Question

How many moles of sodium chloride solute are in 155 grams of an 85.5 percent by mass solution?

Answer 1

Hint: The mass of solution and the percentage by mass is given to us in the question and we can find the mass of solute by using the following formula and then dividing it by the molar mass of NaCl will give the number of moles.
\[\text{Percent by mass}=\dfrac{\text{mass of solute}}{\text{mass of solution}}\times 100\]

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 sodium chloride, and the solution of it is prepared in water.
We are given the value of mass percent of the solution of sodium chloride as 85.5%, which means that 85.5 g of NaCl is present in 100 g of its solution in water. And we need to find the moles of NaCl that would present in 155 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:
\[\begin{align}
  & \text{85}\text{.5}=\dfrac{\text{mass of solute}}{\text{155 g}}\times 100 \\
 & \Rightarrow \text{mass of solute}=\dfrac{\text{85}\text{.5}\times \text{155 g}}{\text{100}} \\
 & \Rightarrow \text{mass of solute}=132.52\text{ g} \\
\end{align}\]
Now, the molar mass of sodium chloride is 58.44 grams per mole. Then, the number of moles (n) present in 132.52 grams of sodium chloride can be calculated as follows:
\[\begin{align}
  & \text{n}=\dfrac{\text{Given mass of NaCl}}{\text{Molar mass of NaCl}} \\
 & \Rightarrow \text{n}=\dfrac{132.52}{58.44} \\
 & \Rightarrow \text{n}=2.27 \\
\end{align}\]
Hence, 2.27 moles of sodium chloride are present in 155 grams of an 85.5 percent by mass solution

Additional information:
The highly concentrated solution of NaCl in water is known as brine 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.