Pragya tested the solubility of four different substances at different temperatures and collected the data as given below (results are given in the following table,as grams of substance dissolved in $100 \,g$ of water to form a saturated solution).
Substance Dissolved $283 \,K$ $293 \,K$ $313 \,K$ $333 \,K$ $353 \,K$ Potassium nitrate $21$ $32$ $62$ $106$ $167$ Sodium chloride $36$ $36$ $36$ $37$ $37$ Potassium chloride $35$ $35$ $40$ $46$ $54$ Ammonium chloride $24$ $37$ $41$ $55$ $66$
$(a)$ What mass of potassium nitrate would be needed to produce a saturated solution of potassium nitrate in $50 \,g$ of water at $313 \,K$?
$(b)$ Pragya makes a saturated solution of potassium chloride in water at $353 \,K$ and leaves the solution to cool at room temperature. What would she observe as the solution cools? Explain.
| Substance Dissolved | $283 \,K$ | $293 \,K$ | $313 \,K$ | $333 \,K$ | $353 \,K$ |
| Potassium nitrate | $21$ | $32$ | $62$ | $106$ | $167$ |
| Sodium chloride | $36$ | $36$ | $36$ | $37$ | $37$ |
| Potassium chloride | $35$ | $35$ | $40$ | $46$ | $54$ |
| Ammonium chloride | $24$ | $37$ | $41$ | $55$ | $66$ |
$(a)$ What mass of potassium nitrate would be needed to produce a saturated solution of potassium nitrate in $50 \,g$ of water at $313 \,K$?
$(b)$ Pragya makes a saturated solution of potassium chloride in water at $353 \,K$ and leaves the solution to cool at room temperature. What would she observe as the solution cools? Explain.
(N/A) According to the table,the solubility of potassium nitrate at $313 \,K$ is $62 \,g$ per $100 \,g$ of water.
To find the mass needed for $50 \,g$ of water:
Mass $= (62 \,g / 100 \,g) \times 50 \,g = 31 \,g$.
Thus,$31 \,g$ of potassium nitrate is required.
$(b)$ As the solution cools,Pragya will observe the formation of crystals of potassium chloride. This occurs because the solubility of most solid solutes in water decreases as the temperature decreases. When the solution cools,it becomes supersaturated,and the excess solute crystallizes out of the solution.
To find the mass needed for $50 \,g$ of water:
Mass $= (62 \,g / 100 \,g) \times 50 \,g = 31 \,g$.
Thus,$31 \,g$ of potassium nitrate is required.
$(b)$ As the solution cools,Pragya will observe the formation of crystals of potassium chloride. This occurs because the solubility of most solid solutes in water decreases as the temperature decreases. When the solution cools,it becomes supersaturated,and the excess solute crystallizes out of the solution.
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