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Question: If \( E_{cell}^0 \) for the reaction \( 2{H_2}O \to {H_3}{O^ + } + O{H^ - } \) at \( {25^0} \) is \(...

If Ecell0E_{cell}^0 for the reaction 2H2O→H3O++OH−2{H_2}O \to {H_3}{O^ + } + O{H^ - } at 250{25^0} is −0.8277V- 0.8277{\text{V}} . The equilibrium constant for the reaction is
(A) 10−14{10^{ - 14}}
(B) 10−23{10^{ - 23}}
(C) 10−7{10^{ - 7}}
(D) 10−21{10^{ - 21}}

Explanation

Solution

We need to find the equilibrium constant of the reaction KK . We can use the Nernst equation to solve this question. We shall find the n-factor, i.e. the number of electrons transferred and substitute the values in the formula.

Formula used: log⁡K=Ecell0×n0.0591\log K = \dfrac{{E_{cell}^0 \times n}}{{0.0591}}
Here KK is the equilibrium constant.
nn is the n- factor.

Complete step by step answer
We already know the given equation.
2H2O→H3O++OH−2{H_2}O \to {H_3}{O^ + } + O{H^ - }
Here, the n-factor of the equation is 1.
Applying the formula,
log⁡K=Ecell0×n0.0591\log K = \dfrac{{E_{cell}^0 \times n}}{{0.0591}}
log⁡K=−0.8277×10.0591=−14\log K = \dfrac{{ - 0.8277 \times 1}}{{0.0591}} = - 14
On further equating,
K=10−14K = {10^{ - 14}}
Thus, the correct option is A.

Additional Information
In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and activities of the chemical species undergoing reduction and oxidation.
The Nernst equation is an important relation which is used to determine reaction equilibrium constants and concentration potentials as well as to calculate the minimum energy required in electrodialysis
The voltage or electric potential difference across the terminals of a cell when no current is drawn from it. The electromotive force (emf) is the sum of the electric potential differences produced by a separation of charges that can occur at each phase boundary in the cell.

Note
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. The equilibrium constant of a chemical reaction (usually denoted by the symbol KK ) provides insight into the relationship between the products and reactants when a chemical reaction reaches equilibrium. For example, the equilibrium constant of concentration of a chemical reaction at equilibrium can be defined as the ratio of the concentration of products to the concentration of the reactants, each raised to their respective stoichiometric coefficients.