Question

Diagram the following galvanic cell, indicating the direction of flow of electrons in the external circuit and the motion of ions in the salt bridge.

$\mathit{P}\mathit{t}\left(s\right)\mathbf{|}\mathit{C}{\mathit{r}}^{\mathbf{2}\mathbf{+}}\left(aq\right)\mathbf{,}\mathbf{}\mathit{C}{\mathit{r}}^{\mathbf{3}\mathbf{+}}\left(aq\right)\mathbf{|}\mathbf{\left|}\mathit{C}{\mathit{u}}^{\mathbf{2}\mathbf{+}}\left(aq\right)\mathbf{\right|}\mathit{C}\mathit{u}\left(s\right)$

Write a balanced equation for the overall reaction in this cell.

Short answer

Balanced equation for the overall reaction in given galvanic cell is,

$2C{r}^{2+}\left(aq\right)+C{u}^{2+}\left(s\right)\to 2C{r}^{3+}\left(aq\right)+Cu\left(s\right)$

Step-by-step solution

Introduction to electrochemical reactions

Electrochemical reactions are made up of two half-reactions, the anode electrode and the cathode electrode, which are combined to form the entire cell reaction.

The anode is the electrode where electrons are lost due to oxidation and the cathode is where electrons are acquired due to reduction.

Understanding given parameters

In the galvanic cell electrons flow from left electrode to right as Cr(II) is oxidized to Cr(III). In the salt bridge positive ions flow from left to right and negative ions flow from right to left.

Balancing equation for overall reaction

Anode half-reaction can be written as,

$C{r}^{2+}\left(aq\right)\to C{r}^{3+}\left(aq\right)+e^{-}/2$

Multiply by 2 on both sides of equation to satisfy the number of electrons,

$2C{r}^{2+}\left(aq\right)\to 2C{r}^{3+}\left(aq\right)+2e^{-}$

Now, Cathode half-reaction can be written as,

$C{u}^{2+}\left(aq\right)+2e^{-}\to Cu\left(s\right)$

Overall reaction now written as adding both half-reactions,

$2C{r}^{2+}\left(aq\right)+C{u}^{2+}\left(s\right)\to 2C{r}^{3+}\left(aq\right)+Cu\left(s\right)$

Therefore, balanced equation for the overall reaction in given galvanic cell is,

$2C{r}^{2+}\left(aq\right)+C{u}^{2+}\left(s\right)\to 2C{r}^{3+}\left(aq\right)+Cu\left(s\right)$