Question

A galvanic cell consists of a metallic zinc plate immersed in 0.1M $Zn{(N{O}_3)}_2$ solution and metallic plate of lead in 0.02 M $Pb{(N{O}_3)}_2$ solution. Calculate the emf of the cell at $25{}^{\circ }$C. Write the chemical equation for electrode reactions and represent the cell. (Given $${E^O}_{Z{n}^{+2}/Zn}$$= -0.76 volt and ${E^O}_{P{b}^{+2}/Pb}$= -0.13 volt.

Answer 1

Hint: Zinc undergoes oxidation and Lead undergoes reduction. Two electrons are involved in redox reaction and the emf of the cell can be calculated using Nernst Equation having the following formula. $$E=E^O-{\displaystyle \frac{0.0591}{n}}\log {\displaystyle \frac{[\mathrm{Products}]}{[\mathrm{Reactants}]}}$$
Standard emf of the cell can be calculated using the following formula $E^O={E^O}_{Cathode}-{E^O}_{anode}$

Complete step by step solution:
-Zinc has a tendency to undergo oxidation as it has high standard oxidation potential compared to lead
-Lead has a tendency to undergo reduction as it has a high reduction potential compared to zinc.
-Zinc has standard reduction potential as -0.76 volt and lead has standard reduction potentials as -0.13volt.
-As values suggest, Lead has a higher reduction potential than zinc.
-So at anode zinc undergoes oxidation by losing two electrons and lead undergoes reduction by accepting two electrons.
-Reactions at anode and cathode can be written as:
At Anode: $$Zn\to Z{n}^{+2}+2e^{-}$$
At Cathode: $P{b}^{+2}+2e^{-}\to Pb$
-So standard emf of cell can be calculated using following formula:
$${E^O}_{Cell}={E^O}_{Pb}-{E^O}_{Zn}$$
= -0.13- (-0.76)
=-0.13 + 0.76
= +0.63 volt
-The emf of cell can be calculated using Nernst equation:
$E_{Cell}={E^O}_{cell}-{\displaystyle \frac{0.0591}{n}}\log {\displaystyle \frac{[Product]}{[Reactant]}}$
$$=0.63-{\displaystyle \frac{0.0591}{2}}\log {\displaystyle \frac{[0.1]}{[0.02]}}$$
= 0.63-0.02955 (0.6990)
=0.63-0.0206
=0.6093Volt

The emf of the cell at $25{}^{\circ }$C is 0.6093volt.
Cell representation is given as
$$Zn|Zn{(N{O}_3)}_2(0.1M)||Pb{(N{O}_3)}_2(0.02M)|Pb$$

Note: If Standard Emf of the cell has a value greater than zero, the cell will have a spontaneous reaction and if the value is less than zero, the cell will have a nonspontaneous reaction. Metal with high standard reduction potential undergoes reduction and Metal with low standard reduction potential undergoes oxidation.