Calculate percentage by mass in compounds

Quantitative chemistry • Measurements and conservation of mass

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How does conservation of mass relate to percentage composition?

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Conservation of mass ensures that total mass of reactants equals total mass of products, so calculated percentages predict mass distribution among products and reactants.

Key concepts

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Definition of percentage by mass

Percentage by mass expresses the mass of an element as a percentage of the total mass of the compound. Cause: the compound contains specified numbers of atoms of each element. Effect: the proportion of an element equals its total atomic mass contribution divided by the compound's total mass, converted to a percentage. Limiting factors include impure samples and rounding of atomic masses. Cause: impurities or rounding errors change measured masses. Effect: calculated percentages deviate from theoretical values.

Relative atomic mass and relative formula mass

Relative atomic mass (Ar) gives the average mass of an atom of an element compared with 1/12 of a carbon-12 atom. Cause: each element has an Ar from the periodic table. Effect: Ar values combine to give the relative formula mass (RFM) by summing the Ar of all atoms in the formula. RFM acts as the total mass denominator in percentage calculations. Cause: each atom's Ar contributes to RFM by multiplication with atom count. Effect: accurate RFM produces accurate percentage composition values.

Step-by-step calculation method

Step 1: Multiply each element's Ar by its number of atoms to find the element mass in the formula. Cause: multiple atoms increase total element mass. Effect: the element's contribution becomes an absolute mass value. Step 2: Sum all element contributions to obtain the RFM. Step 3: Divide the element mass by the RFM and multiply by 100 to obtain the percentage by mass. Cause: division finds the fraction of total mass. Effect: multiplication by 100 converts the fraction to a percentage.

Worked examples and cause→effect reasoning

Example: water (H2O). Cause: hydrogen Ar = 1 and oxygen Ar = 16, and formula contains 2 H and 1 O. Effect: hydrogen mass = 2 × 1 = 2, oxygen mass = 1 × 16 = 16, RFM = 18. Calculation: (2 / 18) × 100 = 11.11% hydrogen; (16 / 18) × 100 = 88.89% oxygen. Example: magnesium oxide (MgO). Cause: magnesium Ar = 24.3 and oxygen Ar = 16, one atom each. Effect: Mg mass = 24.3, O mass = 16, RFM = 40.3. Calculation: (24.3 / 40.3) × 100 ≈ 60.3% Mg; (16 / 40.3) × 100 ≈ 39.7% O.

Sources of error and significant figures

Rounding of Ar values introduces small discrepancies. Cause: periodic table Ar values are given to limited decimal places. Effect: final percentages vary slightly depending on rounding rules. Measured samples introduce larger errors when impurities or incomplete reactions occur. Cause: non-pure reagents or incomplete separation change measured mass. Effect: experimental percentages diverge from theoretical values; clear statement of accuracy and significant figures helps interpret results.

Key notes

Important points to keep in mind

Multiply Ar by atom count to find each element's mass contribution.

Sum all element contributions to obtain the relative formula mass (RFM).

Divide element mass by RFM and multiply by 100 to get percentage by mass.

Use the periodic table Ar values and state the Ar values used when required.

Keep consistent significant figures and state rounding rules applied.

Impure samples and incomplete reactions cause experimental percentages to differ from theory.

Convert percentages to masses by multiplying the sample mass by the percentage (as a decimal).

Re-check atom counts in the formula to avoid systematic calculation errors.

Report percentages that sum approximately to 100%; small deviations indicate rounding.

State assumptions (pure substance, accurate Ar values) when comparing theory to experiment.