Chemistry - Liquid Solution Question with Solution | TestHub

ChemistryLiquid SolutionColligative PropertiesMedium2 minQB

ChemistryMediumnumerical

Passage / Comprehension

A 10% by mass sugar solution has undergone partial inversion according to the reaction: Sugar (aq) + water → Glucose (aq) + Fructose (aq).

After 5 hours from the start of the reaction, the elevation in boiling point of the solution is $5/18$ . The reaction follows first-order kinetics with respect to sugar, and $K_{b}$ for water is $0.57 k g K m o l^{- 1}$ .

The time for $75%$ completion of the hydrolysis reaction is 5 y . What is the value of ' y ' (hrs) -

Answer:

2.00

Solution:

Initial Molality ( $m_{0}$ ): In a 10% sugar solution, $m_{0} = \frac{10 g}{342 g / m o l} \times \frac{1000}{90 g} \approx 0.325 m o l / k g$ .

Reaction Progress: For the reaction $S + H_{2} O \to G + F$ , the total molality at time $t$ is $(m_{0} - x) + x + x = m_{0} + x$ .

Find $x$ at $t = 5$ hrs: Using $Δ T_{b} = K_{b} \cdot m$ , we get $\frac{5}{18} = 0.57 \cdot (m_{0} + x)$ , which yields $m_{0} + x \approx 0.487 m o l / k g$ .

Determine Half-life: Since $x = 0.487 - 0.325 = 0.162$ , the remaining sugar is $m_{0} - x = 0.163$ , which is exactly half of $m_{0}$ . Thus, $t_{1/2} = 5 h o u rs$ .

Calculate $y$ : For a first-order reaction, 75% completion takes two half-lives: $t_{75%} = 2 \times 5 = 10 h o u rs$ .

Final Value: Comparing $t_{75%} = 10$ with the given expression $5 y$ , we find $y = 2$ .

Stream:JEESubject:ChemistryTopic:Liquid SolutionSubtopic:Colligative Properties

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...