Potassium trioxochlorate (V)has a solubility of 1.5 mol dm -3 at 45 oC.On cooling this solution to a…

1. Analyze the Question

We are given the solubility of Potassium trioxochlorate (V) ($KClO_3$) at two different temperatures. We need to find the mass of the salt that crystallizes out when the solution is cooled from $45^\circ C$ to $20^\circ C$.

2. Explain the Concept

• Solubility: This is the amount of solute that dissolves in a given volume of solvent (usually $1 dm^3$ or $1000 cm^3$) at a specific temperature.
• Crystallization: When a saturated solution is cooled, its solubility decreases. The difference between the initial solubility and the final solubility represents the amount of solute that can no longer stay dissolved and therefore forms crystals.
• Molar Mass Calculation: To convert moles to grams, we use the formula: $$\text{Mass} = \text{Number of moles} \times \text{Molar Mass}$$

3. Show the Solution

Step 1: Calculate the molar mass of $KClO_3$

• $K = 39$
• $Cl = 35.5$
• $O = 16 \times 3 = 48$
• $\text{Molar Mass} = 39 + 35.5 + 48 = 122.5 \, g/mol$

Step 2: Calculate the number of moles that crystallized out

• Solubility at $45^\circ C = 1.5 \, mol/dm^3$
• Solubility at $20^\circ C = 0.5 \, mol/dm^3$
• $\text{Moles crystallized} = 1.5 - 0.5 = 1.0 \, mol$

Step 3: Convert the moles to mass

• $\text{Mass} = \text{moles} \times \text{molar mass}$
• $\text{Mass} = 1.0 \, mol \times 122.5 \, g/mol$
• $\text{Mass} = 122.5 \, g$

4. Identify the Answer

Comparing our result to the given options, the correct value is 122.50g.

This matches option D.

5. Exam Tip

When dealing with solubility questions, always check the units carefully. If the question gives you solubility in $mol/dm^3$ but asks for mass in grams, you must calculate the molar mass of the compound and multiply it by the change in concentration. Don't forget to sum the atomic masses correctly!