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166. Zn | Zn²⁺ (α = 0.1 M) || Fe²⁺ (α = 0.01 M) | Fe. The emf of the above cell is 0.2905 V. What is the equilibrium constant for the cell reaction?

For cell
$Zn vertical line Zn to the power of 2 plus end exponent left parenthesis straight alpha space equals space 0.1 space straight M right parenthesis space vertical line vertical line space Fe to the power of 2 plus end exponent space left parenthesis straight alpha space equals space 0.01 space straight M right parenthesis space vertical line space Fe$
The cell reaction
$left parenthesis straight i right parenthesis space Zn left parenthesis straight s right parenthesis space rightwards arrow space Zn to the power of 2 plus end exponent left parenthesis aq right parenthesis space plus space 2 straight e left parenthesis ii right parenthesis space Fe to the power of 2 plus end exponent left parenthesis aq right parenthesis space plus space 2 straight e space rightwards arrow space Fe left parenthesis straight s right parenthesis$

On applying Nernst equation
   $straight E subscript cell space equals space straight E degree subscript cell space minus space fraction numerator 0.0591 over denominator straight n end fraction log space 10 fraction numerator open square brackets Zn to the power of 2 plus end exponent close square brackets over denominator open square brackets Fe to the power of 2 plus end exponent close square brackets end fraction 0.2905 space equals space straight E degree subscript cell minus fraction numerator 0.0591 over denominator 2 end fraction log subscript 10 fraction numerator 0.1 over denominator 0.01 end fraction$

or $0.2905 space equals space straight E degree subscript cell minus 0.0295 cross times log subscript 10 10$
or $0.2905 space space equals space straight E degree subscript cell space minus space 0.0295 space cross times space 1$
or $straight E degree subscript cell space equals space 0.2905 space plus space 0.0295 space equals space 0.32 space straight V$
At equilibrium $left parenthesis straight E subscript cell space equals space 0 right parenthesis$
   $straight E subscript cell space equals space straight E degree subscript cell space minus space fraction numerator 0.0591 over denominator straight n end fraction log subscript 10 straight K subscript straight c$
∴    $0 space equals space straight E degree subscript cell space minus space fraction numerator 0.0591 over denominator straight n end fraction log subscript 10 space straight K subscript straight c$
or $straight E degree subscript cell space equals space fraction numerator 0.0591 over denominator straight n end fraction log subscript 10 space straight K subscript straight c$
or $0.32 space equals space fraction numerator 0.0591 over denominator straight n end fraction space log subscript 10 space straight K subscript straight c$
or    $straight K subscript straight c space equals space 10 to the power of 0.32 divided by 0.0295 end exponent.$

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167. When a certain conductivity cell was filled with 0.1 M KCl, it has a resistance of 85 Q at 25°C. When the same cell was filled with an aqueous solution of 0.052 M unknown electrolyte, the resistance was 96 Ω. Calculate the molar conductivity of the unknown electrolyte at this concentration. (Specific conductivity of 0.1 M KCl = 1.29 x 10^–2 ohm^–1cm^–1).

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168. In a fuel cell, H₂ and O₂ react to produce electricity. In the process H₂ gas is oxidised at the anode and O₂ at cathode. If 67.2 litre of H₂ at STP reacts in 15 minutes, what is the average current produced? If the entire current is used for electro-deposition of Cu from Cu²⁺, how many grams of copper are deposited?

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169.

The following electrochemical cell has been set up
Pt(1) | Fe³⁺, Fe²⁺ (a = 1) || Ce⁴⁺, Ce³⁺ (a = 1) | Pt (2)
E°_(Fe²⁺) = 0.77 V, and E°_{(Ce⁴⁺,Ce³⁺)} = 1.61 V
If an ammeter is connected between the two platinum electrodes, predict the direction of flow of current. Will the current increase or decrease with time?

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Short Answer Type

170. How many grams of silver could be placed out on a shild by electrolysis of a solution containing Λ° ions for a period of 4 hours by a current strength of 8.5 amperes? [F = 96,500 C mol^–1, Molar mass of Ag = 107.8 g]

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