Question

In Victor Meyer’s experiment, 0.23 g of a volatile solute displaced air which measures 112 mL at NTP. The vapour density is ______?

Answer 1

Hint: We need to find the molar mass of the solute by using the ideal gas equation. Once we know the molar mass, then we can easily calculate the vapour density since it is the ratio of the molar mass of a substance to the molar mass of hydrogen gas.

Complete step by step solution:
To solve this question, we first need to understand the meaning of NTP. It refers to Normal Temperature and pressure. It refers to air at a temperature of $ 20^{ o }{ C }$ (293.15 K) and a pressure of 1 atm. The molar volume of an ideal gas at NTP conditions is 24.05 L.
Now, let us solve the question.
Since the solute is displacing the gas at NTP conditions, therefore
The volume occupied by the solute at NTP conditions = Volume of the gas displaced by the solute = 112 mL
At, NTP, The temperature = 293.15 K and pressure = 1 atm.
Mass of the solute = 0.23 g
We need to find the molar mass of the solute. Employing the ideal gas equation we get,
$PV =$ $nRT$….(1)
Where n is the number of moles of the solute. Since the number of moles of the solute is the ratio of the mass of the solute and the molar mass of the solute, therefore equation (1) becomes:
$PV=\dfrac { m }{ M } RT $, where m is the mass of the solute and M is the molar mass of the solute.
Substituting the value of T, P, m and R in the above equation we get,
$1atm\times 112\times { 10 }^{ -3 }L=\dfrac { 0.23\quad g }{ M } \times 0.0821\quad Latm{ K }^{ -1 }{ mol }^{ -1 }\times 293.15K $
$\Rightarrow M=49.42\quad g/mol $
Vapour density and molar mass of a substance are linked to each other by the following relationship:
$M=vapour\quad density\times 2 $
$\Rightarrow vapour\quad density=\dfrac { 49.42\quad g/mol }{ 2 } =24.7\simeq 25 $

Hence the vapour density is 25.

Note: Remember that the vapour density is a unitless quantity since it is a relative quantity. It is the ratio of the mass of a certain volume of a substance to the mass of the same volume of hydrogen gas. Also do not get confused between STP and NTP. STP refers to Standard Temperature and Pressure. It refers to air at a $0^{ o }{ C }$ (273.15 K) temperature and 1 bar pressure.