Question

What is the mole fraction of glucose in \[10\% {\text{w/w}}\] glucose solution?
A. $0.01$
B. $0.02$
C. $0.03$
D. $0.04$

Answer 1

Hint: To answer this question, you should recall the formula for calculating mole fraction which involves the calculation of moles of solute and solvent. Number of moles can be calculated by dividing the given mass with the molecular mass of the component. Now use these values to arrive at the final answer.

Formula used:
1) Mole fraction = $\dfrac{{{{\text{X}}_{\text{A}}}}}{{{{\text{X}}_{\text{A}}}{\text{ + }}{{\text{X}}_{\text{B}}}}}$(from the above definition) where ${{\text{X}}_{\text{A}}}$ is no. of moles of glucose and \[{{\text{X}}_{\text{B}}}\] is the no. of moles of solvent---(i)
2) No. of Moles = \[\dfrac{{{\text{Given mass}}}}{{{\text{Molar Mass}}}}\]---(ii)

Complete Step by step answer:
We know the definition of mole fraction i.e. it is a way of expressing the concentration of a solution and can be calculated by dividing the number of molecules of a particular component in a mixture by the total number of moles in the given mixture. Now using the above definition let’s find the answer to this question. The components of a solution are solute and solvent, therefore we need to calculate the number of moles of these components to find the correct answer.
The question states \[10\% {\text{w/w}}\] glucose solution. \[{\text{w/w}}\] is used to depict the strength of a solution. For example, Magnesium Hydroxide \[10\% {\text{w/w}}\] means that a given solution contains 10g of Magnesium Hydroxide in 100g of solution. Thus, \[10\% {\text{w/w}}\] glucose will mean that 10g glucose is present in 100g of solution. We can conclude that given mass of solute (glucose) = 10g and given mass of solvent (water) = 90g
To calculate the no. of moles of glucose we know the molar mass of glucose = \[180{\text{ gmo}}{{\text{l}}^{ - 1}}\] and substituting this value in equation (i)
Thus, no. of moles of glucose ${{\text{X}}_{\text{A}}} = \dfrac{{10}}{{180}} = 0.0555$ moles
Again, we need to calculate the moles of water so substituting the molar mass of water = \[18{\text{ gmo}}{{\text{l}}^{ - 1}}\] in equation (i)
Thus, no. of Moles of water \[{{\text{X}}_{\text{B}}} = \dfrac{{90}}{{18}} = 5\] moles
We now can calculate the total moles of the solution ${{\text{X}}_{\text{A}}}{\text{ + }}{{\text{X}}_{\text{B}}}$ and put this value in equation (ii)
Now plugging the values into the formula of mole fraction = \[\dfrac{{0.0555}}{{0.0555 + 5}}\]
We get the value of Mole fraction as = \[0.01\]

Therefore, we can conclude that the correct answer to this question is option A.

Note: Make sure that you observe the units of the given concentration. \[\% {\text{w/w}}\] is weight concentration of a solution: If a solution is labelled as \[10\% \] glucose in water by mass, it refers to that 10g of glucose is dissolved in 90 g of water resulting in 100g of solution. $\% $\[{\text{v/v}}\] is the volume concentration of a solution: it refers that if 50 mL of acetic acid is added to 50 mL of water, the acetic acid is labelled as \[50\% {\text{v/v}}\]. $\% {\text{w/v}}$ is the mass concentration of a solution: if x grams/ml of solute are present in solution it means x gram of solute is dissolved in 100ml of solution.