Question

0.24 g of a volatile substance, upon vaporisation, gives $45\operatorname{ml}$vapour at NTP. What will be the vapour density of the substance?
(A) $95.93$
(B) $59.8$
(C) $95.39$
(D) $5.993$

Answer 1

Hint: The formula of vapour density is dividing the molar mass of an entity with two. The molar mass of the given compound can be calculated by the volume of the gas provided in the question.

Complete step by step solution:
Let’s make sure you know this-
One mole of any gaseous substance has the volume of$22400\operatorname{ml}$.
As we have been given the volume of the volatile gas evolved, we can therefore find the number of moles of the given compound from this information. The formula for number of moles is given by: \[n=\dfrac{Given\operatorname{volume}}{22400}=\dfrac{45}{22400}\]
Solving the above equation we get, $n=0.002$. To calculate the vapour density of a compound, we need its molar mass, as the formula for vapour density (VD) is: $\dfrac{molar\text{ mass of compound}}{2}$ . As now we have calculated the number of moles, we can easily calculate its molar mass. We know that: $n=\dfrac{Given\operatorname{mass}}{Molar\operatorname{mass}}\Rightarrow Molar\operatorname{mass}=\dfrac{Given\operatorname{mass}}{n}$
\[\Rightarrow Molar\operatorname{mass}=\dfrac{0.24}{0.002}=120\operatorname{g}\]
Putting the value of molar mass in the formula for vapour density, we get:
\[VD=\dfrac{120}{2}=60\]
The closest value to our calculated answer from the options is $59.8$. That makes option (B) as the right answer.

Note: Keep in mind that, $22400\operatorname{ml}$is volume occupied by one mole of any gas .This is true for any liquid too.