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Question: Find the solubility of $KNO_3$ at $20^\circ C$, when the mass of the empty dish is 50 g, the mass of...

Find the solubility of KNO3KNO_3 at 20∘C20^\circ C, when the mass of the empty dish is 50 g, the mass of dish and solution is 65 g, while the mass of dish and residue is 54.3 g.

Answer

40.2 g per 100 g of water

Explanation

Solution

The solubility of a substance is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature, expressed as grams of solute per 100 grams of solvent.

Given:

  1. Mass of empty dish = 50 g
  2. Mass of dish and solution = 65 g
  3. Mass of dish and residue (KNO3KNO_3) = 54.3 g

1. Calculate the mass of the solution:

Mass of solution=Mass of dish and solution−Mass of empty dish\text{Mass of solution} = \text{Mass of dish and solution} - \text{Mass of empty dish}

Mass of solution=65 g−50 g=15 g\text{Mass of solution} = 65 \, \text{g} - 50 \, \text{g} = 15 \, \text{g}

2. Calculate the mass of the solute (KNO3KNO_3):

Mass of KNO3=Mass of dish and residue−Mass of empty dish\text{Mass of } KNO_3 = \text{Mass of dish and residue} - \text{Mass of empty dish}

Mass of KNO3=54.3 g−50 g=4.3 g\text{Mass of } KNO_3 = 54.3 \, \text{g} - 50 \, \text{g} = 4.3 \, \text{g}

3. Calculate the mass of the solvent (water):

Mass of solvent=Mass of solution−Mass of solute\text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute}

Mass of solvent=15 g−4.3 g=10.7 g\text{Mass of solvent} = 15 \, \text{g} - 4.3 \, \text{g} = 10.7 \, \text{g}

4. Calculate the solubility of KNO3KNO_3:

Solubility=(Mass of KNO3Mass of water)×100\text{Solubility} = \left( \frac{\text{Mass of } KNO_3}{\text{Mass of water}} \right) \times 100

Solubility=(4.3 g10.7 g)×100\text{Solubility} = \left( \frac{4.3 \, \text{g}}{10.7 \, \text{g}} \right) \times 100

Solubility≈40.2 g per 100 g of water\text{Solubility} \approx 40.2 \, \text{g per 100 g of water}