# 6.8: Percent-By-Mass Composition

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⚙️ Learning Objectives

• Determine percent composition of each element in a compound based on mass.

Packaged foods that you eat typically have nutritional information provided on the label. The label on a jar of peanut butter reveals that one serving size is considered to be $$32 \: \text{g}$$. The label also gives the masses of various types of compounds that are present in each serving. One serving contains 7 g of protein, 15 g of fat, and 3 g of sugar. By calculating the fraction of protein, fat, or sugar in one serving size of peanut butter and converting to percent values, we can determine the composition of peanut butter on a percent by mass basis.

#### Percent Composition

Chemists often need to know what elements are present in a compound and in what percentage. In general, percentages may be found by taking the part, dividing it by the whole and multiplying by 100:

$\%=\frac{\mathrm{part}}{\mathrm{whole}}\times100$

The percent-by-mass composition is the percent by mass of each element in a compound. It is calculated in a similar way to that of the composition of the peanut butter.

$\% \: \text{by mass} = \dfrac{\text{mass of element in compound}}{\text{mass of compound}} \times 100\%$

The sample problem below shows the calculation of the percent composition of a compound based on mass data.

✅ Example $$\PageIndex{1}$$: Percent Composition from Mass Data

A certain newly synthesized compound is known to contain the elements zinc and oxygen. When a 20.00 g sample of this compound is decomposed, 16.07 g of zinc remains. Determine the percent-by-mass composition of the compound.

Solution

Steps for Problem Solving
Identify the "given" information and what the problem is asking you to "find."
Given : Mass of compound = 20.00 g

Mass of Zn = 16.07 g

Find: % Composition (%Zn and %O)

List known relationships.
Subtract to find the mass of oxygen in the compound.

Mass of oxygen = 20.00 g - 16.07 g = 3.93 g O

Calculate the percent by mass of each element by dividing the mass of that element by the mass of the compound and multiplying by 100%.

$$\%\:\mathrm{Zn}=\dfrac{16.07\:\text{g}\:\mathrm{Zn}}{20.00\:\text{g}}\times100\%=\boxed{80.35\%\:\mathrm{Zn}}$$

$$\%\:\mathrm O=\dfrac{3.93\:\text{g}\:\mathrm O}{20.00\:\text{g}}\times100\%=\boxed{19.65\%\:\mathrm O}$$

The calculations make sense because the sum of the two percentages adds up to 100%. By mass, the compound is mostly zinc.

✏️ Exercise $$\PageIndex{1}$$

Sulfuric acid, H2SO4 is a very useful chemical in industrial processes. If 196.0 g of sulfuric acid contained 64.0 g of sulfur and 4.0 g of hydrogen, what is the percent composition of the compound?

2.0% H, 32.65% S, and 65.31% O

#### Summary

• Processes are described for calculating the percent composition of a compound based on mass.

This page is shared under a CK-12 license and was authored, remixed, and/or curated by Melissa Alviar-Agnew, Henry Agnew, Vicki MacMurdo (Anoka-Ramsey Community College), and Lance S. Lund (Anoka-Ramsey Community College).