JEE Advance - Chemistry (1983 - No. 5)

3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molality if the solution is _____.
0.1 m
0.2 m
0.3 m
0.4 m
0.5 m

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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