Consider the following galvanic cell: What happens to \(\mathscr{E}\) as the concentration of \(\mathrm{Zn}^{2+}\) is increased? As the concentration of \(\mathrm{Ag}^{+}\) is increased? What happens to \(\mathscr{E}^{\circ}\) in these cases?

To write the complete cell reaction, add the oxidation and reduction half-reactions, making sure the number of electrons in each half-reaction is equal: Zn(s) + 2 Ag+(aq) -> Zn^2+(aq) + 2 Ag(s) Step 2: Write the Nernst equation

The Nernst equation helps us to quantify the relationship between the cell potential (E), standard cell potential (\( \mathscr{E}^{\circ} \)), concentration of reactants and products, temperature, and the number of electrons transferred in a redox reaction. The Nernst equation is written as: \( \mathscr{E} = \mathscr{E}^{\circ} - \dfrac{0.0592}{n} \log Q \) Where: - \( \mathscr{E} \) is the cell potential at non-standard conditions - \( \mathscr{E}^{\circ} \) is the standard cell potential - n is the number of electrons transferred in the redox reaction - Q is the reaction quotient, which represents the ratio of concentrations of products to reactants Step 3: Calculate the effect of increasing Zn^2+ concentration

We will first determine the effect of increasing the concentration of Zn^2+ ions on the cell potential (E). From the Nernst equation: \( \mathscr{E} = \mathscr{E}^{\circ} - \dfrac{0.0592}{2} \log \dfrac{[Zn^{2+}]}{[Ag^+]^2} \) As the concentration of Zn^2+ increases, the value of Q increases. This then results in a decrease in the value of E because of the negative sign in front of the second term. The standard cell potential (\( \mathscr{E}^{\circ} \)) remains unchanged as it is a constant value that does not depend on the concentration of ions. Step 4: Calculate the effect of increasing Ag+ concentration

Now we will determine the effect of increasing the concentration of Ag+ ions on the cell potential (E): \( \mathscr{E} = \mathscr{E}^{\circ} - \dfrac{0.0592}{2} \log \dfrac{[Zn^{2+}]}{[Ag^+]^2} \) As the concentration of Ag+ ions increases, the value of Q decreases. This then results in an increase in the value of E since we have a negative sign in front of the second term. The standard cell potential (\( \mathscr{E}^{\circ} \)) again remains unchanged, as it is a constant value that does not depend on the concentration of ions. Conclusions: - As the concentration of Zn^2+ ions increases, E decreases, and \( \mathscr{E}^{\circ} \) remains unchanged. - As the concentration of Ag+ ions increases, E increases, and \( \mathscr{E}^{\circ} \) remains unchanged.