Percent Concentration — Calculation & Role in Solutions

We've been looking at the different types of solution concentration. So far, we've looked at molarity and molality. Both are important to laboratory chemists. But, in chemical engineering and industrial production, molarity and molality are inconvenient. The quantities of chemicals are too large! So we need a unit for enormous amounts.

We created percentage concentrations to deal with non-laboratory applications. There are three types of percent concentration. We'll look at each one in turn.

Mass Percent

We use mass percent when it's easiest to measure the weight of the solute and solvent. Mass percent is most common in industrial applications. For example, we mix 400.0 pounds of sodium chloride ($NaCl$) with 500.0 pounds of water. In industrial applications, we don't care about using SI units.

The formula is $Mass\,Percent= \frac{mass_{solute}}{mass_{total}}\times 100\%$.

Volume Percent

We use volume percent when we mix pure liquids. So, it's easiest to measure the solute's and solvent's volume. Again, volume percent is most common in industrial applications. For example, we might add 500.0 gallons of liquid solute to 1000.0 gallons of water. However, we need to account for the density change. That's because liquid volumes are not additive. In the example, our final solution is not 1500.0 gallons.

Why don't liquid volumes add? Volume depends on intermolecular forces. For example, in pure water, each hydrogen-oxygen bond is polar. So, each molecule of water hydrogen bonds twice. But, the organic compound ethanol only has one hydrogen-oxygen bond. So it only hydrogen bonds once. We've disrupted water's electrostatic interactions. We account for this by factoring in the change in density. This is also true for molecules that experience dispersion, dipole-dipole, or ion-dipole interactions.

The formula is $Volume\,Percent = \frac{Volume_{Solute}}{Volume_{Total}}\times \frac{density_{solution}}{density_{Solute}}\times 100\%$.

Mass/Volume Percent

Sometimes we have the mass of the solute and volume of the solvent. Mass/Volume percent is unique because the units don't cancel. Instead, we get grams of solute per volume of solvent. But isn't that density? Not quite. Density is mass per volume. But, this is specifically solute mass per solution volume. So, it tells us the grams of solute in 100.0 ml of solution. Typically, these solutions are dilute enough that we can ignore changes in density.

The most common application for mass/volume percent is in medical care. Many medicines are in grams per 100.0 ml of solvent. These drugs are delivered intravenously.

The fromula is $Mass/Vol.\, Percent=\frac{mass_{solute}}{Volume_{solution}}\times 100\%$.

Example Problems

Mass Percent

Say we make a saline solution from 400.0 pounds of NaCl and 500.0 pounds of water. What is the mass percent of NaCl?

$Mass\,Percent=\frac{400.0Lb_{NaCl}}{500.0Lb_{water}+400.0LB{NaCl}}\times 100\%=44.4 (m/m)\%$

What is the mass percent of NaCl if we mix 35.0g NaCl with 130.0ml of water?

For this problem, we need to remember that the density of water is $1.0\frac{g}{ml}$.

$Mass\, Percent=\frac{35.0g_{NaCl}}{35.0g+130.0g}\times 100\%= 21.2(m/m)\%$

You want to make 2500.0 grams of 3.0 (m/m)% sodium chloride solution. What mass of sodium chloride do you need? (Hint: this is just a dimensional analysis problem.)

$2500.0 g_{NaCl\,solution} \times \frac{3.0g_{NaCl}}{100g_{NaCl\,Solution}} = 75.0g_{NaCl}$

Volume Percent

Calculate the volume percent from mixing 500.0 gallons of ethanol with 1000.0 gallons of water. The density of ethanol is $6.5 \frac{Lb}{gal}$. The density of the final solution is $7.7\frac{Lb}{gal}$.

$Volume\, Percent=\frac{Volume_{Solute}}{Volume{Total}}\times \frac{density_{solution}}{density{Solute}}\times 100\% = \frac{500.0 gal}{1500.0 gal}\times\frac{7.7}{6.5}\times 100\% = 39.4 (v/v)\%$

Mass/Volume Percent

We create a 700.0 ml solution by dissolving 232.0 grams of Sodium Chloride in water. What is the mass/volume percent?

$Mass/Vol.\,Percent=\frac{mass_{solute}}{Volume_{solution}}\times 100\%=\frac{232.0g}{700.0ml} \times 100\% = 33.1 (m/v)\%$

(Video) Expressing Concentration by Mass Percent

by Professor Dave Explains

In this video, Professor Dave explains percent concentration. He'll tell you what it is, why we use it, and how to calculate it. He'll also show a couple of example problems. This video is a clear and concise explanation!