Write Nernst equation and find out the emf of the following cell at 25 degree Celsius.

Pt,Br2(l)/Br-(0.010M)//H+(0.030M)/H2(1atm),Pt
E• Br2/2Br-=1.08V,R=8.134Jk-1mol-1,F=96500C mol-1.

The Nernst equation is an equation that relates the standard electrode potential (E°) of a redox reaction to the actual cell potential (E) at non-standard conditions. The Nernst equation is given as:

E = E° - (RT / nF) * ln(Q)

Where:
E: Cell potential at non-standard conditions (in volts)
E°: Standard electrode potential (in volts)
R: Gas constant (8.314 J K^(-1) mol^(-1))
T: Temperature (in Kelvin)
n: Number of moles of electrons transferred in the balanced redox reaction
F: Faraday's constant (96,500 C mol^(-1))
ln: Natural logarithm
Q: Reaction quotient

In the given cell, the cell reaction is:

Pt, Br2(l) | Br^-(0.010 M) || H^+(0.030 M) | H2(1 atm), Pt

The half-reactions involved are:

Br2(l) + 2e^- → 2Br^-
H^+ + e^- → H2(g)

The balanced redox equation for the cell reaction is:

Br2(l) + 2H^+ + 2e^- → 2Br^- + H2(g)

From the given data, we have:
E° (Br2/2Br^-) = 1.08 V

To find the cell potential (E) at 25 degrees Celsius, we need to calculate the reaction quotient (Q) and substitute the values into the Nernst equation.

Q = [Br^-]^2 / [H^+]^2

Since the concentrations of Br^- and H^+ are given as 0.010 M and 0.030 M respectively, we can substitute the values into the equation:

Q = (0.010 M)^2 / (0.030 M)^2
Q = 0.1111

Now, substituting the values into the Nernst equation:

E = E° - (RT / nF) * ln(Q)
E = 1.08 V - ((8.314 J K^(-1) mol^(-1)) * (298 K) / (2 * (96500 C mol^(-1)))) * ln(0.1111)

Solving the equation will give you the value of E, which represents the emf of the cell at 25 degrees Celsius.