A 1 M solution of a compound 'X' has a density of 1.25 g/mL. If the molar mass of compound X is 85 g, what is

Question

A 1 M solution of a compound 'X' has a density of 1.25 g/mL. If the molar mass of compound X is 85 g, what is the molality (m) of the solution?

Accepted Answer

1. **Understand Definitions:**
   - Molarity (M) = 1 mol/L [Class 12 Chemistry, Unit 1, Sec 1.2 (vi)]. This means there is 1 mole of solute 'X' in 1 Liter (1000 mL) of solution.
   - Density (d) = 1.25 g/mL.
   - Molar Mass (M_w) of X = 85 g/mol.

2. **Calculate Mass of Solution:**
   $$ 	ext{Mass of solution} = 	ext{Volume} 	imes 	ext{Density} $$
   $$ 	ext{Mass} = 1000 	ext{ mL} 	imes 1.25 	ext{ g/mL} = 1250 	ext{ g} $$

3. **Calculate Mass of Solute:**
   $$ 	ext{Mass of solute} = 	ext{Moles} 	imes 	ext{Molar Mass} $$
   $$ 	ext{Mass} = 1 	ext{ mol} 	imes 85 	ext{ g/mol} = 85 	ext{ g} $$

4. **Calculate Mass of Solvent:**
   $$ 	ext{Mass of solvent} = 	ext{Mass of solution} - 	ext{Mass of solute} $$
   $$ 	ext{Mass} = 1250 	ext{ g} - 85 	ext{ g} = 1165 	ext{ g} = 1.165 	ext{ kg} $$

5. **Calculate Molality (m):**
   $$ 	ext{Molality (m)} = \frac{	ext{Moles of solute}}{	ext{Mass of solvent in kg}} $$ [Class 12 Chemistry, Unit 1, Sec 1.2 (vii)]
   $$ m = \frac{1 	ext{ mol}}{1.165 	ext{ kg}} \approx 0.858 	ext{ mol kg}^{-1} $$

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