Formula for Percentage Purity

This calculator works out the percentage purity of a substance from its measured and theoretical masses (or from related quantities). Enter the mass of the pure substance you actually obtained and the total mass of the sample you started with; the calculator returns the percentage purity. The formula is simple: (mass of pure substance ÷ total mass of sample) × 100.

Formula

Percentage purity is defined as the mass of the pure substance divided by the total mass of the sample, multiplied by 100:

Percentage purity (%) = (mass of pure substance ÷ total mass of sample) × 100

Where:

• Mass of pure substance – the mass of the desired compound only, in grams (g).
• Total mass of sample – the mass of everything in the sample, including impurities, in grams (g).

The result is a percentage, so it has no unit. If the sample is completely pure, the two masses are equal and the purity is 100%. If the sample contains impurities, the purity is less than 100%.

Worked Example

Using the default values from the calculator:

• Mass of pure substance = 4.5 g
• Total mass of sample = 5.0 g

Step 1: Divide the mass of pure substance by the total mass of sample:

4.5 ÷ 5.0 = 0.9

Step 2: Multiply by 100 to get a percentage:

0.9 × 100 = 90%

The percentage purity is 90%. This matches the calculator’s output.

Why Percentage Purity Matters

In chemistry, few substances are 100% pure. Reagents, ores, and pharmaceutical compounds often contain impurities from manufacturing, natural sources, or decomposition. Knowing the purity is essential because it affects the actual amount of active ingredient in a given mass. For example, if you need 10 g of a reagent for a reaction, but the bottle is only 85% pure, you actually have only 8.5 g of the reagent – the rest is inert material. This can change reaction yields, dosages, and experimental results.

Percentage purity is also used in quality control, environmental analysis, and the food and drug industries. It is a straightforward way to express how much of a sample is the desired substance, without needing to know the identity of the impurities.

How to Measure the Masses

In practice, you usually do not directly weigh the pure substance. Instead, you measure the total mass of the sample, then use a chemical method to isolate or quantify the pure substance. Common methods include:

• Gravimetric analysis – precipitate the pure substance, filter, dry, and weigh it.
• Titration – react the sample with a standard solution to find the amount of pure substance, then convert to mass.
• Spectroscopy – use absorbance or other signals to determine concentration, then calculate mass.

Once you have both masses, plug them into the formula. If you are working from a titration, you may have moles rather than mass – convert moles to mass using molar mass first.

Common Mistakes and Misconceptions

A frequent error is mixing up the mass of pure substance with the mass of the sample. The numerator must always be the pure substance alone, not the total mass. Another mistake is using volumes or concentrations directly without converting to mass. For example, if you have a solution, you need to know the mass of solute, not just the volume of solution.

Rounding can also cause problems. Keep intermediate values to at least three significant figures, and round only at the end. Also, be consistent with units – both masses must be in the same unit (usually grams). If one is in kilograms and the other in grams, convert first.

A common misconception is that percentage purity and percentage yield are the same. They are different: purity compares the pure substance to the sample, while yield compares the actual amount produced to the theoretical maximum from a reaction. You can have a high yield but low purity, or vice versa.

Limits of the Formula

The formula assumes that the impurities are inert and do not interfere with the measurement. In reality, some impurities may react or have similar properties, leading to over- or under-estimation. Also, the formula works only when you can accurately determine the mass of the pure substance. If the substance is volatile, hygroscopic, or decomposes on heating, the measured mass may be incorrect.

For mixtures with multiple components, percentage purity alone is not enough – you may need to know the identity and amount of each impurity. The formula gives a single number, which is useful but not a complete analysis.

Frequently Asked Questions

What is the difference between percentage purity and percentage yield?

Percentage purity compares the mass of pure substance to the total mass of the sample. Percentage yield compares the actual amount of product obtained from a reaction to the theoretical maximum. A reaction can have a 100% yield but produce an impure product, or a low yield but a very pure product.

Can percentage purity be more than 100%?

No, not if the measurements are correct. The mass of pure substance cannot exceed the total mass of the sample, so the ratio is always ≤ 1, and the percentage is ≤ 100%. If you get more than 100%, there is likely an error in measurement, such as the pure substance absorbing moisture or the sample not being fully dried.

How do I calculate percentage purity from a titration?

From the titration, you find the number of moles of the pure substance. Multiply moles by the molar mass to get the mass of pure substance. Then divide by the total mass of the sample and multiply by 100.

What units can I use for the masses?

Any mass unit works as long as both masses are in the same unit. Grams are most common, but kilograms, milligrams, or even tonnes work. The percentage is unitless, so the unit cancels out.

Does temperature or pressure affect percentage purity?

Not directly, but they can affect the measurement. If the substance absorbs moisture from the air, the measured mass may be higher, making the purity appear lower. If the substance decomposes at high temperatures, drying it too much can reduce the mass of pure substance, making purity appear higher. Always follow the appropriate analytical procedure for the substance.

Why is percentage purity important in pharmaceuticals?

In medicines, the active ingredient must be present in a precise amount. If the purity is lower than stated, a patient may receive a sub-therapeutic dose. If it is higher, the dose could be toxic. Regulatory agencies set strict purity limits for pharmaceutical products.

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in m_pure | Mass of pure substance | g | 4.5 | 0
in m_sample | Total mass of sample | g | 5.0 | 0
out purity | Percentage purity | % | (m_pure / m_sample) * 100 | 2