Question

Question:Consider the standard galvanic cell based on the following

half-reactions

$$\begin{gathered} {\mathbf{Cu}}^{\mathbf{+}\mathbf{2}}\mathbf{+}\mathbf{2}{\mathbf{e}}^{\mathbf{-}}\stackrel{}{\mathbf{\to }}\mathbf{Cu} \\ {\mathbf{Ag}}^{\mathbf{+}}\mathbf{+}{\mathbf{e}}^{\mathbf{-}}\stackrel{}{\mathbf{\to }}\mathbf{Ag} \end{gathered}$$

The electrodes in this cell are Ag(s) and Cu(s). Does thecell potential increase, decrease or remain the samewhen the following changes occur to the standard cell?

a. CuSO₄(s) is added to the copper half-cell compartment(assume no volume change).

b. NH₃(aq) is added to the copper half-cell compartment.[Hint:Cu²⁺ reacts with NH₃ to form $\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4(\mathrm{aq})\right]$

c. NaCl(s) is added to the silver half-cell compartment.[Hint:Ag⁺ reacts with Cl₂ to form AgCl(s).]

d. Water is added to both half-cell compartments untilthe volume of solution is doubled.

e. The silver electrode is replaced with a platinumelectrode.

${\mathbf{Pt}}^{\mathbf{2}\mathbf{+}}\mathbf{+}\mathbf{2}{\mathbf{e}}^{\mathbf{-}}\stackrel{}{\mathbf{\to }}\mathbf{}\mathbf{Pt}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{E}}^{\mathbf{\circ }}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{19}\mathbf{}\mathbf{V}$

Short answer

1. E _cell= decreases
2. E _cell= increases
3. E _cell= decreases
4. E _cell= decreases
5. E _cell= no change

Step-by-step solution

Analyzing the given data

The equation is
$Cu\left(s\right)+2A{g}^{+}\left(aq\right)\stackrel{}{\to }Ag\left(s\right)+C{u}^{+2}\left(aq\right)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{E}^{\circ }=0.46\mathrm{V}$

The two half equations are;

$$\begin{gathered} \mathrm{Cu}\stackrel{}{\to }{\mathrm{Cu}}^{+2}+2{\mathrm{e}}^{-}{\mathrm{E}}^{\circ }=-0.34\mathrm{V} \\ {\mathrm{Ag}}^{+}+{\mathrm{e}}^{-}\stackrel{}{\to }\mathrm{Ag}{\mathrm{E}}^{\circ }=0.80\mathrm{V} \end{gathered}$$

$$\begin{gathered} E_{cell}=E_{cell}^{\circ }-\frac{0.0591}{n}\log Q \\ Q=\frac{\left[C{u}^{+2}\right]}{{\left[A{g}^{+}\right]}^2} \end{gathered}$$

The relation is to be used to determine the change in cell potential.

determining whether the cell potential increases, decreases, or remains the same in case (a)

When${\mathrm{CuSO}}_4$ is added to the copper half-cell compartment, the concentration of Cu increases, the value of Q increases.

after taking the log, the value will be larger than the previous value and while subtracting it from E°, the value of cell potential will decrease.

Determining whether the cell potential increases, decreases, or remains the same in case (b)

NH₃ is added to the copper half-cell compartment. Cu²⁺ reacts with NH₃ to form [Cu (NH₃)₄] ^{+ 2}. The concentration of [Cu⁺²] decreases. And E_CELLincreases.

 Step 4: determining whether the cell potential increases, decreases, or remains the same in case (c)

if NaCl is added to the silver half-cell compartment.Ag⁺ reacts with Cl⁺ to form AgCl. And the concentration of [Ag⁺] decreases. And the cell potential also decreases.

determining whether the cell potential increases, decreases, or remains the same in case (d)

When Water is added to both half-cell compartments until the volume of solution is doubled. The concentration of Cu²⁺and Ag⁺decreases. But also, at the same time the ratio of $\frac{\left[C{u}^{+2}\right]}{{\left[A{g}^{+}\right]}^2}$ increases. Hence, the cell potential decreases.

determining whether the cell potential increases, decreases, or remains the same in case (e)

When the silver electrode is replaced with a platinum electrode, there is no change in the cell potential.