How Do You Find Percent by Mass With Given Percentages?
Mixture labels often give contents proportions by volume instead of mass. You may need to know the mass proportions, however—for example, to measure out solids to recreate the mixture yourself. To determine the mass percentages, multiply each substance's volume percentages by its corresponding density, followed by a renormalization so the new percentages add up to 100 percent. Follow a similar procedure to convert to percentages by moles, a unit for counting the total number of molecules.
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Instructions
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Starting with Percent by Volume
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1
Identify the substances in the mixture and their proportions by volume. For example, mixture labels often give proportions by volume.
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2
Identify the density of each substance, if it were standing alone, unmixed (see Resources section). Use the same units for each substance.
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3
Multiply each substance’s percentage by its corresponding density.
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4
Normalize the new percentages by mass that you calculated in Step 3 by dividing each substance’s result in Step 3 by the sum of all the results in Step 3. This way, you ensure that the new percentages by mass will add up to 100 percent. For example, if Substance A, B and C have equal volume proportions (33.3 percent) and densities 1g/cubic cm, 2g/cubic cm and 3g/cubic cm, respectively, then Step 3 gives proportions by mass of 33.3 percent, 66.6 percent and 99.9 percent. Add these figures together to get 200 percent, after rounding. Divide each of the percentages by 200 percent, or by 2; the proportions by mass for Substances A, B and C become 16.7, 33.3 and 50.0 percent, respectively. These of course add up to 100 percent and are therefore normalized.
Starting with Percent by Moles
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Identify the substances in the mixture and their proportions in the mixture by moles. Check whether the label has this information.
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Determine the molar density of each substance (see Resources section). Use the same units for each substance.
For example, if water (H2O) is one of the components, calculate its molar density from the atomic masses for hydrogen (H) and oxygen (O), given on most periodic tables of the elements in atomic mass units (amu)—see Resources section. H has a mass of 1.0079 amu, and O has a mass of 15.9994 amu. So H2O has 2 x 1.0079 + 15.9994 g per mole, or 18.0152 g per mole.
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7
Multiply each substance’s percentage by its corresponding molar density.
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8
Normalize the new percentages by mass you calculated in Step 3 by dividing each substance’s result in Step 3 by the sum of all the results in Step 3. This way, you ensure that the new percentages by mass will add up to 100 percent.
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Tips & Warnings
Scientists define atomic mass units (amu) such that a carbon-12 atom equals exactly 12 amu; a proton weighs a little more than 1 amu.
