# What do you divide the mass of to calculate the percent concentration of a solution?

May 1, 2014

You divide by the mass of the solution.

Percent by mass is the mass of the solute divided by the mass of the solution, multiplied by 100.

% by mass = $\left(\text{mass of solute")/("mass of solution}\right)$ × 100 % = $\left(\text{mass of solute")/("mass of solute + mass of [solvent](http://socratic.org/chemistry/solutions-and-their-behavior/solvent)}\right)$ × 100 %

Example:

You dissolve a 4.00 g sugar cube in 350 mL of tea at 80 °C. The density of water at 80 °C is 0.975 g/mL. What is the percent by mass of sugar in the solution?

Solution

Step 1 — Determine mass of the solute.

The solute is the sugar cube. Mass of solute = 4.00 g.

Step 2 — Determine mass of solvent.

The solvent is the 80 °C water. Use the density of the water to find the mass.

mass of solvent = 350 mL × $\left(0.975 \text{ g")/(1" mL}\right)$ = 341 g

Step 3— Determine the total mass of the solution

mass of solution = mass of solute + mass of solvent = 4.00 g + 341 g = 345 g

Step 4 — Determine percent composition by mass of the sugar solution.

% by mass = $\left(\text{mass of solute")/("mass of solution}\right)$ × 100 % = $\left(4.00 \text{ g")/(345" g}\right)$ × 100 % = 1.159 %

The percent composition by mass of the sugar solution is 1.159 %.