Problem 58 - Chemistry: The Central Science

Question

(a) A voltaic cell is constructed with all reactants and products in their standard states. Will this condition hold as the cell operates? Explain. (b) Can the Nernst equation be used at temperatures other than room temperature? Explain. (c) What happens to the emf of a cell if the concentrations of the products are increased?

Step-by-Step Solution

Answer

(a) No, the standard condition will not hold as the cell operates, as the concentrations of reactants and products change during operation. (b) Yes, the Nernst equation can be used at temperatures other than room temperature, provided the temperature is in Kelvin. (c) When the concentrations of the products are increased, the emf of the cell decreases, as per the Nernst equation.

Step 1: a) Standard states while operating

Once a voltaic cell starts operating, the concentrations of the reactants and products change as the chemical reactions proceed. In the beginning, reactants and products were in their standard states, but as the cell operates, their concentrations change and deviate from the standard states. Therefore, the standard condition cannot hold as the cell operates.

Step 2: b) Nernst equation at different temperatures

The Nernst equation is given by: \[E = E_0 - \frac{RT}{nF} \ln Q \] Here, E is the cell's emf, E₀ is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the redox reaction, F is the Faraday constant, and Q is the reaction quotient. Notice that the Nernst equation has a term 'T,' which represents the temperature. The equation is temperature-dependent, and it can be used at temperatures other than room temperature, as long as the temperature is in Kelvin.

Step 3: c) Effect of increasing product concentrations on emf

When the concentrations of the products in a voltaic cell are increased, the reaction quotient, Q, increases. According to the Nernst equation: \[E = E_0 - \frac{RT}{nF} \ln Q \] As Q increases, the value of the logarithmic term (\(\ln Q\)) increases, and since it is multiplied by a negative coefficient, the difference between E₀ and E increases. Consequently, the emf (E) of the cell decreases. Thus, when the concentrations of the products are increased, the emf of the cell decreases.