Problem 187 - A Complete Resource Book in Chemistry for JEE Main

Question

In a cell that utilizes the reaction \(\mathrm{Zn}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g})\) Addition of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to cathode compartment, will (a) lower the \(E\) and shift equilibrium to the right (b) lower the \(E\) and shift the equilibrium to the left (c) increase the \(E\) and shift the equilibrium to the left (d) increase the \(E\) and shift the equilibrium to the right.

Step-by-Step Solution

Answer

(d) Increase the \( E \) and shift the equilibrium to the right.

Step 1: Understanding the Reaction

First, let's understand the reaction. The given reaction is \( \mathrm{Zn} + 2 \mathrm{H}^+ \rightarrow \mathrm{Zn}^{2+} + \mathrm{H}_2 \). The zinc solid metal reacts with protons from the solution to form zinc ions and hydrogen gas.

Step 2: Le Chatelier's Principle

According to Le Chatelier's Principle, the system will respond to counteract any changes made to the reaction conditions. Adding \(\mathrm{H}_2\mathrm{SO}_4\) introduces more \(\mathrm{H}^+\) ions to the system, increasing the concentration of reactants.

Step 3: Effect of Increased \( \mathrm{H}^+ \) on Equilibrium

With the increase in \(\mathrm{H}^+\) concentration due to \(\mathrm{H}_2\mathrm{SO}_4\), the equilibrium will shift to the right, favoring the forward reaction, in order to reduce the concentration of \(\mathrm{H}^+\) ions.

Step 4: Impact on Electrode Potential \( E \)

Increasing the concentration of \(\mathrm{H}^+\) ions increases the likelihood of the forward reaction, meaning more electrons are transferred, increasing the cell's electrode potential \(E\). This is predicted by the Nernst equation.

Step 5: Conclusion

Adding \( \mathrm{H}_2\mathrm{SO}_4 \) raises \( \mathrm{H}^+ \) and shifts the equilibrium right while increasing \( E \), which corresponds to option (d) increase the \( E \) and shift the equilibrium to the right.

Key Concepts

Le Chatelier's Principle

When a chemical system at equilibrium is disturbed by changes in concentration, pressure, or temperature, the system will adjust itself to counteract the disturbance and restore a new equilibrium. This is known as Le Chatelier's Principle. In the case of our electrochemical cell reaction, the addition of \( \text{H}_2\text{SO}_4 \) introduces extra \( \text{H}^+ \) ions to the solution.
This shifts the equilibrium position due to the increase in reactants' concentration.

• The system seeks to reduce the added \( \text{H}^+ \) by shifting the equilibrium towards the products - zinc ions and hydrogen gas.
• The direction the equilibrium shifts is known as the *forward reaction*, favoring the products.

By understanding this principle, one can predict how changes in environmental conditions affect chemical reactions in electrochemical cells.

Nernst Equation

The Nernst Equation plays a vital role in predicting the electrode potential of an electrochemical cell. It relates the cell potential to the standard cell potential, temperature, and reaction quotient, providing insight into how changes in concentration affect the potential. For the reaction \( \text{Zn} + 2 \text{H}^+ \rightarrow \text{Zn}^{2+} + \text{H}_2 \), the Nernst Equation is expressed as:\[E = E^0 - \frac{RT}{nF} \ln Q\]Where:

• \( E \) is the cell potential.
• \( E^0 \) is the standard cell potential.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.
• \( n \) is the number of moles of electrons transferred.
• \( F \) is Faraday's constant.
• \( Q \) is the reaction quotient.

Adding \( \text{H}_2\text{SO}_4 \) increases the concentration of \( \text{H}^+ \), thus increasing \( Q \) and directly impacting \( E \). As \( Q \) decreases with a shift in equilibrium towards products, \( E \) increases.

Reaction Equilibrium

In chemical reactions, equilibrium refers to a state where the rate of the forward reaction equals the rate of the reverse reaction. In such a state, the concentrations of reactants and products remain constant over time. For the electrochemical cell reaction \( \text{Zn} + 2 \text{H}^+ \rightarrow \text{Zn}^{2+} + \text{H}_2 \),

• Adding \( \text{H}_2\text{SO}_4 \) disturbs the equilibrium by increasing the \( \text{H}^+ \) concentration.
• This causes the system to "shift right," enhancing conversion from reactants to products and establishing a new equilibrium.

Shifts in reaction equilibrium can have significant effects on system behavior, affecting parameters like cell voltage and reaction rates. Understanding equilibrium helps in managing essential chemical processes within cells.