Problem 47 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction, \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\), the equilibrium concentrations of \(\mathrm{H}_{2}, 1_{2}\) and \(\mathrm{HI}\) are 8,3 and \(28 \mathrm{~mol} \mathrm{~L}^{-1}\) respectively. Equilibrium constant of the reaction is (a) \(32.67\) (b) \(31.67\) (c) \(34.67\) (d) \(36.67\)

Step-by-Step Solution

Answer

The equilibrium constant is (a) 32.67.

Step 1: Write the Equilibrium Expression

For the given chemical reaction \( \mathrm{H}_2 + \mathrm{I}_2 \rightleftharpoons 2 \mathrm{HI} \), the equilibrium constant expression \( K_c \) is derived from the concentrations of the products and reactants at equilibrium. It is given by: \[ K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]} \].

Step 2: Plug in Equilibrium Concentrations

Substitute the provided equilibrium concentrations into the equilibrium expression: \[ K_c = \frac{(28)^2}{(8)(3)} \].

Step 3: Perform the Calculation

Calculate \( K_c \) by solving the expression: 1. Calculate the numerator: \((28)^2 = 784\)2. Calculate the denominator: \(8 \times 3 = 24\)3. Divide the numerator by the denominator: \[ \frac{784}{24} = 32.67 \].

Step 4: Compare with Options

Compare the calculated value of \( K_c = 32.67 \) with the given choices and select the closest match. The closest option is (a) \(32.67\).

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction where the concentrations of reactants and products remain constant over time. This happens because the forward and reverse reactions occur at the same rate, resulting in no net change in the concentrations of the substances involved. At this point, the reaction is said to be at equilibrium. It's important to note that equilibrium does not mean that the amounts of reactants and products are equal; rather, their rates of formation are balanced.

This dynamic condition can be achieved regardless of whether the reaction starts with only reactants or only products. As the reaction progresses, the concentration of reactants decreases while the concentration of products increases until equilibrium is reached. At this stage, it’s crucial to understand that the reaction is still ongoing, but the ratio of products to reactants (determined by the equilibrium constant) remains stable.

The equilibrium constant, represented as \( K_c \), helps predict the extent to which a reaction will proceed before reaching equilibrium. It is specific to a given reaction and is influenced by temperature, but not by the initial concentrations or the presence of a catalyst.

Equilibrium Concentration

Equilibrium concentration is the specific amount of reactants and products present in a reaction mixture once chemical equilibrium is achieved. In the given exercise, the concentrations of \( \mathrm{H}_2 \), \( \mathrm{I}_2 \), and \( \mathrm{HI} \) are 8, 3, and 28 \( \mathrm{mol} \cdot \mathrm{L}^{-1} \) respectively at equilibrium.

Calculating equilibrium concentrations can be a stepping stone to understanding the chemical dynamics at constant conditions. It’s essential for determining the equilibrium constant \( K_c \), as these concentrations are plugged into the equilibrium expression. This expression involves balancing the concentrations of products against those of the reactants. When these concentrations are inserted into the equilibrium expression, they allow for the calculation of \( K_c \), which indicates the position of equilibrium.

Understanding equilibrium concentrations is crucial for analyzing how external changes, such as temperature or pressure, may shift the equilibrium position. Le Chatelier’s principle predicts how changes will affect the concentrations and ultimately the system's return to equilibrium, where concentrations adjust to restore balance.

Reaction Quotient

The reaction quotient, denoted as \( Q \), is an expression that uses the current concentrations or pressures of the reacting species to predict the direction in which a reaction mixture will proceed to reach equilibrium. It is calculated in a similar way to the equilibrium constant \( K_c \), but at any given point in time, not necessarily at equilibrium.

In mathematical terms, the reaction quotient is expressed as:
\[ Q = \frac{{[\mathrm{HI}]^2}}{{[\mathrm{H}_2][\mathrm{I}_2]}} \]
Using given concentrations, if \( Q \) equals \( K_c \), the system is at equilibrium. If \( Q < K_c \), the forward reaction is favored, meaning the production of more products is necessary to reach equilibrium. Conversely, if \( Q > K_c \), the reverse reaction is favored, suggesting that the concentration of products should decrease to reach equilibrium.

This tool becomes very valuable when assessing reactions in a lab setting, where you might wonder if equilibrium has been reached or needs intervention. Understanding \( Q \) and its relationship with \( K_c \) helps chemists manipulate conditions to obtain the desired concentration of products in a reaction.