An electrochemical cell, consist of the following two redox couples, M^ x+ (aq)/M(s)[E_ red ^ =+0.15 V ] and Fe³⁺(aq)/Fe(s)[E_ red ^ =-0.036 V ] . The cell EMF (E_ cell ) 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 2.303RT F =0.059 V]

Step-by-step solution

Given standard reduction potentials: E^ _ M^ x+ /M = +0.15 V E^ _ Fe³⁺/Fe = -0.036 V Since E^ _ M^ x+ /M > E^ _ Fe³⁺/Fe , reduction occurs at the M^ x+ /M electrode (cathode) and oxidation occurs at the Fe³⁺/Fe electrode (anode). Cathode reaction: (M^ x+ + x e⁻ M) 3 Anode reaction: (Fe Fe³⁺ + 3 e⁻) x Overall balanced cell reaction: 3 M^ x+ + x Fe 3 M + x Fe³⁺ The number of electrons transferred in the balanced reaction is n = 3x . Standard cell potential E^ _ cell is: E^ _ cell = E^ _ cathode - E^ _ anode E^ _ cell