(a) Will pH value of water be same at temperature `25^(@)C` and `4^(@)C`? Justify in not more than 2 or 3 sentences.
(b) Two student use same stock solution of `ZnSO_(4)` and a solution of CuSO4. The emf of one cell is 0.03 V higher than the other. The concentration of `CuSO_(4)` in the cell with higher emf value is 0.5 M. Find out the concentration of `CuSO_(4)` in the other cell. Given : 2.303RT/F = 0.06V.

Explanation

(a) `pH=-log[H^(+)]`
In pure water, `[H^(+)]`depends on value of `K_w` which is
`K_w=[H^(+)] [OH^(-)]` Q `K_w` is a function of temperature, `[H^(+)]`will change with temperature.
(b) Let the emf of first cell be X volt.
`implies` emf of `2^(nd)` cell `=(X+0.03)` Volt
`[Cu^(2+)]` in `2^(nd)` cell `=0.50 m`
`[Cu^(2+)]` in` 1^(st)` cell=?
`E_1=E_1^(@)-(2.303RT)/(2F)log`. `([Zn^(2+)])/([Cu^(2+)])` ....(i)
`E_2=E_1^(@)-(2.303RT)/(2F)log. ([Zn^(2+)])/([Cu^(2+)]_2)` ....(ii)
`imlplies` Subtract (i) form (ii) `E_2=E_1^(@)-(2.303RT)/(2F)log. [[[Cu^(2+)]_2)/([Cu^(2+)]_1]]`
`implies 0.03=0.03 log. 0.50/([Cu^(2+)]_1 ) implies 0.50/([Cu^(2+)]_1 )=10implies [Cu^(2+)]_1=0.05 M`