Question

The value of reaction quotient Q, for the cell.
\[{\text{Zn}}({\text{s}})|{\text{Z}}{{\text{n}}^{2 + }}(0.01{\text{M}})||{\text{A}}{{\text{g}}^ + }(1.25)|{\text{Ag}}({\text{s}})\]
A.\[156\]
B.\[125\]
C.\[1.25 \times {10^{ - 2}}\]
D.\[6.4 \times {10^{ - 3}}\]

Answer 1

Hint: Reaction quotient is defined as the ratio of the relative amount of products and reactants that are present in a reaction during a particular time. We need to consider the stoichiometry of the reactant and product while calculating the reaction quotient. Putting the appropriate values in the formula, the reaction quotient can be calculated.
Formula used:
 \[{\text{Reaction quotient}} = \dfrac{{{{[{\text{A}}]}^{\text{a}}}}}{{{{[{\text{B}}]}^{\text{b}}}}}\]
Where A and B is the concentration of the products and reactants and a and b are their stoichiometric coefficient.

Complete step by step answer:
Reaction quotient is defined as the ratio of the relative amount of products and reactants that are present in a reaction during a particular time. We need to consider the stoichiometry of the reactant and product while calculating the reaction quotient.
First of all we need to write the reaction for the given cell at anode and cathode.
Reaction at anode: anode is that terminal where oxidation occurs and zinc is being oxidized to zinc ion in the above cell. Oxidation is termed as loss of electron. The reaction will be:
\[{\text{Zn}} \to {\text{Z}}{{\text{n}}^{2 + }} + 2{{\text{e}}^ - }\]
Reaction at cathode: cathode is that terminal where reduction occurs and silver ion is being reduced to silver. Reduction is termed as gain of electron. The reaction will be:
\[A{g^ + }{\text{ }} + {\text{ }}{{\text{e}}^ - } \to {\text{Ag}}\]
To balance the equation we need to multiply the reduction equation with 2. Hence we will get the overall equation as:
\[{\text{Zn }} + {\text{ 2A}}{{\text{g}}^ + }{\text{ }} \to 2{\text{Ag + Z}}{{\text{n}}^{2 + }}\]
Reaction quotient will be the ratio of concentration of product and reactants raised to the power equal to the stoichiometry of each of them respectively.
\[{\text{Reaction quotient}} = \dfrac{{[{\text{Z}}{{\text{n}}^{2 + }}]}}{{{{[{\text{A}}{{\text{g}}^ + }]}^2}}}\]
Concentration is given to us, we will find the value as:
\[{\text{Reaction quotient}} = \dfrac{{0.01}}{{{{(1.25)}^2}}} = 6.4 \times {10^{ - 3}}\]

Hence, the correct option is D.

Note:
It is a common misconception that anode always has positive charge and cathode has negative charge. An electrolytic cell anode has negative charge whereas an electrochemical cell anode has positive charge. Electrodes are never classified on the basis of their charge but are classified on the basis of process happening. Always oxidation occurs on the anode and reduction on cathode.