Question

At what relative humidity will \[N{a_2}HP{O_4}.7{H_2}O\] (s) deliquescent when exposed to the air at \[{27^o}C\]?
A. below \[75\% \]
B. above \[7.0\% \]
C. equal \[7.5\% \]
D. above \[7.5\% \]

Answer 1

Hint: When the vapour pressure of the solution formed is less than the partial vapour pressure of water in the air, it leads to the process of delinquency. This concept is used to form an approach to find relative humidity.

Complete answer:
To answer this question, we should know about the concept of relative humidity. Relative humidity is defined as the ratio between the actual amount of water vapour present in a volume of air and the maximum water vapour amount of the air that can be held at that temperature. Relative humidity is always expressed in terms of percentage.
The deliquescent is a process by which a substance absorbs the moisture from the surrounding atmosphere until it gets dissolved completely in the absorbed water solvent and forms a solution.
According to the given question, here the compound \[N{a_2}HP{O_4}.7{H_2}O\] is exposed to the air at \[{27^o}C\]which means that vapour pressure of water is considered at \[{27^o}C\] temperature.
Relative humidity = \[\dfrac{{Partial\,vapour\,pressure}}{{Vapour\,pressure\,of\,water\,at\,\,same\,\,temperature}}\, \times 100\]
Relative humidity = \[\dfrac{{3 \times {{10}^{ - 3}}}}{{4 \times {{10}^{ - 2}}}}\, \times 100\]
Relative humidity= \[7.5\,\% \]
Also, we know that, \[pressure \propto \dfrac{1}{{humidity}}\]
For deliquescence, relative humidity should be equal to \[7.5\,\% \]
Thus option C is the correct answer.

Note:
The relative humidity is always as a percentage. If the percentage of relative humidity is high means that the air- water mixture is more humid. It means that there is a lot of moisture in the atmosphere. This concept is used in weather forecasts and reports. Humidity only indicates the relation to the condition of the air present. Here, two terms are given i.e. humidity and relative humidity, they are not the same concept.