# Spontaneity

Some redox equations are spontaneous; they will proceed without outside assistance. The others are spontaneous in the backward direction; they require an electrical current to be applied to force the reaction forward. The electric potential difference, or voltage, of a redox reaction is

$\displaystyle \Delta{} E^{0} = E_{\text{r(cathode)}}^{0} - E_{\text{r(anode)}}^{0}$.

The $\displaystyle E_{\text{r}}^{0}$ values come from the redox table titled “Relative Strengths of Oxidizing and Reducing Agents” on page 805 of the textbook. All $\displaystyle E_{\text{r}}^{0}$ values are to the standard hydrogen electrode:

2 H+(aq) + 2 e → H2(g), $\displaystyle E_{\text{r}}^{0} = 0.00 \, \text{V}$.

The value of $\displaystyle \Delta{} E^{0}$ tells us about spontaneity:

• $\displaystyle \Delta{} E^{0} > 0 \Rightarrow$ spontaneous
• $\displaystyle \Delta{} E^{0} < 0 \Rightarrow$ non-spontaneous

You can tell that a galvanic cell is spontaneous right away by checking if the species that gets reduced at the cathode is above the species that gets oxidized at the anode in the redox table.