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Question

A hydrocarbon contains 82.76% carbon by mass.  If 0.90 g of the hydrocarbon occupies a volume of 390 $cm^3$ at STP, what is its molecular formula?

P SRAVAN KUMAR · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Empirical and Molecular Formula Determination
	**Related Topics**: Stoichiometry, Ideal Gas Law
	**Prerequisites**: Percentage composition, Mole concept, Molar volume at STP
## SOLUTION PATHWAY
**Given Information**:
	* Percentage of carbon: 82.76%
	* Percentage of hydrogen: 100 - 82.76 = 17.24%
	* Mass of hydrocarbon: 0.90 g
	* Volume of hydrocarbon at STP: 390 $cm^3$ = 0.39 L
**Method & Steps**:
	1. **Determine the empirical formula:**
		Reasoning: Assume 100g of the compound.  Convert percentages to grams and then to moles.
		Carbon: $\frac{82.76 g}{12.01 g/mol} = 6.89 mol$
		Hydrogen: $\frac{17.24 g}{1.008 g/mol} = 17.10 mol$
		Mole ratio: C:H = $\frac{6.89}{6.89} : \frac{17.10}{6.89} \approx 1:2.5 \approx 2:5$
		Empirical formula: $C_2H_5$
	2. **Calculate the molar mass:**
		Working: Use the ideal gas law at STP (1 mol occupies 22.4 L).
		$\frac{0.90 g}{0.39 L} = \frac{Molar Mass}{22.4 L/mol}$
		Molar Mass $= \frac{0.90 g 	imes 22.4 L/mol}{0.39 L} \approx 51.85 g/mol$
		Key Point: Molar volume at STP is crucial for determining molar mass.
	3. **Determine the molecular formula:**
		Result: Empirical formula mass of $C_2H_5$: $(2 	imes 12.01) + (5 	imes 1.008) = 29.06 g/mol$
		$\frac{Molar Mass}{Empirical Formula Mass} = \frac{51.85 g/mol}{29.06 g/mol} \approx 1.78 \approx 2$
		Molecular formula: $2 	imes C_2H_5 = C_4H_{10}$
		Verification: The calculated molar mass is close to the theoretical molar mass of butane.
 ## OPTION ANALYSIS
[A] :x: $C_2H_5$ is the empirical formula, not the molecular formula.
[B] :x: $C_3H_8$ does not match the calculated molar mass.
[C] ✓: $C_4H_{10}$ matches the calculated molar mass and empirical formula ratio.
[D] :x: $C_5H_{12}$ does not match the calculated molar mass.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. Using the wrong molar volume at STP: Ensure you use 22.4 L/mol.
		2. Confusing empirical and molecular formulas: Remember that the molecular formula is a whole number multiple of the empirical formula.
	**Quick Tips**:
		1. Simplify mole ratios by dividing by the smallest number of moles.
		2. Double-check calculations to avoid rounding errors.

P SRAVAN KUMAR · Answer

$C_2H_5$

P SRAVAN KUMAR · Answer

$C_3H_8$

P SRAVAN KUMAR · Answer

The correct Option is "$C_4H_{10}$"

P SRAVAN KUMAR · Answer

$C_5H_{12}$

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