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Gibb's Energy and Nernst Equation

Consider the ...

Question

Consider the following equations for a cell reaction :
$A + B \to C + D; E^{o} = x v o l t, Δ G = Δ G_{1}$
$2 A + 2 B \to 2 C + 2 D; E^{o} = x v o l t, Δ G = Δ G_{2}$

A

x = y, Δ G_{1} = Δ G_{2}

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B

x > y, Δ G_{1} > Δ G_{2}

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C

x = y, Δ G_{2} = 2 Δ G_{1}

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D

x < y, Δ G_{2} = 2 Δ G_{1}

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Solution

The correct option is B $x = y, Δ G_{2} = 2 Δ G_{1}$
$x = y, Δ G_{2} = 2 Δ G_{1}$ because $Δ G$ is an expensive property and eletrode potential is an intensive property i.e, electrote potential doesnt denpends upon the coefficient of the reactant and product in the equation of reaction
$∵ Δ G = - n F E_{c e l l}$ where $n = n o$ , of electrons used in the reaction which depends upon the coefficient of the reactant

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