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Question: A galvanic cell consists of a metallic zinc plate immersed in 0.1M \(Zn{{(N{{O}_{3}})}_{2}}\) soluti...

A galvanic cell consists of a metallic zinc plate immersed in 0.1M Zn(NO3)2Zn{{(N{{O}_{3}})}_{2}} solution and metallic plate of lead in 0.02 M Pb(NO3)2Pb{{(N{{O}_{3}})}_{2}} solution. Calculate the emf of the cell at 25∘25{}^\circ C. Write the chemical equation for electrode reactions and represent the cell. (Given EOZn+2/Zn{{E}^{O}}_{Z{{n}^{+2}}/Zn}= -0.76 volt and EOPb+2/Pb{{E}^{O}}_{P{{b}^{+2}}/Pb}= -0.13 volt.

Explanation

Solution

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=EO−0.0591nlog⁡[Products⁡][Reactants⁡]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 EO=EOCathode−EOanode{{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→Zn+2+2e−Zn\to Z{{n}^{+2}}+2{{e}^{-}}
At Cathode: Pb+2+2e−→PbP{{b}^{+2}}+2{{e}^{-}}\to Pb
-So standard emf of cell can be calculated using following formula:
EOCell=EOPb−EOZn{{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:
ECell=EOcell−0.0591nlog⁡[Product][Reactant]{{E}_{Cell}}={{E}^{O}}_{cell}-\dfrac{0.0591}{n}\log \dfrac{[Product]}{[Reactant]}
=0.63−0.05912log⁡[0.1][0.02]=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∘25{}^\circ C is 0.6093volt.
Cell representation is given as
Zn∣Zn(NO3)2(0.1M)∣∣Pb(NO3)2(0.02M)∣Pb 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.