Question

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is _______.

Use: Universal gas constant (R) = 8.3 J K$^{-1}$ mol$^{-1}$; Atomic mass (in amu): H = 1, O = 16

Answer 1

29.88

Answer 2

The electrolysis of water is represented by the balanced chemical equation:

$2\text{H}_2\text{O(l)} \rightarrow 2\text{H}_2\text{(g)} + \text{O}_2\text{(g)}$

First, calculate the number of moles of water electrolyzed.
The molar mass of water ($\text{H}_2\text{O}$) is $2 \times 1 \text{ g/mol} + 16 \text{ g/mol} = 18 \text{ g/mol}$.
The mass of water is 144 g.
Number of moles of water = Mass / Molar mass = $144 \text{ g} / 18 \text{ g/mol} = 8 \text{ mol}$.

According to the balanced equation, 2 moles of liquid water produce 2 moles of hydrogen gas and 1 mole of oxygen gas, for a total of $2 + 1 = 3$ moles of gas.
Since 8 moles of water are electrolyzed, the total number of moles of gas produced is:
Moles of gas produced = $(8 \text{ mol } \text{H}_2\text{O}) \times \frac{3 \text{ mol gas}}{2 \text{ mol } \text{H}_2\text{O}} = 12 \text{ mol}$.

Initially, the reactant is liquid water, so the number of moles of gas is 0.
The final number of moles of gas is 12 mol.
The change in the number of moles of gas is $\Delta n_g = n_{g, \text{final}} - n_{g, \text{initial}} = 12 \text{ mol} - 0 \text{ mol} = 12 \text{ mol}$.

The expansion work done at constant pressure is given by $W = P\Delta V$. Assuming ideal gas behavior, $P\Delta V = \Delta n_g RT$.
The work done by the system during expansion is $W_{\text{by system}} = P\Delta V = \Delta n_g RT$.
Given:
$\Delta n_g = 12 \text{ mol}$
$R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$
$T = 300 \text{ K}$

$W_{\text{by system}} = (12 \text{ mol}) \times (8.3 \text{ J K}^{-1} \text{ mol}^{-1}) \times (300 \text{ K})$
$W_{\text{by system}} = 12 \times 8.3 \times 300 \text{ J}$
$W_{\text{by system}} = 29880 \text{ J}$

The question asks for the work done in kJ.
$1 \text{ kJ} = 1000 \text{ J}$
$W_{\text{by system}} = 29880 \text{ J} / 1000 \text{ J/kJ} = 29.88 \text{ kJ}$.

The term "expansion work done" refers to the work done by the system on the surroundings, which is positive when the volume increases (as gas is produced from liquid).