Chemical samples are rarely perfectly pure. A container labeled calcium carbonate, sodium chloride, or magnesium may contain the intended compound alongside moisture, unreactive minerals, leftover manufacturing materials, or other impurities. To determine how much of the desired substance is actually present, chemists use stoichiometry, the study of quantitative relationships between reactants and products in a chemical reaction.
The basic method is to measure how much of a sample reacts, use a balanced chemical equation to calculate the amount of pure substance involved, and compare that amount with the sample’s original mass. The result is the sample’s percentage purity.
Percentage purity = (Mass of pure substance ÷ Total mass of sample) × 100%
The challenge is determining the mass of the pure substance when the sample also contains unknown impurities. Stoichiometry provides a way to solve this problem by connecting measurable experimental results to the quantities of substances involved in a chemical reaction.
What chemical purity means
Chemical purity describes the proportion of a sample that consists of the desired substance. A pure sample contains only that substance, while an impure sample contains additional components.
For example, a 20-gram sample of sodium chloride might contain 18 grams of sodium chloride and 2 grams of other materials. Its percentage purity would be:
Percentage purity = (18 g ÷ 20 g) × 100% = 90%
This means that 90% of the sample’s mass is sodium chloride.
The remaining 10% consists of other materials. These could include insoluble minerals, other salts, or moisture, depending on the sample’s origin and handling.
Purity is not the same as concentration. Purity describes the proportion of a desired substance in a sample, whereas concentration describes the amount of a substance in a specified quantity of a mixture or solution. Although the concepts are related, they answer different questions.
Stoichiometric purity calculations are particularly useful when the desired substance reacts in a known way with another chemical. By measuring the reaction or one of its products, a chemist can determine how much of the desired substance was present before the reaction began.
Why stoichiometry is essential for calculating purity
Stoichiometry relies on the principle that chemical reactions follow fixed quantitative relationships. These relationships can be determined from a balanced chemical equation.
Consider the reaction between calcium carbonate and hydrochloric acid:
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂
The balanced equation shows that one mole of calcium carbonate reacts with two moles of hydrochloric acid to produce one mole of calcium chloride, one mole of water, and one mole of carbon dioxide.
A mole is a unit representing a specific number of particles. In chemical calculations, it provides a convenient way to relate the amounts of different substances in a reaction.
The coefficients in a balanced equation give the mole ratios between reactants and products. These ratios allow chemists to work backward from an experimental measurement to the amount of the original substance.
For example, if a sample of calcium carbonate reacts with excess hydrochloric acid, the reaction releases carbon dioxide gas. If the amount of carbon dioxide produced can be measured, the balanced equation reveals how much calcium carbonate reacted.
This is useful for purity analysis because calcium carbonate impurities that do not react under the experimental conditions will not contribute to the measured carbon dioxide. Provided the reaction and measurement are reliable, the gas produced can therefore indicate the amount of calcium carbonate in the original sample.
The same general approach applies to many chemical systems, including acid-base reactions, precipitation reactions, redox reactions, and reactions that produce measurable gases.
How to calculate percentage purity step by step
A typical stoichiometric purity calculation involves several connected steps. The exact measurements depend on the reaction, but the underlying method remains the same.
First, measure the original sample.
Determine the total mass of the sample before the reaction. This includes both the desired chemical and any impurities.
Next, carry out a suitable chemical reaction.
Choose a reaction that involves the desired substance in a known stoichiometric ratio. Ideally, the reaction should proceed completely under the experimental conditions, and the impurities should not interfere with the measurement.
Then, measure a reaction quantity.
This could be the mass of a product, the volume of a gas, the amount of a titrant required to reach an endpoint, or another measurable quantity linked to the desired substance.
Convert the measurement into moles.
Use the appropriate relationship. For a substance with a known mass, divide its mass by its molar mass:
Moles = Mass ÷ Molar mass
For a gas, the conversion may require its pressure, volume, and temperature, or a suitable molar gas volume under specified conditions. For a solution, the amount of dissolved substance can be calculated from its concentration and volume.
Use the balanced equation to determine the amount of the desired substance.
Apply the mole ratio between the measured reactant or product and the target compound. This gives the number of moles of the desired substance that participated in the reaction.
Convert those moles into mass.
Multiply the calculated number of moles by the molar mass of the desired substance:
Mass of pure substance = Moles of pure substance × Molar mass
Finally, calculate the percentage purity.
Divide the calculated mass of the pure substance by the original sample mass and multiply by 100%.
Percentage purity = (Calculated mass of pure substance ÷ Original sample mass) × 100%
The result represents the percentage of the original sample’s mass attributable to the desired substance, assuming the experimental method and chemical relationships support that interpretation.
Worked example: Determining the purity of calcium carbonate
Suppose a 5.00-gram sample of limestone contains calcium carbonate along with impurities that do not release carbon dioxide when treated with excess hydrochloric acid.
The sample reacts according to the equation:
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂
After the reaction, the carbon dioxide produced is collected and found to have a mass of 1.76 grams.
