# How can I find percent concentration from density?

Jul 21, 2014

This is usually part of a problem that asks you to convert from one set of concentration units to another.

For example, you need the density to convert from molarity to percent concentration.

Here's a typical problem.

What is the percent concentration of a 13.0 mol/L solution of phosphoric acid that has a density of 1.464 g/mL?

1, Assume some fixed volume of the solution.

For convenience, let's assume a volume of 1 L.

2. Calculate the mass of H₃PO₄.

1 L soln × $\left(13.0 \text{mol H₃PO₄")/(1"L soln") × (98.00"g H₃PO₄")/(1"mol H₃PO₄}\right)$ = 1274 g H₃PO₄ (3 significant figures + 1 guard digit)

3. Use the density to calculate the mass of the solution.

1000 mL soln × $\left(1.464 \text{g soln")/(1"mL soln}\right)$ = 1464 g soln

4. Calculate the percent concentration

% by mass = $\text{mass of [solute](http://socratic.org/chemistry/solutions-and-their-behavior/solute)"/"mass of solution}$ × 100 % = $\left(1274 \text{g")/(1464"g}\right)$ × 100 % = 87.0 % (3 significant figures)

The solution is 87.0 % H₃PO₄ by mass.