What is the apparent molecular mass (in g/mole) of a weak acid HA (molecular mass $= 30 g / mole$ ) in an aqueous solution, which shows elevation in boiling point by $0.015 6^{\circ} C$ ?(Assume molality = molarity)
Given: $K_{a}$ (HA) = $1 0^{- 2}$ , $k_{b}$ (H₂O) = $0.52 K kg mo l^{- 1}$

Question

What is the apparent molecular mass (in g/mole) of a weak acid HA (molecular mass $= 30 g / mole$ ) in an aqueous solution, which shows elevation in boiling point by $0.015 6^{\circ} C$ ?(Assume molality = molarity)

Given: $K_{a}$ (HA) = $1 0^{- 2}$ , $k_{b}$ (H₂O) = $0.52 K kg mo l^{- 1}$

TestHub · Accepted Answer

The boiling point elevation Δ T b ​ = i K b ​ m . Given Δ T b ​ = 0.015 6 ∘ C and K b ​ = 0.52 K k g m o l − 1 , the observed molality im = 0.52 0.0156 ​ = 0.03 . For HA ⇌ H⁺ + A⁻, i = 1 + α . K a ​ = 1 − α C α 2 ​ = 1 0 − 2 . From im = C ( 1 + α ) = 0.03 and K a ​ = 1 0 − 2 , we find C = 0.02 M and α = 0.5 . The apparent molecular mass is M a c t u a l ​ / i = 30/ ( 1 + 0.5 ) = 30/1.5 = 20 g / m o l e .

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