Step 1: Determine the mass of Carbon and Hydrogen in the hydrocarbon
Given that the hydrocarbon contains 92.3\% Carbon, the mass of Carbon in 52 g of the hydrocarbon is:
\[
\text{Mass of Carbon} = \frac{92.3}{100} \times 52 = 48 \text{ g}
\]
Since the hydrocarbon consists of only Carbon and Hydrogen, the remaining mass is Hydrogen:
\[
\text{Mass of Hydrogen} = 52 - 48 = 4 \text{ g}
\]
Step 2: Determine the number of moles of CO\(_2\) and H\(_2\)O formed
The number of moles of CO\(_2\) formed from the complete combustion of Carbon:
\[
\text{Moles of CO}_2 = \frac{\text{Mass of Carbon}}{\text{Molar mass of Carbon}} = \frac{48}{12} = 4 \text{ moles}
\]
The number of moles of H\(_2\)O formed from the complete combustion of Hydrogen:
\[
\text{Moles of H}_2O = \frac{\text{Mass of Hydrogen}}{\text{Molar mass of Hydrogen in H}_2O} = \frac{4}{2} = 2 \text{ moles}
\]
Step 3: Calculate the mass of O\(_2\) consumed
Using the reaction equation:
\[
\text{C} + O_2 \rightarrow CO_2
\]
\[
\text{H}_2 + \frac{1}{2} O_2 \rightarrow H_2O
\]
For the 4 moles of CO\(_2\) produced, the required oxygen is:
\[
\text{Moles of O}_2 = 4
\]
For the 2 moles of H\(_2\)O produced, the required oxygen is:
\[
\text{Moles of O}_2 = 1
\]
Total oxygen moles:
\[
\text{Total Moles of O}_2 = 4 + 1 = 5
\]
Since 1 mole of O\(_2\) weighs 32 g, the total mass of oxygen required is:
\[
\text{Mass of O}_2 = 5 \times 32 = 160 \text{ g}
\]