Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

One mole of HI was heated in a sealed tube at \(440^{\circ} \mathrm{C}\) till the equilibrium was reached. HI was found to be \(22 \%\) decomposed. The equilibrium constant for dissociation reaction, \(2 \mathrm{HI} \rightleftharpoons \mathrm{H}_{2}+\mathrm{I}_{2}\) is (a) \(1.99\) (b) \(0.282\) (c) \(0.01988\) (d) \(0.0796\)

Step-by-Step Solution

Answer

The equilibrium constant \( K_c \) is 0.01988, therefore option (c) is correct.

Step 1: Identify Initial Conditions

Initially, there is 1 mole of HI, and no H₂ or I₂ present. The reaction is \(2 \text{ HI } \rightleftharpoons \text{ H}_2 + \text{ I}_2\).

Step 2: Calculate Change in Moles

Since 22% of HI decomposes, we have: \[ \text{Change in moles of HI} = 0.22 \times 1 = 0.22 \text{ moles}\]. Thus, \[ \text{Moles of HI remaining} = 1 - 0.22 = 0.78 \].

Step 3: Determine Moles at Equilibrium

For every 2 moles of HI that decompose, 1 mole of H₂ and 1 mole of I₂ are formed. Thus, the formation of H₂ and I₂ is 0.11 moles each. Therefore, at equilibrium we have: \[ \text{HI} = 0.78 \text{ moles}, \quad \text{H}_2 = 0.11 \text{ moles}, \quad \text{I}_2 = 0.11 \text{ moles} \].

Step 4: Write Equilibrium Expression

The expression for the equilibrium constant \(K_c\) for the reaction is: \[ K_c = \frac{[\text{H}_2][\text{I}_2]}{[\text{HI}]^2} \]. Here, the brackets denote concentration, but as the reaction vessel's volume is constant, we use moles.

Step 5: Substitute Values to Find Kc

Substitute the moles at equilibrium into the equilibrium expression: \[ K_c = \frac{0.11 \times 0.11}{(0.78)^2} = \frac{0.0121}{0.6084} \approx 0.01988 \].

Step 6: Select Correct Answer

The computed value of \(K_c\) is 0.01988, which matches option (c).

Key Concepts

Chemical Equilibrium

Chemical equilibrium is reached in a chemical reaction when the rate of the forward reaction equals the rate of the backward reaction. This means the concentrations of the reactants and products remain constant over time, although they are not necessarily equal. In the context of the exercise, the equilibrium is achieved when the decomposition of hydroiodic acid (HI) balances with the formation of iodine (I₂) and hydrogen (H₂).

At equilibrium:

• The concentration of HI is stable, even as some molecules continue to dissociate into H₂ and I₂.
• The concentrations of H₂ and I₂ also become constant as they are produced in the reaction.

In practical terms, chemical equilibrium in a closed system like a sealed tube means that, over time, the macroscopic properties such as color or pressure (in gaseous systems) do not change, indicating that equilibrium has been reached.

Mole Concept

The mole concept is a fundamental principle in chemistry that allows chemists to count particles (such as atoms, molecules, or ions) by relating them to a quantity of substance. One mole is equivalent to Avogadro's number, approximately 6.022 x 10²³ particles. This concept is central to solving the given problem, where it helps determine the amount of each substance at equilibrium.

Key applications of the mole concept in this problem include:

• Determining the initial moles of HI present in the system.
• Calculating the change in moles of HI due to the decomposition (22% in this case). This change is expressed in terms of moles rather than just a percentage.
• Finding the number of moles of products (H₂ and I₂) formed at equilibrium, showing how stoichiometry relates to the mole concept in chemical reactions.

This approach ensures accurate calculations of the amounts of each species present when equilibrium is reached.

Dissociation Reaction

Dissociation reactions involve the separation of a compound into two or more simpler substances, usually when heat is applied. In the exercise, the dissociation of HI is the main focus, where each HI molecule breaks down to form H₂ and I₂:

• For each two molecules of HI that dissociate, one molecule of H₂ and one molecule of I₂ are produced.
• The percentage dissociation can help calculate how much of the original substance remains unchanged at equilibrium.
• By analyzing the moles at the start, the dissociation percentage, and the stoichiometry of the reaction, we can determine the equilibrium concentrations of all involved substances.

Understanding dissociation reactions is crucial for interpreting how compounds like HI behave when heated in a closed system, providing insights into temperatures and conditions at which such reactions occur efficiently.