What is the mass of acetylene ( C_2H_2 ) gas produced when 32 g of...

Mass of pure $CaC_2$ in the sample = $32 \times \dfrac{75}{100} = 24\text{ g}$

Molar mass of $CaC_2 = 40 + 2 \times 12 = 64\text{ g/mol}$

Moles of $CaC_2$ reacting = $\dfrac{24}{64} = \dfrac{3}{8}\text{ mol}$

The balanced chemical equation is:
$CaC_2 + 2H_2O \rightarrow Ca(OH)_2 + C_2H_2$

From the stoichiometry of the reaction, $1\text{ mol}$ of $CaC_2$ produces $1\text{ mol}$ of $C_2H_2$.

Moles of $C_2H_2$ produced = $\dfrac{3}{8}\text{ mol}$

Molar mass of $C_2H_2 = 2 \times 12 + 2 \times 1 = 26\text{ g/mol}$

Mass of $C_2H_2$ produced = $\dfrac{3}{8} \times 26 = 9.75\text{ g}$

Answer: $9.75\text{ g}$