Question

The standard emf of the cell $ (E^{\circ}_{cell} $ and equilibrium constant $ (K_{eq}) $ of the following reaction of $ 298\, K $ $ Cd^{2+} + 4NH_{3} {\rightleftharpoons} Cd (NH_{3})^{2+}_{4} $

• A. $ E^{\circ}_{cell}=1.0V, K_{eq}=126\times10^{7} $
• B. $ E^{\circ}_{cell}=0.21 V, K_{eq}=126\times10^{7} $
• C. $ E^{\circ}_{cell}=1.0 V, K_{eq}=6.60\times10^{33} $
• D. $ E^{\circ}_{cell}=0.21 V, K_{eq}=6.60\times10^{33} $

Answer 1

The Correct Option is B

(we assume that standard emf of the cell \(E^{\circ}_{cell}\) is known) 
For the given equilibrium, 
\(Cd^{2+}+4NH_{3} {<=>} Cd(NH_{3})^{2+}_{4}\) 
At equilibrium, 
\(E^{\circ}_{cell}=0\) 
Hence, we can calculate the equilibrium constant for reaction as follows : 
\(E^{\circ}_{cell}=\frac{0.0591\,V}{n} log \,K_{c}\) 
Where, \(K_{c}\) is unknown 
\(E^{\circ}_{cell}=0.21\,V\)
\(0.21\,V=\frac{0.0591}{2}log K_{c}\)
\(log\,K_{c}=\frac{0.21\times2}{0.0591}\)
\(log\,K_{c}=\frac{0.42}{0.0591}=7.1065\)
\(K_{c}=1.27\times10^{7}\)

The largest potential difference between two electrodes of a cell, while no current is being pulled from the cell, is known as the electromotive force, or EMF. The charges in an electric circuit move, and in order for the charges in a specific electric circuit to move, we must apply an external force to that electric circuit.

A battery or any other possible difference-making mechanism can serve as the source of an external force. The electromotive force, which is applied by the external electric source and accelerates the charges, is a physical force. 

Considering the formula for electromotive force as,

ε = V + Ir

Where

• The voltage of the cell is V.
• Current across the circuit is I.
• The internal resistance of the cell is R.
• The electromotive force is ε.

Kp is the equilibrium constant determined from the partial pressure of the equation of a reaction. It's a mathematical expression to determine the relation between product and reactant pressures. Although it connects the pressures, it is a unitless number. 

Kc is the equilibrium constant for a reversible reaction, which depicts the ratio of the equilibrium concentrations of products over the concentrations of reactants, where each is raised to the power of their stoichiometric coefficients.