Question

A gas is found to have the formula ${(CO)_x}$ , if its vapour density is 70 then the value of x must be:
A.$7$
B.$5$
C.$4$
D.$6$

Answer 1

Hint:Vapour Density is calculated as the ratio of mass of a volume of a vapour to the mass of hydrogen, under the same temperature and pressure. It is thus, the density of a vapour in relation with the mass of hydrogen gas. Molecular weight is related to vapour density.
Formula used: $\text{Molecular Weight }= 2 \times{\text{ vapour density}}$

Complete step by step answer:
Vapour density is defined as the ratio of mass of a volume of a vapour, that is the density of a vapour to the mass of hydrogen with equal volume, when measured under the same temperature and pressure.
Vapour Density = $\dfrac{\text{mass of molecules of gas}} {\text{mass of molecules of hydrogen}}$
Thus, the vapour density is the density of a vapour in relation with the mass of hydrogen gas.
Molecular weight is also known as the molecular mass of a substance which is relatively the ratio of the mass of one molecule of the substance to the mass of one twelfth of the carbon atom. Thus, we say that,
$\text{Molecular Weight }= 2 \times{\text{ vapour density}}$
For the above given question,
We know that, $\text{Molecular Weight }= 2 \times{\text{ vapour density}}$
$ \Rightarrow M = 2 \times {\text{vapour density}}$
$ \Rightarrow M = 2 \times 70 = 140$
Therefore, molecular mass of ${[CO]_x} = 140$
 $ \Rightarrow x \times {\text{molecular mass of CO}}= 140$
$ \Rightarrow x \times 28 = 140$
 $ \Rightarrow x = \dfrac{{140}}{{28}}$
 $\therefore x = 5$
So, the correct option is (B) $5$ .

Note:
The mass of any substance per unit volume is considered as the absolute density of the substance. The unit of absolute density is grams per cubic centimetre whereas specific gravity is defined as the ratio of the mass in air of a given volume to the mass of volume of water.
$C{O_5}$ is carbon pentoxide which is an unstable oxide of carbon. It is found in grass known as napier grass which is a hybrid grass and can be grown in a variety of soils. It improves soil fertility and prevents soil erosion. It is also used in biogas and bio-oil production.