Percent by Mass (Weight Percent)

The Percent by Mass or Weight calculator computes the concentration of a solution based on the mass or weight of the solute (Ws) and solution (WS).

INSTRUCTIONS: Choose units and enter the following:

• (Ws)  Mass of Solute
• (WS)  Mass of Solution

Percent Concentration of Solution (PCS): The calculator returns the concentration as a percentage.

The Math / Science

The Percent Concentration by Mass formula is:

PCS = [Ws / WS] x 100

where:

• PCS is the percent concentration of solution by mass or weight.
• Ws is the mass or weight of the solute
• WS is the mass or weight of the solution.

This  is a method of expressing the concentration of a solution. This formula gives the mass of solute per 100 units of solution. This method of expressing concentration is not only known as percent by mass, but also weight percent, volume percent, mass percent, and other variations of this. 

The mass of solute should be directly given, however, the mass of solution can be calculated. The mass of solution = mass of the solute + mass of solvent. Each of these inputs have default units of grams, but can be calculated using any mass units (i.e., milligrams, kilograms...etc.).

Example

A 10% calcium gluconate solution, Ca(C₆H₁₁O₇)₂, contains 10 grams by mass of calcium gluconate in 100 grams of solution. This is the same as 10 grams of calcium gluconate in 90 grams of water. In chemistry, unless stated otherwise, the solvent is assumed to be water. So, if we wanted to use the percent by mass formula, it would look like this:

Define variables: 

• mass of solute = 10 grams calcium gluconate
• mass of solution = (10g + 90g) = 100 grams

Substitute variables in the formula:

percent solute = [(mass of solute) / (mass of solution)] x 100

percent solute = [(10g) / (100g)] x 100 = 10% calcium gluconate in solution

The Measurement of Concentration Calculator computes the percent concentration based on an amount of solute and an amount of solution.  The three functions are:

• (w/v) Weight Solute / Volume Solution Percent
• (w/w) Weight Solute / Weight Solution Percent
• (v/v) Volume Solute / Volume Solution Percent

Chemists frequently like to express their concentration using terms of percentage.  Percentage is parts per hundred.  There are a number of common methods for describing percent composition of solutions, such as: weight percent, volume percent, or weight/volume percent.  These different variations of % are practical to chemists and cooks. Solids are easier to weigh, while liquids are easier to measure volume.

Examples

If you want to make a gin and tonic. You might mix 10 mLs of gin with 90 mLs of tonic. In that case you would have a 10% (v/v) solution. 

If you are making instant coffee, you might blend 10 g of Santa with 100 mLs of water. That would be a 10% (w/v) solution. 

If you had a rock that weighted 100g and contained 10g of gold, you would say that it was 10% (w/w) ore.

* Note: "weight" is really entered as mass

Supplemental Materials

Chemistry.about.com: How to Calculate Mass Percent Composition of a Compound

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 98