A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{3}{5}\]
D) \[\frac{2}{3}\]
Correct Answer: B
Solution :
Assume that the total masses of solutes in the two solutions 1 and 2 are 3 m and 5 m respectively. Then, if \[{{M}_{1}}\] and \[{{M}_{2}}\] are the molar masses, the total number of moles in a given volume of solution 1 at T K is \[\frac{1.5m}{{{M}_{1}}}+\frac{1.5m}{{{M}_{2}}}\] In solutions 2, this number is \[\frac{0.5m}{{{M}_{1}}}+\frac{4.5m}{{{M}_{2}}}\] The solutions are isotonic \[\therefore \] \[\frac{1.5m}{{{M}_{1}}}+\frac{1.5m}{{{M}_{2}}}=\frac{0.5m}{{{M}_{1}}}+\frac{4.5m}{{{M}_{2}}}\] By calculation, \[\frac{1}{{{M}_{1}}}=\frac{3}{{{M}_{2}}}\] \[\therefore \] \[\left( \frac{{{M}_{1}}}{{{M}_{2}}} \right)=\frac{1}{3}\]
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