Grade 10

Advanced

5 min

Lesson 3 of 12

Percent Composition by Mass

Not Started

Analyzing the chemical makeup of substances by determining the mass percentage of each constituent element.

How do jewelers distinguish a genuine 18-karat gold ring from a high-quality gold-plated fake without melting it down? The secret lies in the 'chemical fingerprint' of the substance—its percent composition by mass.

Learning Objectives

1.Calculate the percent composition of elements within any known chemical formula
2.Determine the precise mass of a specific element within a bulk sample size
3.Analyze the purity of a chemical sample by comparing experimental data to theoretical mass percentages

The Chemical Recipe

Every chemical compound is like a precise recipe. Just as a cake might be 20% sugar by weight, a molecule of carbon dioxide (

CO_2

) always contains a fixed percentage of carbon and oxygen. Percent Composition is the percentage by mass of each element in a compound. To find it, we compare the mass of an individual element in one mole of the compound to the total Molar Mass of that compound. The formula is:

\text{Mass \% of element} = \frac{n \times \text{molar mass of element}}{\text{molar mass of compound}} \times 100

where

n

is the number of atoms of that element in the formula.

Find the percent composition of Hydrogen and Oxygen in water ( $H_2O$ ).

1. Find the molar mass of $H$ ( $1.01\text{ g/mol}$ ) and $O$ ( $16.00\text{ g/mol}$ ). 2. Calculate total molar mass: $(2 \times 1.01) + 16.00 = 18.02\text{ g/mol}$ . 3. Calculate $\%H$ : $\frac{2.02}{18.02} \times 100 = 11.21\%$ . 4. Calculate $\%O$ : $\frac{16.00}{18.02} \times 100 = 88.79\%$ .

Note: The percentages must sum to 100%.

Quick Check

If a compound has a total molar mass of $100\text{ g/mol}$ and contains $40\text{ g}$ of Calcium, what is the percent composition of Calcium?

Divide the mass of the element by the total mass and multiply by 100.

Answer

40%

Scaling Up: Elements in Samples

Once you know the percentage of an element, you can predict exactly how much of that element is in any sample size. This is vital in mining and medicine. If you know an ore is

30\%

iron, you can calculate how many tons of iron you will get from

1,000

tons of rock. Mathematically, we treat the percentage as a conversion factor:

\text{Mass of element} = \text{Total sample mass} \times \left(\frac{\text{Mass \%}}{100}\right)

How many grams of Iron ( $Fe$ ) can be extracted from a $500\text{ g}$ sample of Iron(III) oxide ( $Fe_2O_3$ )?

1. Molar mass of $Fe_2O_3$ : $(2 \times 55.85) + (3 \times 16.00) = 159.70\text{ g/mol}$ . 2. Theoretical $\%Fe$ : $\frac{111.70}{159.70} \times 100 = 69.94\%$ . 3. Apply to sample: $500\text{ g} \times 0.6994 = 349.7\text{ g}$ of Iron.

Quick Check

If a substance is 25% Carbon by mass, how many grams of Carbon are in a 200g sample?

Multiply 200 by 0.25.

Answer

50g

Purity and Forensics

In the real world, chemicals are rarely

100\%

pure. Scientists use percent composition to verify the purity of a substance. If a lab synthesizes Aspirin (

C_9H_8O_4

), the theoretical carbon content should be

60.0\%

. If testing shows only

55\%

carbon, the sample is contaminated. Percent Purity is calculated by comparing the mass of the 'pure' compound to the total mass of the 'impure' sample:

\text{\% Purity} = \frac{\text{Mass of pure substance}}{\text{Total mass of sample}} \times 100

A $10.0\text{ g}$ sample of impure Glucose ( $C_6H_{12}O_6$ ) is analyzed and found to contain $3.5\text{ g}$ of Carbon. If pure glucose is $40.0\%$ Carbon by mass, what is the percent purity of the sample?

1. Find the mass of pure glucose that should contain $3.5\text{ g}$ of Carbon: $\frac{3.5\text{ g Carbon}}{0.40} = 8.75\text{ g pure glucose}$ . 2. Calculate purity: $\frac{8.75\text{ g pure}}{10.0\text{ g sample}} \times 100 = 87.5\%$ purity.

Key Takeaways

1Percent composition is the ratio of an element's total mass in a compound to the compound's molar mass.
2The sum of all elemental percentages in a compound must equal 100%.
3Mass percentages act as conversion factors to find the weight of an element in any given sample size.
4Discrepancies between theoretical and experimental percent composition indicate impurities in a sample.

Quick Check

Multiple Choice

What is the percent composition of Oxygen in $MgO$ (Molar masses: $Mg = 24.31, O = 16.00$ )?

Multiple Choice

A 50g sample of a compound is 10% Nitrogen. How many grams of Nitrogen are present?

True/False

The percent composition of an element changes if you have a larger sample of the substance.

What's Next?

Review Tomorrow

In 24 hours, try to calculate the percent composition of Carbon in Methane ( $CH_4$ ) from memory.

Practice Activity

Find a nutrition label on a food item. Calculate the 'percent composition' of sugar in the total serving weight.

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Percent Composition by Mass

Learning Objectives

The Chemical Recipe

Scaling Up: Elements in Samples

Purity and Forensics

Key Takeaways

Quick Check

What's Next?

Percent Composition by Mass

Learning Objectives

The Chemical Recipe

Scaling Up: Elements in Samples

Purity and Forensics

Key Takeaways

Quick Check

What's Next?