# How to Calculate Mole Fractions Using Mass Percent

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You can determine the concentration of solute in a solution as a weight-to-weight percentage, a weight-to-volume percentage or volume-to-volume percentage. In this context, weight is synonymous with mass, so a mass percentage means the relative weight of the solute to the weight of the solution, and you can express it as "percent by weight." However, it's also common to relate weight to volume and express the result as "percent weight to volume." Either way, as long as you know the chemical formulas for the solute and solvent (which is usually water), the weight percentage allows you to calculate how many moles of solute are present in the solution. From this, it's possible to determine the molarity of the solution, which is the number of moles of solute per liter of solution.

#### TL;DR (Too Long; Didn't Read)

If you know the percent by weight of a solution, you can find the weight of solute. Divide this by its molecular weight to find the number of moles and divide by the volume of solution to find the molarity.

## Percent by Weight vs. Percent Weight to Volume

You can express a percent by weight solution as x percent of solute by weight. This is the preferred method for expressing concentration of commercial acid solutions. For example, commercial concentrated hydrochloric acid is usually a 37 percent by weight solution. It makes more sense to express very dilute aqueous solutions, such as those used in biological research, as percent weight to volume. Since water has a density of 1 g/ml, this amounts to a percent by weight, since a given number of milliliters of water weighs that number of grams.

## Molarity of a Percent by Weight Solution

Suppose you have an x percent solution that weighs W grams. The weight of solute is then Ws = x/100 • W. Look up the molecular weight of the compound and divide that number into Ws to find the number of moles you have on hand. To find molarity, measure the volume of the solution and divide that into the number of moles. For this calculation work, be sure to convert weight units to grams and volume units to liters first.

## Molarity Examples

What is the molarity of 900 milliliters of a 37 percent by weight solution of HCl?

The weight of solute in the solution is 37/100 •50 g = 18.5 g. HCl consists of one hydrogen atom (atomic weight 1 g/mole) and one chlorine atom (atomic weight 35 g/mole), so its molecular weight is 36 g/mole. Divide this into the weight in the solution, to get 0.51 moles. To find molarity, divide this number by the volume, which is 0.09 liters. The answer is 5.7 moles/liter.

What is the molarity of 3 ounces of a 3 percent saline solution?

You can assume this is a weight-to-volume concentration. It makes calculations easier if you convert volume to liters, so use this conversion: 1 ounce = 0.03 liters. You have 0.09 liters of solution or 90 milliliters. Since water weighs 1 gram per milliliter, the weight of the sample is 90 grams. It's a 3 percent solution, so the weight of the solute is 3/100 • 90 = 2.7 g.

The chemical formula of salt is NaCl, and given that the atomic weights of sodium and chlorine are 23 g/mole and 35 g/mole respectively, its molecular weight is 58 g/mole.

Divide the molecular weight into the weight of solute in the solution to find the number of moles: 2.7 g ÷ 58 g/mole = 0.047 moles.

Divide by the volume of the solution to find molarity: M = (0.047 moles ÷ 0.09 liters) = 0.52 moles/liter.