How to Calculate Mass Ratio

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In chemistry, mass ratio, often called "percent composition by mass," is the proportion of a particular molecule that consists of each that molecule's constituent elements. For example, water consists of 11.1 percent hydrogen (H) and 88.9 percent oxygen (O), meaning that a 1,000-gram sample of water (equal to 1 liter in volume) consists of 111 g of H (0.111 × 1,000 = 111) and 889 g of O (0.889 × 1,000).

This principle gives rise to the Law of Constant Composition, put forth by Joseph Proust in 1800: A given compound always has the same proportion by mass of its constituent elements. For instance, water always has exactly 8 grams of oxygen for every gram of hydrogen. Carbon dioxide always has 2.67 g of oxygen for every gram of carbon.

Calculating mass ratios is easy enough if you have access to a periodic table (see Resources) and the means to do basic algebra.

Say you want to calculate the mass ratio of sulfuric acid, H2SO4.

  1. Determine the Molar Mass of Each Element Present

  2. H2SO4 contains hydrogen (H), sulfur (S) and oxygen (S). From the periodic table, you can see that the molar masses of these elements are:

    H = 1.00

    S = 32.06

    O = 16.00

Step 2: Determine the Mass of Each Individual Element Present

In this step, you multiply the number of atoms in one molecule of the compound by the molar masses you collected in Step 1. The number of atoms is simply the subscript after the element's abbreviation in the molecular formula, with the omission of a subscript signifying "1."

There are two H atoms present, one S atom and four O atoms, so you have:

H = (2)(1.00) = 2 g

S = (1)(32.06 g) = 32.06 g

O = (4)(16.00 g) = 64 g

Step 3: Determine the Molar Mass of the Compound

Add together the figures you calculated in Step 2:

2 + 32.06 + 64 = 98.06 g

Step 4: Divide the Mass of Each Element Present by the Molar Mass

This means dividing the individual masses from Step 2 by the result of Step 3.

For H, you have 2 ÷ 98.06 = 0.0204 = 2.04 percent hydrogen

For S, you have 32.06 ÷ 98.06 = 0.3269 = 32.69 percent sulfur

For O, you have 64 ÷ 98.06 = 0.6527 = 65.27 percent oxygen

Tip

To check your work, make sure your percentages sum to 100, allowing for tiny differences owing to rounding:

2.04 + 32.69 + 65.27 = 100.0

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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