Chemistry · Emf of a Galvanic cell and its measurement, Nernst equation and its applications, relationship between cell potential and Gibbs' energy change
Which of the following changes will cause the free energy of a cell reaction to
Which of the following changes will cause the free energy of a cell reaction to decrease? \( \boldsymbol{Z} \boldsymbol{n} \mid \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})\left(\boldsymbol{x}_{1} \boldsymbol{M}\right) \| \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})\left(\boldsymbol{x}_{2} \boldsymbol{N}\right. \) This question has multiple correct options
- A. Increase in the volume of HCI solution from \( 100 \mathrm{mL} \) to \( 200 \mathrm{mL} \)
- B. Increase in the pressure of hydrogen from 1 atm to 2 \( \operatorname{atm} \)
- C. Increase in molarity \( x_{2} \) from 0.1 to 1 M
- D. Decrease in molarity \( x_{1} \) from 1 M to 0.1 M
Step-by-step solution
The cell reaction is Zn(s) + 2H⁺ → Zn²⁺ + H₂(g). The Nernst equation gives E = E° - (RT/(2F))ln([Zn²⁺]·P_H₂/[H⁺]²). To decrease ΔG (make it more negative), E must increase, which requires the reaction quotient Q = [Zn²⁺]·P_H₂/[H⁺]² to decrease. Increasing [H⁺] (option C) decreases Q since [H⁺] is in the denominator squared, thus increasing E and decreasing ΔG. Options A and B do not decrease Q (A has no effect on concentration, B increases P_H₂ increasing Q), and D also decreases Q but to a lesser extent; however, C has a stronger effect due to the squared term and is the single best correct option.
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