Question

The standard free energy change for the formation of ${\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$ from ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}$ is $∆{\mathbf{G}}^{°}=+237.13\mathbf{KJ}$ The reactions are

$$\begin{gathered} \mathrm{cathode}:2{\mathrm{H}}_2\mathrm{O}+2{\mathrm{e}}^{-}\rightleftharpoons {\mathrm{H}}_2\left(\mathrm{g}\right)+20{\mathrm{H}}^{-} \\ \mathrm{Anode}:{\mathrm{H}}_2\mathrm{O}\rightleftharpoons \frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-} \end{gathered}$$

Calculate the standard voltage${\mathrm{E}}^{°}$needed to decompose water into its elements by electrolysis. What does the word standard mean in this question?

Short answer

• The standard voltage E = -1.229 V needed to decompose water into its elements by electrolysis.

Step-by-step solution

Definition of Standard free energy:

• The standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions.

Step 2: Method of calculating Standard Voltage:

We can calculate standard voltage using this equation:

$∆G=-n.F.E$

So, the is,

$$\begin{gathered} \mathrm{E}=-\frac{∆\mathrm{G}}{\mathrm{n}.\mathrm{F}} \\ \mathrm{E}=-\frac{237.13.{10}^3\mathrm{j}}{2.96485\mathrm{C}/\mathrm{mol}} \\ \mathrm{E}=--1.229\mathrm{V} \end{gathered}$$

Elucidating the word Standard:

• The word standard mean that the reluctant and products are in standard states.