Question

Maltose is converted to A by Maltase. The mole fraction of A in $ 10\% \left( {{\text{w}}/{\text{w}}} \right) $ aq. Solution is approximately.
(A) $ 0.989 $
(B) $ 0.012 $
(C) $ 0.1 $
(D) $ 0.017 $

Answer 1

Hint: Percentage by mass gives us the mass of A present in 100 gram of solution. Using molecular mass we will first calculate the number of moles and hence the mole fraction of A.

Complete step by step solution:
Percentage by weight is defined as the mass of substance that is present in 100 gram of solution. We have been given the solution of A is $ 10\% \left( {{\text{w}}/{\text{w}}} \right) $ . According to this the mass of A is 10 gram. The total mass of the solution is 100 gram. Hence the mass of water will be $ 100 - 10 = 90 $
The compound A produced is glucose.
The molecular formula for glucose is $ {{\text{C}}_6}{{\text{H}}_{12}}{{\text{O}}_6} $ hence we will calculate the molecular mass as:
 $ 6 \times 12 + 12 \times 1 + 6 \times 16 = 180 $
Using the given mass of glucose and molecular mass of maltose we will calculate the number of moles of glucose as:
 $ {\text{number of moles}} = \dfrac{{10}}{{180}} = 0.056 $
Now we know that the molecular weight of water is 18 and the given mass of water is 90. So the number of moles of water will be:
 $ {\text{number of moles}} = \dfrac{{90}}{{18}} = 5 $
The mole fraction for any substance is defined as the number of moles of that substance to the total number of moles present in solution. In our case the solution contains only two substances that are water and maltose. Hence the mole fraction of glucose will be:
 $ \dfrac{{0.056}}{{0.056 + 5}} = 0.011 $
The closest option to this value is option B and hence, is the correct option.

Note:
Maltase is an enzyme that is present in the small intestine. It helps in breaking down of the disaccharide that is Maltose into glucose. Enzymes are biological catalysts. First of all starch breaks down to Maltose and then further to glucose.