# Nickel and aluminum electrodes are used to build a galvanic cell. What is the theoretical cell potential assuming standard conditions? What is the shorthand notation for this cell?

Jul 4, 2016

See below:

#### Explanation:

List the 1/2 equations in order least positive to most positive:

$\textsf{\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times \times} {E}^{\circ} \left(\text{V}\right)}$

stackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxx))(color(blue)(larr)

$\textsf{A {l}_{\left(a q\right)}^{3 +} \text{ "+3e" "rightleftharpoons" "Al_((s))" } - 1.662}$

$\textsf{N {i}_{\left(a q\right)}^{2 +} \text{ "+2e" "rightleftharpoons" "Ni_((s))" } - 0.25}$

stackrel(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxx))(color(red)(rarr)

Note we use the $r i g h t \le f t h a r p \infty n s$ symbol to show that the 1/2 cells can go in either direction depending on what they are coupled with.

The 1/2 cell with the most +ve ${\text{E}}^{\circ}$ is the one which will take in the electrons.

From this we can see that the 2nd 1/2 cell will be driven left to right and the 1st 1/2 cell right to left in accordance with the arrows.

So the 2 half - reactions are:

$\textsf{N {i}_{\left(a q\right)}^{2 +} + 2 e \rightarrow N {i}_{\left(s\right)}}$

$\textsf{A {l}_{\left(s\right)} \rightarrow A {l}_{\left(a q\right)}^{3 +} + 3 e}$

To get the equation to balance we need to X the first 1/2 equation by 3 and the 2nd half equation by 2 then add to get the overall cell reaction:

$\textsf{3 N {i}_{\left(a q\right)}^{2 +} + 2 A {l}_{\left(s\right)} \rightarrow 3 N {i}_{\left(s\right)} + 2 A {l}_{\left(a q\right)}^{3 +}}$

To calculate $\textsf{{E}_{c e l l}^{\circ}}$ you subtract the least positive electrode potential value from the most positive:

$\textsf{{E}_{c e l l}^{\circ} = - 0.25 - \left(- 1.662\right) = + 0.41 \text{ ""V}}$

The shorthand notation is:

$\textsf{A {l}_{\left(s\right)} \textcolor{red}{I} \textcolor{w h i t e}{g} A {l}_{\left(a q\right)}^{3 +} \textcolor{red}{\setminus l l \setminus} \textcolor{w h i t e}{4} N {i}_{\left(a q\right)}^{2 +} \textcolor{w h i t e}{4} \textcolor{red}{l} \textcolor{w h i t e}{5} N {i}_{\left(s\right)}}$

Note the most oxidised form goes next to the salt bridge which is $\textsf{\textcolor{red}{l l}}$.