The goal is to calculate the percentage purity of the original sample.
Step 1: Calculate the moles of carbon dioxide produced.
The molar mass of carbon dioxide, CO₂, is approximately 44.01 grams per mole.
Moles of CO₂ = 1.76 g ÷ 44.01 g/mol
Moles of CO₂ ≈ 0.0400 mol
Step 2: Determine the moles of calcium carbonate that reacted.
The balanced equation shows a 1:1 mole ratio between calcium carbonate and carbon dioxide.
CaCO₃ : CO₂ = 1 : 1
Therefore:
Moles of CaCO₃ = 0.0400 mol
Step 3: Calculate the mass of calcium carbonate.
The molar mass of calcium carbonate is approximately 100.09 grams per mole.
Mass of CaCO₃ = 0.0400 mol × 100.09 g/mol
Mass of CaCO₃ ≈ 4.00 g
This means the original 5.00-gram sample contained approximately 4.00 grams of calcium carbonate.
Step 4: Calculate the percentage purity.
Percentage purity = (4.00 g ÷ 5.00 g) × 100%
Percentage purity = 80.0%
The sample is approximately 80.0% calcium carbonate by mass.
The remaining 20.0% of the sample’s mass is attributable to other material, assuming the experiment accounts for the carbon dioxide correctly and the impurities do not produce or consume carbon dioxide in a way that affects the measurement.
This example illustrates the central advantage of stoichiometry: the mass of the desired compound can be calculated indirectly from the mass of a reaction product.
Calculating purity from gas volume
Sometimes a reaction produces a gas whose volume is easier to measure than its mass. In these cases, the gas volume can be used to calculate the amount of the desired substance.
For example, magnesium reacts with hydrochloric acid to produce hydrogen gas:
Mg + 2HCl → MgCl₂ + H₂
The balanced equation establishes a 1:1 mole ratio between magnesium and hydrogen gas.
If an impure magnesium sample reacts with excess hydrochloric acid, and the impurities do not produce hydrogen or interfere with the reaction, the amount of hydrogen collected can indicate how much magnesium reacted.
If the gas volume is measured under conditions where the molar gas volume is known, the number of moles can be estimated using:
Moles of gas = Gas volume ÷ Molar gas volume
The result can then be used with the balanced equation to calculate the moles and mass of magnesium.
For greater accuracy, especially when pressure and temperature differ from standard reference conditions, the ideal gas equation can be used:
PV = nRT
Here, P is the absolute pressure of the gas, V is its volume, n is the number of moles, R is the ideal gas constant, and T is the absolute temperature in kelvins.
Rearranging the equation gives:
n = PV ÷ RT
Once the number of moles of hydrogen is known, the 1:1 mole ratio gives the amount of magnesium that reacted. Multiplying by magnesium’s molar mass gives the mass of magnesium in the original sample.
The percentage purity then follows from the usual formula.
Gas-based calculations require care because gases can escape during collection, dissolve in the liquid, or be measured incorrectly. If the gas is collected over water, its measured pressure includes water vapor, which may need to be accounted for when calculating the pressure of the dry gas. Such effects can cause the calculated purity to differ from the true value.
Calculating purity using titration
Another common method uses titration, a technique in which a solution of known concentration reacts with a measured amount of an unknown sample.
Suppose an impure sample contains a substance that reacts with a known solution in a predictable mole ratio. The chemist dissolves the sample, adds the titrant gradually, and determines the volume needed to reach the reaction’s endpoint.
The moles of titrant used are calculated from its concentration and volume:
n = cV
Here, n is the amount in moles, c is the molar concentration in moles per liter, and V is the solution volume in liters.
The balanced chemical equation is then used to calculate the moles of the desired substance in the sample. Those moles are converted into mass, and the percentage purity is calculated using the original sample mass.
For example, sodium carbonate reacts with hydrochloric acid according to this equation:
Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂
The equation shows that one mole of sodium carbonate reacts with two moles of hydrochloric acid.
If a known mass of an impure sodium carbonate sample requires a measured amount of hydrochloric acid for complete reaction, the amount of sodium carbonate can be determined from that 1:2 mole ratio, provided other sample components do not consume the acid or interfere with the endpoint.
Titration is valuable because accurately prepared solutions and carefully measured volumes can provide precise quantitative information. However, the result depends on selecting an appropriate reaction, identifying the endpoint correctly, and ensuring that interfering substances do not affect the amount of titrant consumed.
The importance of balanced chemical equations and molar masses
A purity calculation is only as reliable as the chemical relationships used to perform it.
A balanced chemical equation conserves the number of atoms of each element. It therefore establishes the correct mole ratios between reactants and products. Using an unbalanced equation can produce an incorrect estimate of the amount of the desired substance, even when every measurement is accurate.
Molar mass is equally important. It connects the amount of a substance in moles to its mass in grams. Molar masses are calculated from the chemical formula and the atomic masses of the constituent elements.
