Empirical and Molecular Formulas from Composition
Masses or percentages from an analysis give the simplest whole-number ratio of atoms, and one extra measurement of relative mass turns that ratio into the real formula. It is the calculation that connects what a balance reads to what a molecule is.
What a learner can do afterwards
- Convert masses or percentage composition into an empirical formula
- Scale an empirical formula to a molecular formula given the relative molecular mass
- Explain why two different compounds can share an empirical formula
1 · Read
A balance reads masses, but a formula counts atoms. You already know about moles. Change each mass into moles using its atomic mass. Use 12 for carbon, 1 for hydrogen, 16 for oxygen. Divide every value by the smallest one. If you get 1.5, multiply all numbers by 2. With percentages, pretend you hold 100 grams, so each percent becomes grams.
A sample holds 12 grams of carbon and 2 grams of hydrogen. Divide: 12 by 12 is 1 mole of carbon, and 2 by 1 is 2 moles of hydrogen. The ratio is 1 to 2. Divide by 1 to keep 1 and 2. The empirical formula, the simplest ratio, is CH2.
The simplest ratio is not always the true molecule. Hydrogen peroxide is H2O2, but its empirical formula is HO. Acetylene (C2H2) and benzene (C6H6) both reduce to CH. To scale up you need the molar mass. Divide it by the empirical mass to get whole number n, then multiply every subscript by n. CH2O has empirical mass 30. Molar mass 180 gives n of 6, so glucose is C6H12O6.
Work in the same order. Masses to moles, divide by the smallest, clear decimals, and write the empirical formula. Then find n from the molar mass and scale up. One ratio can hide two compounds, so a ratio alone never proves the molecule.
Masses give a ratio, the ratio gives the empirical formula, and molar mass scales it up.
Readings written for this dataset.
More to read
Turn composition into a formula
Elemental analysis can establish how much of each element a substance contains. A balance measures mass, rather than counting atoms. Converting the elemental masses lets you work out their atom ratio.
For each element, divide its mass in grams by its molar mass in grams per mole. The resulting mole amounts are proportional to atom counts. Divide them all by the smallest amount. Whole-number results become empirical-formula subscripts. This formula expresses the lowest whole-number atom ratio. Allow for measurement uncertainty when results are close to integers. A ratio containing 1.5 requires multiplying every value by 2.
For percentage data, assume a sample weighing 100 grams. Each mass percentage then gives an elemental mass in grams. Continue with the same calculation.
An empirical formula may differ from a molecule's actual formula. Acetylene, C2H2, and benzene, C6H6, both reduce to CH. To identify the molecular formula, also measure the compound's molar mass. Divide this by the empirical formula's molar mass to obtain an integer n. Scale all empirical subscripts by n. The result specifies how many atoms of each element one molecule contains.
Use elemental analysis
Elemental analysis measures each element's contribution to a sample. Chemists use these measurements to identify an unknown formula.
Divide each elemental mass in grams by that element's molar mass in grams per mole. The mole amounts give relative atom counts. Reduce them to the lowest whole-number ratio to obtain the empirical formula.
Percent composition expresses each element's share of the compound's mass as a percentage. A known formula lets you calculate these shares. Measured percentages let you work in the opposite direction toward a formula.
For a molecular substance, a measured molar mass identifies the integer multiplier connecting its empirical and molecular formulas. Compare the compound's molar mass with the empirical formula's molar mass, then scale the subscripts accordingly. These calculations also apply to compounds containing carbon, hydrogen, and oxygen.
What different formulas tell you
Chemical formulas summarize a substance's composition, but different forms provide different information.
In a molecular formula, element symbols identify the atoms and subscripts count them. H2O means one molecule contains two hydrogen atoms plus one oxygen atom. A count of one needs no written subscript.
An empirical formula reduces atom counts to their lowest whole-number ratio. Water's empirical and molecular formulas match. Hydrogen peroxide instead has molecular formula H2O2 and empirical formula HO: its 2:2 ratio reduces to 1:1. Distinct compounds may therefore have identical empirical formulas.
Structural formulas describe bonds between atoms. Substances can share a molecular formula while having different structures and very different properties.
The mole and Avogadro's number connect particle counts with measurable quantities. Together with molar mass, they allow conversion between a sample's mass and its number of molecules or atoms.
Three routes to an empirical formula
An empirical formula identifies a compound's elements and their lowest whole-number atom ratio.
For mass percentages, assume a 100-gram sample. A carbon content of 40 percent then represents 40 grams of carbon. Do this for every element. Divide each mass by its elemental molar mass to obtain moles. Next, divide all mole amounts by the smallest. Use integer ratios as subscripts. Ratios near 1.33 suggest multiplying every value by 3; a ratio containing 2.5 requires multiplying them all by 2. Allow for measurement uncertainty rather than forcing arbitrary decimals into integers.
Measured elemental masses follow the same route: calculate moles, normalize by the smallest amount, then obtain whole-number ratios. Such data may come from burning a sample and weighing its products.
With a known molecular formula, divide its subscripts by their greatest common factor. For example, C6H12O6 reduces to CH2O.
Find the molecular multiplier
A molecular formula counts each element's atoms within one molecule. Its subscripts are an integer multiple of those in the empirical formula. Finding that multiplier requires the compound's measured molar mass.
Calculate the empirical formula from composition: convert elemental masses to moles and reduce their ratio. Then total the elemental molar-mass contributions for that formula. Divide the compound's measured molar mass by this empirical molar mass. The multiplier may be 1, 2, 3, or another positive integer. Round only when measurement uncertainty supports an integer result. Multiply all empirical subscripts by that factor.
For CH2O, the empirical molar mass is about 30 grams per mole. If the measured value is about 180 grams per mole, 180 ÷ 30 = 6. Scaling CH2O by 6 gives C6H12O6, which is glucose's molecular formula.
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