Question

How many grams of sugar would you need to add to water to make 235 grams of a $7\%$ solution? Using this formula:
\[\text{Percent by mass}=\dfrac{\text{mass of solute}}{\text{mass of solution}}\times 100\]

Answer 1

Hint: The mass of solution and the percentage by mass is given to us in the question and we only need to find the mass of solute by using the above formula.

Complete answer:
One of the methods to calculate the chemical composition of a solution is to calculate the percent composition by mass.
It is defined as the mass of solute dissolved per 100 grams of its solution in any solvent. In this case, our solute is sugar, and water is used as a solvent.
We are given the value of mass percent of the solution of sugar in water as 7%, which means that 7 g of sugar is present in 100 g of its solution in water. And we need to find the mass of sugar that would present in 235 g of this solution.
The formula of percent by mass is:
\[\text{Percent by mass}=\dfrac{\text{mass of solute}}{\text{mass of solution}}\times 100\]
Putting the values in the formula, we get:
\[\begin{align}
  & \text{7}=\dfrac{\text{mass of solute}}{\text{235 g}}\times 100 \\
 & \Rightarrow \text{mass of solute}=\dfrac{\text{7}\times \text{235 g}}{\text{100}} \\
 & \Rightarrow \text{mass of solute}=16.45\text{ g} \\
\end{align}\]
Hence, 16.45 grams of sugar would be needed to make 235 grams of a $7\%$ solution.

Note:
The numerator and denominator, in the mathematical equation of percent by mass, denote the mass of solute and solution respectively, and thus they both have the same units (that is, grams). So, the units in numerator and denominator will cancel each other out and we get a percentage value of mass composition.