In an electrochemical reaction of lead, at standard temperature, if E ( Pb 2 + / Pb ) ? = m Volt and E ( Pb 4 + / Pb ) ? = n Volt , then the value of E ( Pb 2 + / Pb 4 + ) ? is given by m - x n . The value of x is ______. (Nearest integer)

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Solution

Q.
In an electrochemical reaction of lead, at standard temperature, if $E_{({Pb}^{2 +} / Pb)}^{\circ} = m Volt$ and $E_{({Pb}^{4 +} / Pb)}^{\circ} = n Volt,$ then the value of $E_{({Pb}^{2 +} + {Pb}^{4 +})}^{\circ}$ is given by $m - x n$ .

The value of $x$ is ______. (Nearest integer) [2023]

Ans.
(2)

${Pb}^{2 +} + 2 e^{-} \to Pb$ $Δ G_{1}^{0} = - 2 F E_{1}^{0}$

${Pb}^{4 +} + 4 e^{-} \to Pb$ $Δ G_{2}^{0} = - 4 F E_{2}^{0}$

${Pb}^{2 +} \to {Pb}^{4 +} + 2 e^{-}$ $Δ G_{3}^{0} = - 2 F E_{3}^{0}$

$Δ G_{3}^{0} = Δ G_{1}^{0} - Δ G_{2}^{0}$

$- 2 F E_{3}^{0} = - 2 F E_{1}^{0} + 4 F E_{2}^{0}$

$E_{3}^{0} = E_{1}^{0} = - 2 E_{2}^{0}$

$∵$ $E_{3}^{0} = m - x n$

$∵$ $x = 2$

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