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Difficulty: MediumSolubility Calculations and Concentration Determination

What is the solubility in mol/dm3\text{mol/dm}^3 of potassium trioxonitrate(V), KNO3\text{KNO}_3, at 40∘C40^\circ\text{C} if 50.5 g50.5\text{ g} of the salt dissolves completely in 250 cm3250\text{ cm}^3 of water to form a saturated solution? [K=39,N=14,O=16][\text{K} = 39, \text{N} = 14, \text{O} = 16]

  1. A
    0.50 mol/dm30.50\text{ mol/dm}^3
  2. 2.00 mol/dm32.00\text{ mol/dm}^3Answer
  3. C
    5.05 mol/dm35.05\text{ mol/dm}^3
  4. D
    202.00 mol/dm3202.00\text{ mol/dm}^3

Answer

The solubility of potassium trioxonitrate(V) at 40∘C40^\circ\text{C} is 2.00 mol/dm32.00\text{ mol/dm}^3.
The correct answer is 2.00 mol/dm32.00\text{ mol/dm}^3. First, determine the molar mass of KNO3\text{KNO}_3, which is 39+14+(3×16)=101 g/mol39 + 14 + (3 \times 16) = 101\text{ g/mol}. Converting 50.5 g50.5\text{ g} of KNO3\text{KNO}_3 into moles gives 0.50 mol0.50\text{ mol}. Converting 250 cm3250\text{ cm}^3 of water into dm3\text{dm}^3 gives 0.25 dm30.25\text{ dm}^3. Dividing 0.50 mol0.50\text{ mol} by 0.25 dm30.25\text{ dm}^3 yields a molar solubility of 2.00 mol/dm32.00\text{ mol/dm}^3.

Step-by-Step Solution

1
Calculate the molar mass of KNO3\text{KNO}_3
Molar mass of KNO3=39+14+3(16)=101 g/mol\text{Molar mass of KNO}_3 = 39 + 14 + 3(16) = 101\text{ g/mol}
Molar mass is required to convert the given mass of salt into number of moles.
2
Convert the mass of KNO3\text{KNO}_3 to moles
Moles of KNO3=50.5 g101 g/mol=0.50 mol\text{Moles of KNO}_3 = \frac{50.5\text{ g}}{101\text{ g/mol}} = 0.50\text{ mol}
Solubility in mol/dm3\text{mol/dm}^3 requires solute quantity to be in moles.
3
Convert the volume of water from cm3\text{cm}^3 to dm3\text{dm}^3
Volume=250 cm31000=0.25 dm3\text{Volume} = \frac{250\text{ cm}^3}{1000} = 0.25\text{ dm}^3
Standard molarity and molar solubility use cubic decimeters (dm3\text{dm}^3) as the volume unit.
4
Calculate molar solubility
Solubility=0.50 mol0.25 dm3=2.00 mol/dm3\text{Solubility} = \frac{0.50\text{ mol}}{0.25\text{ dm}^3} = 2.00\text{ mol/dm}^3
Solubility in mol/dm3\text{mol/dm}^3 is defined as moles of solute per cubic decimeter of saturated solution.

Key Concept

Solubility in mol/dm3\text{mol/dm}^3 measures the maximum number of moles of solute that dissolve in 1 dm31\text{ dm}^3 of solvent at a specific temperature.
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Topics

Solubility Calculations and Concentration Determination

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