Calculate the number of moles of nonvolatile solute dissolved in 0.5 kg solvent if molal elevation constant for solvent is 2 kg K mol$^{-1}$ [$\Delta T_b = 0.8$ K].
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Always ensure the mass of the solvent is in kilograms when using the molality equation. If it is given in grams, divide by 1000 before substituting into the formula.
Step 1: Understanding the Concept:
The elevation in boiling point ($\Delta T_b$) is proportional to the molality ($m$) of the solution: $\Delta T_b = K_b \times m$. Step 2: Formula Application:
$m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}$.
$\Delta T_b = K_b \times \frac{n}{W_{kg}}$. Step 3: Explanation:
$0.8 = 2 \times \frac{n}{0.5}$
$0.8 = 4n$
$n = \frac{0.8}{4} = 0.2$ moles. Step 4: Final Answer:
The number of moles of solute is 0.2.