Consider an electrochemical cell : `A_((s))|A^(n+)((aq,2M)||B^(2n+) ((aq,1M)|B_(s)` The value of `DeltaH^(@)` for the cell reaction is twice that of `DeltaG^(@)` at 300K . If the emf of the cell is zero, the `DeltaS^(@)` (in JK^(-1mol^(-1))` of the cell reaction per mole of B formed at 300 K is _________.
(Given ln (2)= 0.7, R (universal gas constant ) = `8.3JK^(-1)mol^(-1)`. H, S and G are enthalpy , entropy and gibbs energy, respectively).

Explanation

To solve the problem step by step, we will analyze the given electrochemical cell and apply the relevant thermodynamic equations.

### Step 1: Understand the cell reaction
The electrochemical cell is represented as:
\[ A_{(s)} | A^{n+}_{(aq, 2M)} || B^{2n+}_{(aq, 1M)} | B_{(s)} \]

The cell reaction can be written as:
\[ 2A + B^{2n+} \rightarrow 2A^{n+} + B \]
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