Answer:
The molar mass of benzoic acid is 251.3 g/mol
Explanation:
∆T = m × Kb
m (molality) = ∆T/Kb = (77.5 - 76.5)/5.03 = 1/5.03 = 0.199 mol/kg
Molar mass of benzoic acid = mass of benzoic acid ÷ (molality × mass of CCl4 in kilograms) = 5 ÷ (0.199 × 100/1000) = 5 ÷ 0.0199 = 251.3 g/mol
The molar mass of benzoic acid in the solution based on the boiling point elevation is 251.3 g/mol.
The elevation in boiling point (ΔTb) is proportional to the concentration of the solute in the solution.
[tex]\triangle T = m * K_b\\\\m= \frac{\triangle T}{k_b}\\\\m=\frac{(77.5 - 76.5}{5.03} )\\\\m=\frac{1}{5.03}\\\\m= 0.199 mol/kg[/tex]
Given:
Mass of benzoic acid= 5.0g
To find:
Molar mass=?
[tex]\text{ Molar mass of benzoic acid} =\frac{\text{mass of benzoic acid}}{(\text{molality *mass of} CCl_4 \text{ in kilograms)} } \\\\\text{ Molar mass of benzoic acid}=\frac{5}{(0.199 × 100/1000)}\\\\\text{ Molar mass of benzoic acid}=\frac{5}{0.0199}\\\\\text{ Molar mass of benzoic acid} =251.3 g/mol[/tex]
Thus, the molar mass of benzoic acid is 251.3 g/mol.
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