Question

A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives $3.38$ g carbon dioxide, $0.690$ g of water and no other products. A volume of $10.0$ L (measured at STP) of this welding gas is found to weigh $11.6$ g.
Calculate (i) empirical formula, (ii) molar mass of the gas and (iii) molecular formula.

Answer 1

An empirical formula tells us the relative ratios of different atoms in a compound. The molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample (measured in moles). A molecular formula is a chemical formula that gives the total number of atoms of each element in each molecule of a substance.

Complete step by step answer:
Since $3.38$ g of carbon dioxide are obtained the mass of $C$ present in the sample of welding fuel gas is
$\, \Rightarrow \,\,\dfrac{{12}}{{44}} \times 3.38\,$g
$\, \Rightarrow x = 0.92$
Since $0.690$ g of water are obtained the mass of hydrogen present in the welding fuel gas sample is
$\, \Rightarrow \,\dfrac{2}{{18}} \times 0.690\,$
$\Rightarrow 0.077g$
Percentage of $C$ is $\,\,\dfrac{{0.92}}{{0.92 + 0.077}} \times 100\,$
$\, = 92.3\% \,$
Percentage of $H$ is $\,\dfrac{{0.077}}{{0.92 + 0.077}}\,$
$\, = 7.7\% \,$
(i)The number of moles of carbon is$\, = \dfrac{{92.2}}{{12}} = 7.7\,$.
The number of moles of hydrogen is$\, = \dfrac{{7.7}}{1} = 7.7\,$.
The mole ratio of $\,C:H = 7.7:7.7 = 1:1\,$
Hence, the empirical formula of the welding fuel gas will be equal to $\,CH\,$.
(ii) The weight of $\,10.0\,$ L of gas at NTP is $\,11.6\,$g.
$\,22.4\,$L of gas at N.T. P will weigh
$\,\dfrac{{11.6}}{{10}} \times 22.4 = 26g/mol\,$
which is the molar mass.
(iii) Empirical formula mass is $\,12 + 1 = 13.\,$
Molecular mass is $\,26\,$
The ratio of the molecular mass to empirical formula mass is $\,26/13 = 2.\,$
Thus the molecular formula is $\,2\left( {CH} \right) = {C_2}{H_2}.\,$

Note: It can be said that the empirical formulas are the simplest form of notation. They provide the lowest whole-number ratio between the elements of a compound. Unlike molecular formulae, they do not provide information about the absolute number of atoms in a single molecule of a compound. The molecular formula of a compound can be the empirical formula, or it may also be a multiple of the empirical formula.