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Question: All the energy released from the reaction \(X\to Y\), \({{\Delta }_{r}}G{}^\circ =-193kJ.mo{{l}^{-1}...

All the energy released from the reaction X→YX\to Y, ΔrG∘=−193kJ.mol−1{{\Delta }_{r}}G{}^\circ =-193kJ.mo{{l}^{-1}} is used for oxidizing M+{{M}^{+}} as M+→M3++2e−{{M}^{+}}\to {{M}^{3+}}+2{{e}^{-}}, E∘=−0.25VE{}^\circ =-0.25V.
Under the standard conditions, the number of moles of M+{{M}^{+}} oxidized when one mole of X is converted to Y is:
[F=96500C/mol]

Explanation

Solution

Recollect the concept of electrochemistry. The relationship between change in standard Gibbs free energy and standard EMF of a cell is given by the equation, ΔG∘=−nFE∘\Delta G{}^\circ =-nFE{}^\circ . Use this equation and find out the change in standard Gibbs free energy for oxidation reaction. Then just relate the two Gibbs free energies to get the number of moles.

Complete answer:
- Let’s take a look at the data given in the question.
For reaction, X→YX\to Y, ΔrG∘=−193kJ.mol−1{{\Delta }_{r}}G{}^\circ =-193kJ.mo{{l}^{-1}} ….(1)
For reaction, M+→M3++2e−{{M}^{+}}\to {{M}^{3+}}+2{{e}^{-}}, E∘=−0.25VE{}^\circ =-0.25V….(2)
- The relationship between change in standard Gibbs free energy and standard EMF of a cell is given by the equation, ΔG∘=−nFE∘\Delta G{}^\circ =-nFE{}^\circ where, n is the number of electrons and F is Faraday.
- For the oxidation reaction, let’s calculate the change in standard Gibbs free energy. Therefore,

& \Delta G{}^\circ =-nFE{}^\circ \\\ & =-2\times 96500\times \left( -0.25 \right) \\\ & =48250J/mol \\\ & \Delta G{}^\circ =48.25kJ/mol \end{aligned}$$ \- Now we obtained a change in standard Gibbs free energy that is, $\Delta G{}^\circ =48.25kJ.mo{{l}^{-1}}$ for oxidation reaction. \- We need to find the number of moles of ${{M}^{+}}$ getting oxidized. It is given that the energy from the first reaction is used to conduct the second reaction. \- We have found out the change in free energy for a second reaction. So, now we just need to find the number of moles which can be oxidized in 193kJ/mol of energy. \- Therefore, the number of moles of ${{M}^{+}}$ getting oxidized is $\dfrac{193}{48.25}=4mol$. \- Therefore, under the standard conditions, the number of moles of ${{M}^{+}}$ oxidized when one mole of X is converted to Y is 4 moles. **Note:** Remember the relationship between change in standard Gibbs free energy and standard EMF of the cell. Also for such problems, use the idea of comparison with same parameters like in this case, energy. Carefully understand the question as it says energy from one reaction is used in the second reaction, so one needs to find out how many moles of reactant will get reacted in the supplied amount of energy.