If the solubility of KNO$_3$ at 30$^0$C is 3.10 mol/dm$^3$ a solution containing 303g/dm$^3$ KNO$_3$ is likely to be

To determine the state of the solution, we need to compare the concentration of the given solution with the solubility limit at the specified temperature.

1. Analyze the question

• Given Solubility: 3.10 mol/dm³ at 30°C.
• Given Concentration: 303 g/dm³.
• Molar Mass of KNO₃: K = 39, N = 14, O = 16. • Molar mass = 39 + 14 + (16 × 3) = 39 + 14 + 48 = 101 g/mol.

2. Explain the concept

• Solubility: The maximum amount of solute that can dissolve in a given volume of solvent at a specific temperature.
• Conversion: To compare the two values, we must convert the concentration from g/dm³ to mol/dm³ using the formula: $$\text{Concentration (mol/dm³)} = \frac{\text{Concentration (g/dm³)}}{\text{Molar Mass (g/mol)}}$$
• Comparison: • If the calculated concentration < solubility, the solution is unsaturated. • If the calculated concentration = solubility, the solution is saturated. • If the calculated concentration > solubility, the solution is supersaturated.

3. Show the solution

• Step 1: Convert the given concentration (303 g/dm³) to mol/dm³. $$\text{Concentration} = \frac{303 \text{ g/dm}^3}{101 \text{ g/mol}}$$ $$\text{Concentration} = 3.00 \text{ mol/dm}^3$$

• Step 2: Compare the values. • Solubility limit = 3.10 mol/dm³ • Actual concentration = 3.00 mol/dm³ • Since 3.00 mol/dm³ < 3.10 mol/dm³, the solution has not yet reached its maximum capacity to hold the solute.

4. Identify the answer

Because the concentration of the solution (3.00 mol/dm³) is less than the maximum solubility (3.10 mol/dm³), the solution is unsaturated.

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5. Exam Tip

When dealing with solubility questions, always check your units first! If the solubility is in mol/dm³ and the concentration is in g/dm³, you must convert them to the same unit before comparing. Remember: Molar Mass = Mass / Moles.