An electrochemical cell consists of the following two redox couples, Mx+(aq)/M(s) [E red = +0.15 V] and Fe3+(aq)/Fe(s) [E red = -0.036 V]. The cell EMF ( Ecell) is recorded to be 0.2057 V. If the reaction quotient of the electrochemical reaction is found to be 10-2, then the value of x is . (Nearest integer) [Given : M is a p-block metal and 2.303RTF = 0.059 V]
Answer
2
Solution
Higher reduction potential ⇒ Mx+/M is the cathode; Fe is oxidised at the anode.
E cell = 0.15 − (−0.036) = 0.186 V
Nernst equation: Ecell = E cell - 0.059n Q
⇒ 0.2057 = 0.186 − 0.059n log 10-2
⇒ 0.2057 = 0.186 + 0.118n
⇒ 0.118n = 0.0197 ⇒ n = 6
Each Fe loses 3 electrons and each Mx+ gains x electrons ⇒ n = LCM (3, x) = 6
⇒ x = 2 (x = 1 or 3 gives n = 3; x = 6 is not possible for a p-block metal ion)
Cell reaction: 3M2+(aq) + 2Fe(s) 3M(s) + 2Fe3+(aq) (n = 6)
Answer: 2