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 \, \text{J K}^{-1} \text{mol}^{-1} $; Atomic mass (in amu): H = 1, O = 16

Hint:

Expansion work under constant pressure is calculated using: \( w = -\Delta n_{\text{gas}} R T \), where \( \Delta n \) is the change in moles of gas.

Answer 1

Correct Answer: 29.88

Step 1: Write the balanced equation for electrolysis of water \[{2H_2O(l) -> 2H_2(g) + O_2(g)} \] Step 2: Moles of water \[ \text{Molar mass of } {H_2O} = 18 \, \text{g/mol}, \quad \text{Given mass} = 144 \, \text{g} \Rightarrow \frac{144}{18} = 8 \, \text{mol} \] Step 3: Moles of gaseous products \[ \text{From 2 mol } {H_2O} \Rightarrow 2 mol {H_2} + 1 mol {O_2} = 3 mol gas \Rightarrow 8 mol {H_2O} \Rightarrow 12 mol gas (\Delta n = 12) \] Step 4: Expansion work done \[ w = - \Delta n_{\text{gas}} R T = - 12 \times 8.3 \times 300 = -29880 \, \text{J} = \frac{-29880}{1000} = \boxed{29.88 \, \text{kJ}} \]