Question

At what relative humidities, will $N{a_2}S{O_4}$ be deliquescent (i.e. absorb moisture) when exposed to the air at ${0^0}C$ ?
A) Above $33 \cdot 33\% $
B) Below $33 \cdot 33\% $
C) Above $66 \cdot 66\% $
D) Below $66 \cdot 66\% $

Answer 1

Hint: The process of deliquescence happens when the vapour pressure of the solution formed is less than the partial vapour pressure of water in the air. One can apply this concept to form an approach towards the finding of relative humidity.

Complete step by step answer:
1) First of all let us learn the concept of relative humidity which can be elaborated as the ratio between the actual amount of water vapor present in a volume of air and the maximum water vapour amount of the air can be held at that temperature. The relative humidity is always expressed as a percentage.
2) Now let's learn the meaning of deliquescent which is the process by which a substance that absorbs the moisture from the surrounding atmosphere until it gets dissolved completely in the absorbed water solvent and forms a solution with that.
3) The compound ${\text{N}}{{\text{a}}_2}{\text{S}}{{\text{O}}_4}$ is exposed to atmospheric air at the ${0^0}C$ which means we should consider the vapour pressure of water at ${0^0}C$ temperature.
4) Now that the vapour pressure of water which is known value is $0 \cdot 00605{\text{ atm}}$ at the temperature of ${0^0}C$. Therefore, when the relative humidity is $33 \cdot 33\% $ the partial pressure of water will become as $0 \cdot 002{\text{ atm}}$ which is ideal for moisture absorption.
5) Hence, when the relative humidity is higher than $33 \cdot 33\% $ the molecule ${\text{N}}{{\text{a}}_2}{\text{S}}{{\text{O}}_4}$ will absorb moisture from the air which shows

So, the correct answer is “Option A”.

Note:
The relative humidity is always denoted as a percentage. The higher percentage of relative humidity means that the air-water mixture is more humid and this concept is widely used in weather forecasts and reports. The terms humidity and relative humidity are not the same concepts as humidity only shows the relation to the condition of the air present. When a molecule ${\text{N}}{{\text{a}}_2}{\text{S}}{{\text{O}}_4}$ absorbs the moisture from the air it forms the $N{a_2}S{O_4} \cdot 10{H_2}O$ molecule.