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

The correct answer is 29.88.

To find the expansion work done when 144 g of water is electrolyzed completely, we can follow these steps:

Step 1: Write the balanced chemical equation for the electrolysis of water
The decomposition of liquid water into gaseous hydrogen and oxygen is represented as:
$2H_{2}O\left(l\right)\to 2H_2\left(g\right)+O_2\left(g\right)$

Step 2: Calculate the number of moles of water
The molar mass of water ($H_{2}O$) is:
$M=(2\times 1)+16=18\text{g/mol}$

Using the given mass of 144 g, the number of moles of water ($n$) is:
$n=\frac{144\text{g}}{18\text{g/mol}}=8\text{mol}$

Step 3: Determine the change in moles of gas ($\Delta n_g$)
From the balanced equation, 2 moles of liquid water yield 3 moles of gas (2 moles of $H_2$ and 1 mole of $O_2$).
Therefore, the change in the number of moles of gas for 8 moles of water is:
$\Delta n_g=8\times \frac{3}{2}=12\text{mol}$

Step 4: Calculate the expansion work done
Considering ideal gas behavior, the expansion work done ($W$) under constant pressure is given by:
$W=P\Delta V=\Delta n_{g}RT$

Given:
Universal gas constant, $R=8.3{\text{J K}}^{-1}{\text{mol}}^{-1}$
Temperature, $T=300\text{K}$

Substituting the values into the formula:
$W=12\times 8.3\times 300$

Calculating the value in Joules:
$W=29880\text{J}$

Step 5: Convert the work to kilojoules (kJ)
$W=\frac{29880}{1000}=29.88\text{kJ}$

Thus, the expansion work done is 29.88 kJ.