Problem 54 - 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 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) \(38.88\)

Step-by-Step Solution

Answer

The equilibrium constant is 32.66, option (b).

Step 1: Write the Equilibrium Constant Expression

For the reaction \(\text{H}_{2} + \text{I}_{2} \rightleftharpoons 2\text{HI}\), the equilibrium constant \(K_c\) expression is given by:\[ K_c = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \] where \([\text{HI}], [\text{H}_2], [\text{I}_2]\) are the equilibrium concentrations of HI, H2, and I2, respectively.

Step 2: Substitute Known Values

Substitute the given equilibrium concentrations: \([\text{HI}] = 28.0\, \text{mol/L}, [\text{H}_2] = 8.0\, \text{mol/L}, [\text{I}_2] = 3.0\, \text{mol/L}\) into the equilibrium constant expression:\[ K_c = \frac{(28.0)^2}{8.0 \times 3.0} \]

Step 3: Calculate the Equilibrium Constant

Compute the calculation:\[ K_c = \frac{784}{24} \]Calculate this division to find the equilibrium constant.

Step 4: Solve the Calculation

Carry out the division:\[ K_c = 32.66 \] Thus, the equilibrium constant \(K_c\) for the given reaction is \(32.66\).

Key Concepts

Chemical Equilibrium

Chemical equilibrium represents a state in a chemical reaction where the concentrations of reactants and products remain constant over time. It occurs when the forward and reverse reactions proceed at the same rate, creating a balance between the two directions. This does not mean the reactants and products are equal in concentration, but rather their rates are equivalent.

At this point, observable properties, such as concentration and pressure, do not change. This state of balance is dynamic, implying that the reactions continue to occur, but there is no net change in the system's composition. Understanding equilibrium is crucial for predicting how a system responds to changes, like a shift in temperature or pressure, known as Le Chatelier's Principle.

• Balance in rates, not concentrations
• Dynamic state where reactions continue
• Influenced by external changes (temperature, pressure)

Equilibrium Expression

The equilibrium expression, also known as the equilibrium constant expression, is a formula that relates the concentrations of products and reactants in a chemical equilibrium. For a general reaction \[ aA + bB \rightleftharpoons cC + dD \] the equilibrium expression is written as:\[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] where - \(K_c\) is the equilibrium constant,- \([A]\), \([B]\), \([C]\), and \([D]\) represent the molar concentrations,- \(a, b, c, \) and \(d\) are the stoichiometric coefficients from the balanced equation.

This expression allows chemists to calculate the ratio of concentrations of products to reactants at equilibrium. Understanding this concept helps in determining the extent of a reaction and predicting whether a system is more product or reactant-favored.

• Derived from balanced chemical equation
• Indicates ratio of product to reactant concentrations
• Gives insight into reaction favorability

Reaction Quotient

The reaction quotient, \(Q_c\), is a pivotal concept that helps predict the direction a reaction will take to reach equilibrium. At any point in time during a reaction, the reaction quotient is calculated using the same expression as the equilibrium constant:\[ Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] If \(Q_c\) is compared to \(K_c\):

• If \(Q_c = K_c\), the system is at equilibrium.
• If \(Q_c < K_c\), the forward reaction will proceed, forming more products until equilibrium is achieved.
• If \(Q_c > K_c\), the reverse reaction will proceed, converting products back into reactants to reach equilibrium.

This tool is valuable for predicting how a system will shift in response to initial concentrations and determining the outcome of reaction progress.

Homogeneous Equilibrium

Homogeneous equilibrium involves reactions where all reactants and products are in the same phase—typically gases or solutions. Due to their uniform phase, the concentration of each component can be measured directly and used in equilibrium expressions.

In the case of the reaction \( \text{H}_2 + \text{I}_2 \rightleftharpoons 2\text{HI} \), all reactants and products are in the gas phase, making this a classic example of homogeneous equilibrium. The ease of measuring concentrations directly aids in calculating equilibrium constants. Importantly, since all substances are in the same phase, changes like volume or pressure equally impact the entire system, emphasizing the influence of physical changes on equilibrium.

• All components in the same phase
• Concentration measurements straightforward
• System uniformity simplifies reaction analysis