For calcium carbonate, CaCO₃, the molar mass is calculated by adding the contributions from one calcium atom, one carbon atom, and three oxygen atoms:
Molar mass of CaCO₃ ≈ 40.08 + 12.01 + 3(16.00)
Molar mass of CaCO₃ ≈ 100.09 g/mol
The same principle applies to reactants and products throughout a stoichiometric calculation.
Units also provide an important check. When mass is divided by molar mass, the units should reduce to moles. When moles are multiplied by molar mass, the result should be a mass. Percentage purity is a ratio of two masses and is expressed as a percentage.
If the units do not cancel correctly, the calculation may contain a conversion error.
Assumptions that affect the accuracy of purity calculations
Stoichiometry provides a mathematical framework, but it does not automatically guarantee an accurate result. A reliable purity estimate depends on several experimental assumptions.
One important assumption is that the desired substance reacts completely. If some of it remains unreacted, the measured product may underestimate the amount originally present. This would usually cause the calculated purity to be too low.
Another assumption is that the reaction follows the balanced equation without significant competing reactions. If an impurity also produces the measured gas or consumes the titrant, the experiment may attribute its contribution to the desired substance. The calculated purity could then be too high or otherwise inaccurate.
Product recovery is another concern. A gas may escape, a precipitate may remain suspended in a solution, or a solid product may be lost during filtration and transfer. Such losses can affect the measured quantity and distort the result.
Sample composition also matters. Some impurities are chemically inert under the chosen conditions, while others react with the same reagent as the desired substance. A method that works well for one mixture may not work for another.
Moisture can be particularly important. If the original sample contains water, that water contributes to the sample’s total mass. Unless the analytical method specifically defines purity on a dry-mass basis, the moisture remains part of the denominator in the percentage-purity calculation. A wet sample may therefore have a lower measured percentage of the desired compound than an otherwise identical dry sample.
Finally, measurement uncertainty affects the result. Errors in weighing, reading solution volumes, measuring gas pressure, estimating temperature, or determining a titration endpoint can change the calculated mass of the pure substance. Reporting more decimal places than the measurements justify can create a misleading impression of precision.
For these reasons, the experimental method should be selected according to the sample’s known or suspected composition, not merely according to which reaction is easiest to perform.
Why a calculated purity can exceed 100%
A stoichiometric calculation may occasionally produce a purity greater than 100%. For an ordinary sample analyzed correctly on a consistent mass basis, this is not physically meaningful: the mass of the desired substance cannot exceed the total mass of the sample.
Such a result is a warning that something may have gone wrong.
Possible causes include an incorrect mole ratio, an error in the balanced equation, an inaccurate molar mass, an incorrect unit conversion, or a measurement that overestimates the amount of reaction product.
Interfering impurities may also contribute to the measured result. For example, if a substance other than the target compound produces the same gas, the calculated amount of the target compound may be too large.
A result above 100% should therefore prompt a review of the experimental assumptions and calculations rather than an interpretation that the sample contains more than its total mass in pure substance.
Choosing the right method for a particular sample
The most suitable stoichiometric method depends on the chemical properties of the substance being analyzed.
If the desired compound produces a measurable gas, gas collection may be appropriate. If it reacts quantitatively with a known solution, titration may provide a direct route to its amount. If a reaction forms an insoluble product, the product may be isolated, dried, and weighed, provided its identity and composition are established and the recovery is sufficiently complete.
In gravimetric analysis, the amount of a substance is determined from a carefully measured mass, often that of a product with a known chemical composition. The measured product mass is converted into moles and related to the original substance through the balanced equation.
For any method, selectivity is crucial. A selective reaction provides a measurement that can be attributed to the desired substance rather than to multiple components of the sample.
When the composition of the sample is unknown or several substances react in similar ways, a single stoichiometric measurement may not be enough to establish purity. Additional chemical tests or instrumental methods may be needed to identify interfering substances or distinguish components that behave similarly.
It is also important to distinguish chemical purity from the amount of a particular component measured by an analytical method. The method may quantify the target compound accurately without identifying every impurity present. Conversely, an apparently high purity result does not necessarily prove that all other substances are absent.
Interpreting the final purity value
The final percentage expresses the mass of the desired substance relative to the original sample mass. For example, a result of 96.5% indicates that, under the assumptions and conditions of the analysis, approximately 96.5% of the sample’s mass consists of the target substance.
The remaining 3.5% represents material not accounted for as the desired substance, although the calculation alone may not reveal the identities of those materials.
The result should be reported with appropriate significant figures and, when accuracy matters, an estimate of measurement uncertainty. A purity value calculated from approximate measurements should not be presented as though it were exact.
The underlying principle remains straightforward: measure a quantity associated with a chemical reaction, use stoichiometry to determine the amount of the desired substance, convert that amount into mass, and compare it with the original sample mass.
When the reaction is suitable, the measurements are reliable, and interfering substances are properly accounted for, stoichiometry provides a clear and quantitative way to estimate the purity of a chemical sample.
