Question

One mole of an alkane (\(x\)) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (\(x\)) is ______.

Answer 1

Correct Answer: 17

Step 1: Understanding the Concept:
Alkanes follow the general molecular formula \(C_nH_{2n+2}\).
The amount of oxygen required for the complete combustion of any hydrocarbon depends on its stoichiometry.
Step 2: Key Formula or Approach:
The general balanced equation for the combustion of an alkane is:
\[ C_nH_{2n+2} + \left( \frac{3n+1}{2} \right) O_2 \rightarrow n CO_2 + (n+1) H_2O \]
Step 3: Detailed Explanation:
Given: 1 mole of alkane requires 8 moles of \(O_2\).
From the balanced equation, we equate the coefficient of \(O_2\) to 8:
\[ \frac{3n+1}{2} = 8 \]
\[ 3n + 1 = 16 \]
\[ 3n = 15 \implies n = 5 \]
The alkane has 5 carbon atoms.
The formula of the alkane is \(C_5H_{2(5)+2} = C_5H_{12}\) (Pentane).
Number of Carbon atoms = 5.
Number of Hydrogen atoms = 12.
Sum of atoms = \(5 + 12 = 17\).
Step 4: Final Answer:
The total sum of atoms is 17.