Question

one mole of heptane $(V.P = 92mmHg)$ was mixed with 4 moles of octane $(V.P = 31mmHg)$ The vapour pressure of resulting ideal solution is:
A. $46.2mmHg$
B.$40.0mmHg$
C.43.2mmHg
D.$38.4mmHg$

Answer 1

Alkanes are saturated hydrocarbons in which the carbon atoms are bonded to each other by single bonds only. They are nonpolar and insoluble in water. Vapour pressure of a solution is the tendency of solution to change in gaseous state and it increases with increase in temperature.
Formula used:
${P_{solution}} = {X_{solvent}}{P_{solvent}}$

Complete step by step answer:
Hydrocarbons are organic compounds that are made up of carbon and hydrogen atoms bonded together. They are naturally occurring compounds. They are divided into saturated and unsaturated compounds which depend on the bonding between the atoms. When carbon atoms are bonded with each other with a single bond and all the other empty positions are taken by hydrogen atoms then the compound is known as saturated compound and when the carbon atoms in a compound are bonded by double or triple bond then the compounds are known as unsaturated compounds.
The saturated compounds are known as alkanes. They are nonpolar organic compounds which are insoluble in water. Vapour pressure of a solution is the tendency of a solution to change into gaseous state and indicates its evaporation rate. Vapour pressure is directly proportional to temperature and is given by the formula:
${P_{solution}} = {X_{solvent}}{P_{solvent}}$
Where ${P_{solution}}$ is the vapour pressure of the solution, ${X_{solvent}}$ is the mole fraction of the solvent and ${P_{solvent}}$ is the vapour pressure of the solvent.
For the given question,
Total number of moles = $1 + 4 = 5$
Mole fraction of heptane = $\dfrac{1}{5}$
Mole fraction of octane = $\dfrac{4}{5}$
According to the formula,
${P_{solution}} = {X_{solvent}}{P_{solvent}}$
${P_{solution}} = {X_H}P_H^0 + {X_O}P_O^0$
$\Rightarrow \dfrac{1}{5} \times 92 \times \dfrac{4}{5} \times 31$
$\Rightarrow {P_{solution}} = 43.2mmHg$

Thus, the correct option is (C) .

Note:
Heptane is an alkane which is used as a nonpolar solvent. It is used for indicating the presence of organic compounds on a stained paper also it is used for transportation and storage purposes. Octane is present in fuels which increases the performance level of the gasoline engines.