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. \[E={{E}^{O}}-\dfrac{0.0591}{n}\log \dfrac{[\operatorname{Products}]}{[\operatorname{Reactants}]}\]
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: \[Zn\to Z{{n}^{+2}}+2{{e}^{-}}\]
At Cathode: $P{{b}^{+2}}+2{{e}^{-}}\to Pb$
-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:
${{E}_{Cell}}={{E}^{O}}_{cell}-\dfrac{0.0591}{n}\log \dfrac{[Product]}{[Reactant]}$
\[=0.63-\dfrac{0.0591}{2}\log \dfrac{[0.1]}{[0.02]}\]
= 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
\[Zn|Zn{{(N{{O}_{3}})}_{2}}(0.1M)||Pb{{(N{{O}_{3}})}_{2}}(0.02M)|Pb\text{ }\]

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.