A concentration cell consisting of two hydrogen electrodes (PH2 = 1 atm), where the cathode is a standard hydrogen electrode and the anode solution has an unknown pH, has a cell voltage of 0.182 V. What is the pH in the unknown solution? Assume the temperature of the solutions is 298 K. pH =

The pH of the unknown solution is 3.07.

Explanation:

1. Find the cell potential as a function of pH

From the Nernst Equation:

Ecell=E∘cell-RT / zF * lnQ

where

R denotes the Universal Gas Constant

T denotes the temperature

z denotes the moles of electrons transferred per mole of hydrogen

F denotes the Faraday constant

Q denotes the reaction quotient

Substitute the values,

E∘cell=0 lnQ=2.303logQ

E0cell=-2.30/RT / zF * log Q

Solving the equation,

2. Find the Q value

Q=[H+]2prod pH₂, product / [H+]2reactpH₂, reactant

Q=[H+]^2*1/1*1=[H+]2

Taking the log

logQ = log[H+]^2=2log[H+]=-2pH

From the formula,

Ecell=-2.303RT / zF * logQ

E cell = 2.303 * 8.314 CK mol (inverse) * 298.15

K * 2pH / 2*96 485 C⋅mol

(inverse)

E cell = 0.0592 V * pH

3. Finding the pH value

E cell = 0.0592 V * pH

pH = E cell / 0.0592 V = 0.182V / 0.0592V

pH=3.07

The pH of the unknown solution is 3.07.