Question

Complete combustion of $0.858g$ of compound X gives $2.63g$ of $C{O_2}$ and $1.28g$ of ${H_2}O$ . The lowest molecular weight that X can have is?
Options-
a.$43g$
b.$86g$
c.$129g$
d.$172g$

Answer 1

The given mass of carbon dioxide gas and water formed as products can be used to determine the unknown moles of carbon and hydrogens present in the hydrocarbon. Once the molecular formula of the hydrocarbon is known, it can be used to calculate the corresponding molecular mass.

Complete answer:
The reaction of hydrocarbons with an abundant supply of oxygen is called combustion that produces carbon dioxide and water in stoichiometric ratios.
Since, chemical reactions follow the laws of chemical combination and one such important law is the law of conservation of mass that can be used to determine the formula of the unknown compound X.
Since, mass remains the same then the number of atoms of each element remain the same. Thus, the number of carbon and hydrogen atoms present in the hydrocarbon will be the same as those present in carbon dioxide and water respectively.
The general equation for combustion can be written as follows:
${C_x}{H_y} + {O_2} \to \dfrac{y}{2}{H_2}O + xC{O_2}$ where ${C_x}{H_y}$ is the general formula of the unknown compound X.
The number of moles of carbon will be the same as that of carbon dioxide and can be calculated by taking a ratio of the given mass and molar mass:
${\text{Moles of carbon(x)}} = \dfrac{{2.63g}}{{44gmo{l^{ - 1}}}} = 0.05976moles$
The moles of hydrogen atoms in the compound will be twice the number of moles of water molecules that can be calculated as follows:
${\text{Moles of hydrogen(y)}} = 2 \times \dfrac{{1.28g}}{{18gmo{l^{ - 1}}}} = 0.1421moles$
The mole ratio of carbon and hydrogen atoms, expressed in the simplest form can be written as follows:
$C:H = 0.05976:0.1421 = 1:2.38$
Since atoms can have only whole numbers as stoichiometric factors, the simplest ratio is multiplied by the nearest whole number three and the ratio becomes,
$C:H = 3:7.314$
Which tells us that approximately the formula of the unknown compound X is ${C_3}{H_7}$ and the net molecular mass of this compound is:
${\text{Mass of }}{C_3}{H_7} = (3 \times 12) + (7 \times 1) = 43g$

$\Rightarrow$ Hence, the lowest molecular mass of compound X is $43g$ and option (a) is correct.

Note:
The law of conservation of mass states that mass can neither be created nor destroyed which basically means that the total mass of reactants and that of products remains the same. No new elements can be created or destroyed in a chemical reaction.