Question

The EMF of a galvanic cell consisting of two hydrogen electrodes is \[0.17V\]. If the solution of one of the electrodes has $\left[ {{H}^{+}} \right]={{10}^{-3}}M$ . The ph at the other electrode?

Answer 1

Hint:Galvanic cell is defined as an electrochemical cell that helps in converting chemical energy into electrical energy. Galvanic cells are also known as voltaic cells. The work done by the galvanic cell is just because of the Gibbs energy of spontaneous redox reaction.

Complete step-by-step answer:Nernst equation is an equation which helps in determining the cell potential at given temperature, pressure and concentration of reactants and products.
The EMF of the cell is defined as the maximum difference between two electrodes of the cell.
The Nernst equation,
$E={{E}^{{}^\circ }}-0.059\log \dfrac{\left[ P \right]}{\left[ R \right]}$
Where, $E$ is the cell potential
${{E}^{{}^\circ }}$ is the standard cell potential
$P$ is the concentration of the product
$R$ is the concentration of the reactant
The galvanic cell consisting of two hydrogen electrodes-
${{H}_{2}}\left| {{H}^{+}}\left( {{10}^{-3}} \right) \right|\left. {{H}^{+}}\left( x \right) \right|{{H}_{2}}$
Now using Nernst equation,
$E={{E}^{{}^\circ }}-0.059\log \dfrac{\left[ {{H}^{+}} \right]}{\left[ {{10}^{-3}} \right]}$
In this question, it is given that the cell potential $\left( E \right)=0.17V$
The concentration of the reactant $\left( {{H}^{+}} \right)$ is ${{10}^{-3}}M$
The standard cell potential for hydrogen electrode $\left( {{E}^{{}^\circ }} \right)=0$
Now substituting the value in the equation we get,
$\Rightarrow 0.17=0-0.059\log \dfrac{\left[ {{H}^{+}} \right]}{{{10}^{-3}}}$
$\Rightarrow -2.88=\log \left[ {{H}^{+}} \right]-\log {{10}^{-3}}$
$\Rightarrow -2.88=\log \left[ {{H}^{+}} \right]+3$
On further solving we get,
$-\log \left[ {{H}^{+}} \right]=3+2.88$
As we know that,
$pH=-\log \left[ {{H}^{+}} \right]$
Therefore on substituting we get,
$\Rightarrow pH=3+2.88$
$\Rightarrow pH=5.88$
The ph of the other electrode is $5.88$

Note:The ph is used to determine the acidity and the basicity of the aqueous solution. It is defined as the logarithm that inversely indicates the concentration of hydrogen ions in the aqueous solution. If the value of ph is less than seven then it is acidic and if the value of ph is more than seven, it is basic.
The standard cell potential for hydrogen electrodes in galvanic cell is always zero.