25.0g of potassium chloride were dissolved in 80g of distilled water at 30$^0$C. Calculate the solubility of the solute in mol dm$^3$. [K =39, Cl = 35.5]

To solve this problem, we need to determine the concentration of the potassium chloride (KCl) solution in $\text{mol dm}^{-3}$.

1. Analyze the Question

• Mass of solute (KCl): $25.0\text{ g}$
• Mass of solvent (water): $80\text{ g}$
• Molar mass of KCl: $K(39) + Cl(35.5) = 74.5\text{ g/mol}$
• Density of water: $1\text{ g/cm}^3$ (therefore, $80\text{ g}$ of water = $80\text{ cm}^3$ or $0.08\text{ dm}^3$)

2. Explain the Concept

Solubility in $\text{mol dm}^{-3}$ (Molarity) is defined as the number of moles of solute dissolved in $1\text{ dm}^3$ of the solvent.

• Step 1: Calculate the number of moles of KCl.
• Step 2: Convert the volume of the solvent to $\text{dm}^3$.
• Step 3: Divide the moles by the volume in $\text{dm}^3$.

3. Show the Solution

Step 1: Calculate the number of moles of KCl

Step 2: Determine the volume of the solvent in $\text{dm}^3$ Since $1000\text{ cm}^3 = 1\text{ dm}^3$:

Step 3: Calculate Molarity

Rounding to one decimal place, we get $4.2\text{ mol dm}^{-3}$.

4. Identify the Answer

Comparing our result to the given options, the correct value is $4.2\text{ mol dm}^{-3}$. This matches option D.

5. Exam Tip

Always remember that in chemistry calculations involving water as a solvent, the mass of water in grams is numerically equal to its volume in milliliters ($1\text{ g} = 1\text{ cm}^3$). Don't forget to convert $\text{cm}^3$ to $\text{dm}^3$ by dividing by $1000$ before calculating molarity!