Write the Nernst equation and emf of the following cells at 298 K:
(i) Mg(s) | Mg2+(0.001M) || Cu2+(0.0001 M) | Cu(s)
(ii) Fe(s) | Fe2+(0.001M) || H+ (1M)|H2(g)(1bar) | Pt(s)
(iii) Sn(s) | Sn2+(0.050 M) || H+ (0.020 M) | H2(g) (1 bar) | Pt(s)
(iv) Pt(s) | Br2(l) | Br- (0.010 M) || H+ (0.030 M) | H2(g) (1 bar) | Pt(s).
(i) For the given reaction, the Nernst equation can be given as:
Ecell = E⊖cell - \(\frac{0.0591}{n}\)log \(\frac{[Mg^{2+}]}{[Cu^{2+}]}\)
= {0.34 - (-2.36)} - \(\frac{0.0591}{2}\) log \(\frac{0.001}{.0001}\)
= 2.7 - \(\frac{0.0591}{2}\) log 10
= 2.7 - 0.02955
= 2.67 V (approximately)
(ii) For the given reaction, the Nernst equation can be given as:
Ecell = E⊖cell - \(\frac{0.0591}{n}\)log \(\frac{[Fe^{2+}]}{[H^+]^2}\)
= {0 - (-0.44)} - \(\frac{0.0591}{2}\) log \(\frac{0.001}{1^2}\)
= 0.44 - 0.02955(-3)
= 0.52865 V
= 0.53 V (approximately)
(iii) For the given reaction, the Nernst equation can be given as:
Ecell = E⊖cell - \(\frac{0.0591}{n}\)log \(\frac{[Sn^{2+}]}{[H^+]^2}\)
= {0 - (-0.14)} - \(\frac{0.0591}{2}\) log \(\frac{0.050}{(0.020)^2}\)
= 0.14 - 0.0295 × log 125
= 0.14 - 0.062
= 0.078 V
= 0.08 V (approximately)
(iv) For the given reaction, the Nernst equation can be given as:
Ecell = E⊖cell - \(\frac{0.0591}{n}\)log \(\frac{1}{[Br^-]^2[H^+]^2}\)
= (0-1.09) - \(\frac{0.0591}{2}\) log \(\frac{1}{(0.020)^2(0.030)^2}\)
= -1.09 - 0.02955 x log \(\frac{1}{0.00000009}\)
= -1.09 - 0.02955 x log \(\frac{1}{9 \times 10^{-8}}\)
= -1.09 - 0.02955 x log (1.11 x 107)
= -1.09 - 0.02955(0.0453 + 7)
= -1.09 - 0.208
= -1.298 V