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 approximately \(32.67\), option (b).

Step 1: Understanding the reaction and given data

The chemical equilibrium reaction is: \(\mathrm{H}_{2} + \mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\). We are given the equilibrium concentrations: \([\mathrm{H}_{2}] = 8.0\ \text{mol/L}\), \([\mathrm{I}_{2}] = 3.0\ \text{mol/L}\), and \([\mathrm{HI}] = 28.0\ \text{mol/L}\). The task is to find the equilibrium constant \(K_c\).

Step 2: Writing the equilibrium constant expression

For the reaction \(\mathrm{H}_{2} + \mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\), the expression for the equilibrium constant \(K_c\) is given by:\[K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_{2}][\mathrm{I}_{2}]}\]

Step 3: Substituting the given concentrations into the expression

Replace each concentration in the \(K_c\) expression with the given equilibrium concentrations:\[K_c = \frac{(28.0)^2}{(8.0)(3.0)}\]

Step 4: Calculating the numerator and the denominator separately

First, calculate the square of the \([\mathrm{HI}]\) concentration: \[(28.0)^2 = 784\]Now calculate the product of the concentrations of \([\mathrm{H}_{2}]\) and \([\mathrm{I}_{2}]\):\[(8.0) \times (3.0) = 24\]

Step 5: Calculating the equilibrium constant

Substitute the values back into the equation to find \(K_c\):\[K_c = \frac{784}{24} = 32.6667\]

Step 6: Rounding the result

The calculated \(K_c\) value is approximately 32.67 when rounded to two decimal places.

Key Concepts

Chemical Equilibrium

In understanding chemical reactions, it is important to grasp the concept of equilibrium. Chemical equilibrium is a state in a reversible chemical reaction where the concentrations of reactants and products remain constant over time. This doesn't mean that the reactions have stopped. Instead, the forward and reverse reactions occur at the same rate, balancing each other out. This concept is crucial for reactions taking place in closed systems.
When a reaction reaches equilibrium, it implies that the system's conditions, such as temperature and pressure, are stable, and the composition of the mixture is consistent. Learning how to use equilibrium constants can predict the extent of a reaction and help in determining whether the products or reactants are favored when equilibrium is achieved.

Reaction Quotient

To predict the direction a reaction will proceed to achieve equilibrium, scientists use the reaction quotient, denoted as Q. The reaction quotient is calculated using the same expression as the equilibrium constant (K), but with the concentrations measured at any point aside from equilibrium.
Here's how it differs from equilibrium constant:

• If Q < K, the reaction will move in the forward direction to produce more products.
• If Q > K, the reaction will shift in the reverse direction, favoring the formation of reactants.
• If Q = K, the reaction is already at equilibrium and no shift is needed.

Understanding the reaction quotient allows chemists to determine how far a reaction is from equilibrium and predict which direction the reaction needs to progress for equilibrium to be achieved.

Concentration Calculations

Calculating concentrations is a fundamental aspect of chemistry, especially in assessing chemical reactions. When dealing with reactions at equilibrium, concentration calculations are key to finding the equilibrium constant (K). This constant gives insight into the reaction dynamics and the relative quantities of products and reactants at equilibrium.
Perform the calculations by considering the balanced chemical equation. For any reaction \[aA + bB \rightleftharpoons cC + dD\], the equilibrium constant expression in terms of concentration, \(K_c\), is \[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\].
Substitute the equilibrium concentrations of the components into this expression to calculate \(K_c\). Pay attention to units and dimensions; the concentrations must be in moles per liter (mol/L) to keep the constants dimensionally correct. Mastery of concentration calculations aids in developing a fundamental understanding of chemistry and predicting reaction behaviors in dynamic systems.