Problem 111 - A Complete Resource Book in Chemistry for JEE Main

Question

An equilibrium mixture for the reaction, \(2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{S}_{2}(\mathrm{~g})\) had 1 mole of \(\mathrm{H}_{2} \mathrm{~S}, 0.2\) mole of \(\mathrm{H}_{2}\) and \(0.8\) mole of \(\mathrm{S}_{2}\) in a 2 litre flask. The value of \(K\) in \(\operatorname{mol} L^{-1}\) is (a) \(0.08\) (b) \(0.016\) (c) \(0.004\) (d) \(0.160\)

Step-by-Step Solution

Answer

The value of \( K \) is 0.016.

Step 1: Understand the Equilibrium Expression

For the given chemical equation \( 2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) \rightleftarrows 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{S}_{2}(\mathrm{~g}) \), the equilibrium constant expression \( K \) is given by \[ K = \frac{[\mathrm{H}_2]^2 [\mathrm{S}_2]}{[\mathrm{H}_2\mathrm{S}]^2} \]where the square brackets \([ ]\) denote the molarity of the species.

Step 2: Calculate Molar Concentrations

The molar concentrations are calculated using the formula \[ \text{Concentration (mol/L)} = \frac{\text{Number of moles}}{\text{Volume of the flask (L)}} \].So, - \([\mathrm{H}_2\mathrm{S}] = \frac{1 \text{ mole}}{2 \text{ L}} = 0.5 \text{ mol/L} \)- \([\mathrm{H}_2] = \frac{0.2 \text{ mole}}{2 \text{ L}} = 0.1 \text{ mol/L} \)- \([\mathrm{S}_2] = \frac{0.8 \text{ mole}}{2 \text{ L}} = 0.4 \text{ mol/L} \)

Step 3: Substitute Molarities in Equilibrium Expression

Substitute the calculated molarities into the equilibrium expression from Step 1:\[K = \frac{(0.1)^2(0.4)}{(0.5)^2} = \frac{0.01 \times 0.4}{0.25} = \frac{0.004}{0.25}\]

Step 4: Calculate the Equilibrium Constant

Now, calculate the value of \( K \):\[ K = \frac{0.004}{0.25} = 0.016 \]

Key Concepts

Chemical Equilibrium

Chemical equilibrium in a reaction occurs when the rates of the forward and reverse reactions are equal. At this point, the concentrations of all reactants and products remain constant over time. This state does not mean that the reactants and products are present in equal amounts, but rather that their amounts do not change even though both reactions continue to occur.
In chemical equilibrium, the equilibrium constant (K) is a crucial parameter. It is calculated using the concentrations of the products and reactants raised to the power of their coefficients in the balanced equation. This gives us a ratio that tells us about the position of equilibrium:

• If K is much greater than 1, the reaction has a higher concentration of products than reactants at equilibrium.
• If K is much less than 1, the reaction has a higher concentration of reactants than products at equilibrium.
• If K is around 1, the reaction has similar amounts of reactants and products.

Understanding chemical equilibrium is essential for predicting how a system will respond to certain changes according to Le Chatelier's Principle. This principle suggests that a system at equilibrium will shift to counteract any imposed change, striving to reach a new equilibrium state.

Molarity Calculation

Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of solute per liter of solution. It is a vital concept in chemistry, helping us understand the quantitative aspects of chemical reactions and solutions.
To calculate molarity, you use the formula:\[\text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}}\]For example, if you have 1 mole of \(\mathrm{H}_2\mathrm{S}\) dissolved in a 2-liter flask, the molarity will be:

• \([H_2S] = \frac{1 \, \text{mol}}{2 \, \text{L}} = 0.5 \, \text{mol/L}\)

This calculation is repeated for each species in the reaction to find their molarities, which are then plugged into the equilibrium expression to find the equilibrium constant.
Understanding how to calculate molarity is important as it allows you to determine concentrations needed for reactions and helps in predicting how a system changes when the concentration of a reactant or product is altered.

Reaction Quotient

The reaction quotient, denoted as \(Q\), is a value that is used to determine the direction in which a reaction mixture is likely to proceed to reach equilibrium. It is calculated using the same expression as the equilibrium constant (K), but with the current concentrations of the reactants and products at any point in time, not just at equilibrium.
Here's how the reaction quotient works:

• If \(Q < K\), the reaction will proceed in the forward direction to form more products and reach equilibrium.
• If \(Q > K\), the reaction will proceed in the reverse direction to form more reactants and reach equilibrium.
• If \(Q = K\), the reaction is already at equilibrium.

The concept of the reaction quotient is essential when analyzing how a reaction shifts when concentrations are changed. It provides a snapshot of a reaction in progress and helps predict how the equilibrium will be affected by changes in the system, making it a fundamental tool in the study of dynamic chemical systems.