Solutions Question 254

Question: How many grams of sucrose (M. wt. = 342) should be dissolved in 100 g water in order to produce a solution with a $ 105.0{}^\circ C $ difference between the boiling point and the freezing temperatures- $ (K_{f}=1.86C\text{/}m,K_{b}=0.51{}^\circ C\text{/}m) $

Options:

A) 34.2 g

B) 72 g

C) 342 g

D) 460 g

Show Answer

Answer:

Correct Answer: B

Solution:

$ T_{b}-T_{f}=105=100+5 $

$ T_{b}-T_b^{0}-T_{f}=5 $

$ [\because T_b^{o}=100{}^\circ C] $

$ \Delta T_{b}-T_{f}+T_f^{o}-T_f^{o}=5 $
$ \Rightarrow \Delta T_{b}+\Delta T_{f}=5 $

$ [\because T_f^{o}=0{}^\circ C] $

$ \Delta T_{f}+\Delta T_{b}=m(k_{f}+k_{b}) $

$ \Delta T_{f}+\Delta T_{b}=5=\frac{x}{\frac{342}{\frac{100}{1000}}}(1.86+0.51) $

$ 5=\frac{10x}{342}\times 2.37\Rightarrow x=72,g $



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