For the electrochemical cell shown below Pt | H 2 p = 1   atm | H + aq . , xM | Cu 2 + aq , 1 . 0   M Cu s The potential is 0 . 49   V at 298   K . The pH of the solution is closest to [ Given, standard reduction potential, E ° for Cu 2 + / Cu is 0 . 34   V Gas constant, R is 8 . 31   J   K - 1   mol - 1 Faraday constant, F is 9 . 65 × 10 4 JV - 1   mol - 1 ]

Step-by-step solution

According to Nernst equation, E cell = E ° cell - 0 . 0591 n log P R For the given electrochemical cell Pt ∣ H 2 p = 1   atm H + aq · x   M ‖ Cu 2 + aq · 10   M / Cu s E cell = E ° cell - 0 . 0591 n log H + 2 Cu 2 + = 0 . 49 = 0 . 34 - 0 . 0591 2 log x 2 1 0 . 49 = 0 . 34 - 0 . 0591 2 × 2 logx 0 . 15 = - 0 . 0591 × logx 2 . 53 = - logx Also , - log H + = pH Here, H + = x ∴    pH = - logx ⇒ pH = 2 . 53