Question

A 20% sugar solution has a volume of 500mL. How many grams of sugar does it contain?

Answer 1

Hint: Assuming the sugar to be glucose, find the mass of sugar in the respective volume of the solvent by calculating it for 20% solution and the correct answer is obtained by this method of calculation.

Complete step by step solution:
In the previous classes, we have studied the basic calculations that include calculation of molar mass of a compound, calculation of molarity and molality, calculation of normality and also other physical quantities.
Let us see the calculation of grams of sugar present in the given solution.
- The data provided to us is that the volume of the solution is 500 mL and 20% of this solution is nothing but sugar.
- Thus, based on this data we can say that volume of sugar in the solution will be,
\[500mL\times \dfrac{20}{100}\] [Since, 20% = 20/100]
Now, by simplifying this above calculation we get the volume of sugar in the solution as 100 mL.
Let us assume that sugar in this particular case is a pure glucose where this glucose molecule has the molecular formula ${{C}_{6}}{{H}_{12}}{{O}_{6}}$.
To find the molar mass of sugar, we must multiply the volume sugar which was found above by its density.
- Now, glucose has the density $1.54g/c{{m}^{3}}$ . Since, $1g/c{{m}^{3}}=1mL$ , we can write this density also as $1.54g/mL$.
Hence, mass of the sugar in the solution will be$=100mL\times 1.54g/mL=154g$
Thus, the correct answer is that 154g of sugar is present in 20% of sugar solution which has a volume of 500mL.

Note:
Note that density of any solution can be written in different units wherein it is the ratio of mass of an object and its volume and by using this mass and volume of the compound can also be found.