Chemistry

A gaseous hydrocarbon contains 82.76% of carbon. Given that it's vapour density is 29, find it's molecular formula.

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Element	% composition	At. wt.	Relative no. of atoms	Simplest ratio
Carbon	82.76	12	$\dfrac{82.76}{12}$ = 6.89	$\dfrac{6.89}{6.89}$ = 1
Hydrogen	17.24	1	$\dfrac{17.24}{1}$ = 17.24	$\dfrac{17.24}{6.89}$ = $\dfrac{5 }{2}$

Simplest ratio of whole numbers = C : H = 1 : $\dfrac{5 }{2}$ = 2 : 5

Hence, empirical formula is C₂H₅

Empirical formula weight = 2(12) + 5(1) = 29

V.D. = 29

Molecular weight = 2 x V.D. = 2 x 29

$\text{n} = \dfrac{\text{Molecular weight}}{\text{Empirical formula weight}} \\[0.5em] = \dfrac{2 \times 29}{29} =2$

∴ Molecular formula = n[E.F.] = 2[C₂H₅] = C₄H₁₀

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