For spontaneity of a cell, the correct statement is (C)\(ΔG = -ve.\) The spontaneity of a cell reaction is determined by the Gibbs free energy change \((ΔG)\) of the reaction. A negative \( ΔG\) indicates that the reaction is spontaneous, meaning it can occur without the input of external energy. Therefore, for spontaneity, we require \(ΔG\) to be negative. Option A: \((ΔG = +ve, ΔE = +ve)\) is incorrect because a positive \(ΔG\) and positive \(ΔE\) indicate a non-spontaneous reaction. Option B: \((ΔG = 0, ΔE = 0)\) is incorrect because a \(ΔG\) of zero indicates that the reaction is at equilibrium, not necessarily spontaneous. Option D: \((ΔG = -ve, ΔE = 0)\) is incorrect because while a negative \(ΔG\) indicates spontaneity, the value of \(ΔE\) can be non-zero. The cell potential \((ΔE\)\()\) is related to \( ΔG\) through the equation \(ΔG = -nFΔE\), and ΔE can have a non-zero value for spontaneous reactions. Therefore, the correct statement for spontaneity of a cell is \(ΔG = -ve\), indicating a negative Gibbs free energy change.
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For a cell reaction to be spontaneous, the Gibbs free energy change (ΔG) must be negative.
The relation between Gibbs free energy and cell potential is: ΔG = –nFE
where, n = number of electrons F = Faraday constant E = cell potential (electromotive force)
If ΔG is negative, then E must be positive, indicating a spontaneous reaction.
