What will be the emf of the given cell?

\(Pt|H_2(P_1)|H^+(aq)|H_2(P_2)|Pt\)

\(\frac{RT}{2F}ln\frac{P_1}{P_2}\)

Even under the non-standard conditions, Nernst equation can be used to determine cell potentials of the electrochemical cells. The Nernst equation is generally employed in order to calculate the cell potentials of an electrochemical cell at a given temperature, reactant concentration and pressure. The Nernst equation is written below:

\[E = E^o - \frac{RT}{zF}lnQ\]

Where, E is reduction potential, E^o is standard potential, R is universal gas constant, T is temperature (in Kelvin), z is ion charge (i.e. moles of electrons), F is Faraday constant and Q is reaction quotient

In the present case, the redox chemical equations can be written as follows:

\[2H^+ 2e^- \rightarrow H_2(P_2)\]

\[H_2(P_1) \rightarrow 2H^+ + 2e^-\]

(From here, we get to know that z = 2)

Thus, the overall reaction can be written as:

\[H_2(P_1) \rightarrow H_2(P_2)\]

As a result, Nernst equation can be written as:

\[E = E^o - \frac{RT}{zF}ln\frac{P_2}{P_1}\]

\[E = 0 - \frac{RT}{zF}ln\frac{P_2}{P_1}\]

\[E = - \frac{RT}{zF}ln\frac{P_2}{P_1}\] \((Since, E^o_{H^+|H_2} = 0)\)

\[E = \frac{RT}{zF}ln\frac{P_1}{P_2}\]

Since z = 2, the final Nernst equation is

\[E = \frac{RT}{zF}ln\frac{P_1}{P_2}\]