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Question: 0.24 g of a volatile substance, upon vaporization, gives 45 ml of vapour at STP. The vapour density ...

0.24 g of a volatile substance, upon vaporization, gives 45 ml of vapour at STP. The vapour density of the substance is:
A. 5.993
B. 59.73
C. 95.39
D. 95.93

Explanation

Solution

Hint: To answer this question, we should know about vapour density. We should know that vapour density is the density of a vapour in relation to that of hydrogen.

Step by step answer:
So, first of all we should define vapour density. We should know that vapour density is the weight of a volume of pure vapour or gas compared to an equal volume of dry air at the same temperature and pressure. It is obtained by dividing the molecular weight of the vapour by the average molecular weight of air thus, it is unit less.
To calculate the vapour density, mass of volatile substance is given which is 0.24gram. And after vaporisation it gives 45 ml of vapour at STP. We should note that STP is standard temperature pressure.
We will solve this question by using the ideal gas equation.
According to the ideal gas equation,
PV=nRTPV=nRT
Where,
P = Pressure
T = Temperature
V = Volume
In the question, we have STP conditions so we can say that:
Pressure, P = 1 atm
Volume, V=45ml=451000V=45ml=\dfrac{45}{1000}
Number of moles, n=given massmolar mass= 0.24 Mn=\dfrac{given\,mass}{molar\,mass}=\dfrac{\begin{aligned} & \\\ & 0.24 \\\ \end{aligned}}{M}

Gas constant R = 0.082 atm.Lmol.KR\text{ }=\text{ }0.082\text{ }\dfrac{atm.L}{mol.K}
Temperature = 273 K
Substitute the all values in equation in ideal gas equation:
1×45100=0.24M×0.082×273 M=119.392 M=2×Vapour density Vapour density=119.3922=59.73 \begin{aligned} & 1\times \dfrac{45}{100}=\dfrac{0.24}{M}\times 0.082\times 273 \\\ & M=119.392 \\\ & M=2\times Vapour\,density \\\ & Vapour\,density=\dfrac{119.392}{2}=59.73 \\\ \end{aligned}
Therefore, the vapour density of substances is 59.73. So, our correct answer is option B.

Note: We should know that standard temperature is equal to 0 °C, which is 273.15 K. Standard Pressure is 1 atm, 101.3kPa or 760 mmHg or torr. We should know that STP is the "standard" condition often used for measuring gas density and volume. At STP, 1 mole of any gas occupies 22.4L.
We should note that in Density calculations: Density of a gas at STP= molar mass22.4L\dfrac{molar\text{ }mass}{22.4L}