Question

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of $A$?

• A. $C _{11} H _8$
• B. $C _{11} H _4$
• C. $C _5 H _8$
• D. $C _9 H _8$

Hint:

When solving combustion problems, remember that the number of moles of oxygen is related to the number of moles of carbon and hydrogen in the molecule.

Answer 1

The Correct Option is D

To determine the molecular formula of hydrocarbon \( A \), we start by setting up the combustion reaction equation and analyzing the given conditions.

Let the hydrocarbon \( A \) be represented as \( C_xH_y \).

The general equation for the complete combustion of a hydrocarbon is:

\(C_xH_y + O_2 \rightarrow xCO_2 + \frac{y}{2}H_2O\)

According to the problem, \( A \) produces 4 equivalents of water and requires 11 equivalents of oxygen. From this, set up the following two conditions:

1. The number of water molecules formed indicates that \(\frac{y}{2} = 4\). Therefore, \(y = 8\).
2. The total oxygen consumption is 11 equivalents, indicating the relation:

\(x + \frac{y}{4} = 11\). Substituting \( y = 8 \), we get:

\(x + \frac{8}{4} = 11\)

\(x + 2 = 11\)

Solving for \( x \), we have:

\(x = 11 - 2 = 9\)

The molecular formula of hydrocarbon \( A \) is thus \(C_9H_8\).

Let's analyze the options given:

1. \(C_{11}H_8\): This would use more than 11 oxygen equivalents as \( 11 + 2 = 13\), which does not meet the requirement.
2. \(C_{11}H_4\): This would also use more oxygen equivalents than given.
3. \(C_5H_8\): This formula would not produce 4 equivalents of water since \(\frac{y}{2} = 4\) doesn't hold for \(y = 8\).
4. \(C_9H_8\): Matches both the number of required oxygens and produces 4 equivalents of water.

Therefore, the correct molecular formula of hydrocarbon \( A \) is \(C_9H_8\).