equilibrium constant \( K_c \) can be calculated using the equation:\[K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\] where \([\mathrm{HI}], [\mathrm{H}_2], \text{ and } [\mathrm{I}_2]\) are the equilibrium concentrations of \( \mathrm{HI}, \mathrm{H}_2, \text{ and } \mathrm{I}_2\) respectively.

Insert Equilibrium Concentrations into the Formula

Insert the given concentrations into the equilibrium constant equation:\[K_c = \frac{(28.0)^2}{(8.0)(3.0)}\] Here, \([\mathrm{HI}] = 28.0 \text{ mol/L} \), \([\mathrm{H}_2] = 8.0 \text{ mol/L} \), and \([\mathrm{I}_2] = 3.0 \text{ mol/L} \).

Calculate the Numerator

Calculate \([\mathrm{HI}]^2\):\[[\mathrm{HI}]^2 = (28.0)^2 = 784.0\]

Calculate the Denominator

Calculate the product of the concentrations of \(\mathrm{H}_2\) and \(\mathrm{I}_2\):\[[\mathrm{H}_2][\mathrm{I}_2] = (8.0)(3.0) = 24.0\]

Calculate the Equilibrium Constant

Insert the calculations from the previous steps into the equilibrium constant equation:\[K_c = \frac{784.0}{24.0} = 32.6667\] Round this to match the options provided, which is approximately 32.66.

Key concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_c \), is a crucial concept in chemical equilibrium. It provides us with a numerical measure of the position of equilibrium for a particular reaction. This constant is dependent on the specific conditions at which a reaction reaches equilibrium, such as temperature and pressure. The value of \( K_c \) is determined by the relationship between the concentrations of the reactants and products at equilibrium.

For the reaction \( \mathrm{H}_2 + \mathrm{I}_2 \rightleftharpoons 2\mathrm{HI} \), the equilibrium constant expression is:

• \[ K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]} \]

Here, the square term \([\mathrm{HI}]^2\) represents the fact that two moles of \( \mathrm{HI} \) are produced for each mole of \( \mathrm{H}_2 \) and \( \mathrm{I}_2 \). The products' concentration terms are in the numerator because they are products of the forward reaction. Conversely, reactants appear in the denominator. Understanding \( K_c \) aids in predicting the mixture composition at equilibrium.

Reaction Quotient

The reaction quotient, represented as \( Q_c \), is a snapshot of a reaction at any point, not just at equilibrium. It uses the same mathematical expression as the equilibrium constant:

• \[ Q_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]} \]

However, \( Q_c \) applies to initial concentrations or any concentrations before equilibrium is reached. It informs us about the direction in which a reaction will proceed to reach equilibrium.

To analyze \( Q_c \):

• If \( Q_c = K_c \), the system is at equilibrium.
• If \( Q_c < K_c \), the forward reaction will proceed to form more products.
• If \( Q_c > K_c \), the reverse reaction will occur to produce more reactants.

This comparison aids chemists in determining whether a reaction needs to shift forward or backward to reach a steady state.

Equilibrium Concentration

The term 'equilibrium concentration' refers to the concentration of reactants and products when a reaction reaches a point where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of the species remain constant even though the reaction continues.

In our exercise, these values were given as:

• \( [\mathrm{H}_2] = 8.0 \text{ mol/L} \)
• \( [\mathrm{I}_2] = 3.0 \text{ mol/L} \)
• \( [\mathrm{HI}] = 28.0 \text{ mol/L} \)

Using these values allows us to calculate the equilibrium constant, \( K_c \), by substituting them into the equilibrium expression. The conservation of concentration at equilibrium highlights the dynamic balance at this state. In essence, understanding equilibrium concentrations is central to applying the equilibrium constant formula accurately.

Le Chatelier's Principle

Le Chatelier's Principle is a vital guideline in chemistry, which predicts how changes in conditions can affect the position of equilibrium. When a system in equilibrium is subjected to a change in concentration, temperature, or pressure, it will adjust itself to partially counteract that change and re-establish equilibrium.

For instance:

• If the concentration of \( \mathrm{HI} \) is increased, the equilibrium will shift left, favoring the formation of \( \mathrm{H}_2 \) and \( \mathrm{I}_2 \).
• A pressure increase, by decreasing volume, will favor the side of the equilibrium with fewer gas moles, though this specific reaction has equal moles on both sides, leaving it unchanged by pressure.
• Temperature changes are more complex, affecting the energy favorability of reactions, despite not altering the equilibrium constant directly.

Le Chatelier's Principle helps us understand and predict the qualitative shifts in equilibrium due to various changes in reaction conditions.