Question

Find the relative molecular mass of methyl alcohol $\left(C{H}_{3}OH\right)$ , if $160gm$ of the alcohol on vaporization has a volume of $112$ litres at STP.
(A) $16gm$
(B) $32gm$
(C) $160gm$
(D) $80gm$

Answer 1

Hint: Here, we use the concept of moles to calculate the amount of water formed. It can be calculated by dividing the mass of a substance present in a mixture by its molar mass:
$$\text{The number of moles of a substance }={\displaystyle \frac{\text{Mass of the substance in the mixture}}{\text{Molar mass of the substance}}}$$
Another important concept coming into use is that one mole of a gaseous substance occupies $$22.4litres$$volume.

Complete answer:
The questions requires us to calculate the relative molar mass of methyl alcohol under given conditions, where mass $(w)$ and volume of the alcohol vaporized is $160gm$ and $112litres$(at STP) respectively.
We know that one mole of a gaseous substance occupies $$22.4litres$$volume. Using this relation, we can calculate the number of moles occupied by $112litres$.
$\text{Number of moles occupied by }112litres\text{ of gas }\text{ = }{\displaystyle \frac{112}{22.4}}=5moles---(1)$
Since we know the mass of methyl alcohol vaporized, we can substitute it in the following equation relating number of moles:
$\text{The number of moles of a substance }={\displaystyle \frac{\text{Mass of the substance in the mixture}}{\text{Molar mass of the substance}}}$
$={\displaystyle \frac{w}{M}}$
$={\displaystyle \frac{160}{M}}---(2)$
In $(2),$ we can substitute with $(1)$ in the LHS. On rearranging the equation so as to calculate relative molar mass $(M)$of methyl alcohol, we get:
$M={\displaystyle \frac{160}{5}}$
$=32gm$
Hence, the relative molecular mass of methyl alcohol $\left(C{H}_{3}OH\right)$ , if $160gm$ of the alcohol on vaporization has a volume of $112$ litres at STP is (B) $32gm$ .

Note:
There exists an equation relating vapour density and molar mass, where:
$\text{Molar}\text{mass}=2\times \text{Vapour}\text{density}$
This equation comes into play if we are provided with the vapour density of the substance and are supposed to find its molar mass, or vice versa.