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# The weight of an empty china dish is 39 g and when a saturated solution of potassium nitrate is poured into, its weight is 108 g at ${50^0}C$. After evaporating the solution to dryness, if the weight of the dish along with the crystals is 72 g then the solubility of potassium nitrate at ${50^0}C$ is ________ .a.) 83.9b.) 95.6c.) 91.6d.) 87.4

Last updated date: 12th Sep 2024
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Hint: Solubility is the measure of the amount of substance soluble in a given solvent. It can be calculated by the formula as -
$\dfrac{{Mass{\text{ of salt (g)}}}}{{{\text{Mass of water (g)}}}}$ = $\dfrac{{{\text{Solubility of salt (g)}}}}{{{\text{100g water}}}}$

Complete step by step answer :
First, let us see what solubility is.
The solubility may be defined as the measure of the amount of a substance soluble in a solvent.
Let us see what is given to us in question and what we have to find out.
Given :
Weight of an empty china dish = 39 g
Weight of china dish and potassium nitrate = 108 g
Temperature = ${50^0}C$ = 323 K
After evaporation, weight of the dish along with the crystals = 72 g
To find :
Solubility of potassium nitrate
We know that the formula for calculating the solubility can be written as -
$\dfrac{{Mass{\text{ of salt (g)}}}}{{{\text{Mass of water (g)}}}}$ = $\dfrac{{{\text{Solubility of salt (g)}}}}{{{\text{100g water}}}}$
Mass of saturated solution of potassium nitrate = Weight of china dish and potassium nitrate -Weight of an empty china dish
Mass of saturated solution of potassium nitrate = 108 - 39
Mass of saturated solution of potassium nitrate = 69 g
Mass of water = Weight of china dish and potassium nitrate before - weight of the dish along with the crystals after drying
Mass of water = 108 - 72
Mass of water = 36 g
Mass of potassium nitrate = 69 - 36
Mass of potassium nitrate = 33 g
Thus, solubility can be calculated as -
$\dfrac{{Mass{\text{ of salt (g)}}}}{{{\text{Mass of water (g)}}}}$ = $\dfrac{{{\text{Solubility of salt (g)}}}}{{{\text{100g water}}}}$
On filling the values in above formula, we get
$\dfrac{{33}}{{36}}$ = $\dfrac{{{\text{Solubility of salt (g)}}}}{{{\text{100g water}}}}$
Therefore, solubility = 91.66

So, the correct answer is the option c.).

Note: It must be noted that the solubility of a compound in a solvent is fixed at a given temperature. It can be increased by increasing the temperature of the system. With an increase in temperature, the energy of the molecule increases and even solubility also increases.