JEE Advance - Chemistry (1983 - No. 5)
Explanation
To find the molality of the solution, we'll first understand the definition. Molality ($m$) is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:
$m = \frac{\text{moles of solute}}{\text{kg of solvent}}$
Given that the mass of the salt is 3 g and its molecular weight is 30 g/mol, we can calculate the moles of solute (salt) using the formula:
$ \text{moles of solute} = \frac{\text{mass of solute}}{\text{molecular weight of solute}} $
$ \text{moles of salt} = \frac{3 \, \text{g}}{30 \, \text{g/mol}} $
$ \text{moles of salt} = 0.1 \, \text{mol} $
We also have 250 g of water as the solvent. Since molality requires the mass of the solvent to be in kilograms, we convert the mass of water to kilograms:
$ 250 \, \text{g} = 0.250 \, \text{kg} $
Now, we can substitute the values into the molality formula:
$ m = \frac{0.1 \, \text{mol}}{0.250 \, \text{kg}} $
$ m = 0.4 \, \text{mol/kg} $
Therefore, the molality of the solution is $0.4 \, \text{mol/kg}$.
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