Question

10 mL of gaseous hydrocarbon on combustion gives 40 mL of CO\(_2\)(g) and 50 mL of water vapour. The total number of carbon and hydrogen atoms in the hydrocarbon is ______ .

Answer 1

Correct Answer: 14

Let the formula of the hydrocarbon be \( \text{C}_x\text{H}_y \). On complete combustion, the reaction can be represented as:
\[\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right) \text{O}_2 \rightarrow x \text{CO}_2 + \frac{y}{2} \text{H}_2\text{O}\]
Step-by-step Calculation:
According to the given data, 10 mL of hydrocarbon produces 40 mL of \(\text{CO}_2\) and 50 mL of water vapor (\(\text{H}_2\text{O}\)).
From the stoichiometry of the reaction:
\[x \times 10 \, \text{mL} = 40 \, \text{mL} \implies x = 4\]
Similarly, for water:
\[\frac{y}{2} \times 10 \, \text{mL} = 50 \, \text{mL} \implies y = 10\]
Therefore, the hydrocarbon is \( \text{C}_4\text{H}_{10} \).
Total number of carbon and hydrogen atoms:
\[\text{Total atoms} = x + y = 4 + 10 = 14\]
Conclusion: The total number of carbon and hydrogen atoms in the hydrocarbon is 14.