Question

Calculate molality of a solution of 5.0 g of ethanoic acid (CH}_3\textbf{COOH) in 150.0 g of benzene.

Hint:

Molality is particularly useful for temperature-dependent solutions because it does not change with temperature, unlike molarity, which can change due to volume expansion or contraction. Always ensure that the mass of the solvent is converted to kilograms when calculating molality.

Answer 1

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. The formula for molality \( m \) is: \[ m = \frac{n_{\text{solute}}}{m_{\text{solvent}}} \] Where: - \( m_{\text{solute}} \) is the number of moles of solute (in this case, ethanoic acid),
- \( m_{\text{solvent}} \) is the mass of the solvent (benzene) in kilograms.
We are given:
- Mass of ethanoic acid \( = 5.0 \, \text{g} \),
- Mass of benzene \( = 150.0 \, \text{g} = 0.150 \, \text{kg} \),
- Molar mass of ethanoic acid \( (CH_3COOH) = 60.0 \, \text{g/mol} \).
Step 1: Calculate the number of moles of ethanoic acid (solute).
The number of moles \( n_{\text{solute}} \) is calculated by the formula: \[ n_{\text{solute}} = \frac{\text{Mass of solute}}{\text{Molar mass}} = \frac{5.0 \, \text{g}}{60.0 \, \text{g/mol}} = 0.0833 \, \text{mol} \] Step 2: Calculate molality using the formula.
Now, we can use the formula for molality: \[ m = \frac{0.0833 \, \text{mol}}{0.1500 \, \text{kg}} = 0.5567 \, \text{mol/kg} \] Thus, the molality of the solution is \( 0.5567 \, \text{mol/kg} \).