Composition of Mixtures

Define the sample and the components

A homogeneous mixture has uniform composition on the relevant sampling scale; a heterogeneous mixture does not. Neither description means the components have become a new compound. Start by identifying the whole sample, its component identities, and the conserved quantity. For a closed mixing operation without reaction or material loss, component masses add to the total mass.

Choose a composition scale deliberately

Mass fraction compares component mass with total mixture mass. Mole fraction compares component amount with total amount of the defined entities. They need not be numerically equal because different substances have different molar masses.

Each complete set of fractions sums to one. Multiplication by 100 converts a fraction to the corresponding percentage.

Worked example: equal masses do not mean equal counts

Mix 8.00 g He with 8.00 g Ar without loss. Each gas accounts for 50.0% of the mass. Using 4.00 and 39.95 g mol⁻¹, the amounts are 2.00 mol He and 0.200 mol Ar. The helium mole fraction is 2.00/2.200 = 0.909. Roughly 91% of the atoms are helium even though only half of the mass is helium.

Compare the two valid descriptions

The table does not contradict itself. Its last two columns answer different questions. A particle diagram should reflect the mole fractions, not draw equal numbers merely because the measured masses are equal.

An impurity calculation you can audit

A 3.60 g solid mixture contains 2.70 g of the desired salt and 0.90 g of an inert impurity. Its salt purity by mass is 75.0%. If the entire 3.60 g is mistakenly converted to moles using the salt's molar mass, the salt amount is overestimated by one third relative to its actual value. A purity fraction belongs before the mass-to-mole conversion.

Representative sampling is a chemical issue

If dense particles settle to the bottom of a mixture, a scoop from the top may not represent the whole container. Taking repeated top samples gives consistent but biased results. Homogenizing appropriately or combining samples from multiple regions addresses the cause. Report the sampling method when using a measured aliquot to infer the composition of a larger mixture.

Do not add volumes without a model

Mass is additive in ordinary closed mixing, but liquid volumes are not always additive because intermolecular arrangements change. Likewise, evaporation can alter composition by removing a volatile component. Recalculate the denominator after any addition or loss rather than reusing the initial total automatically.