Percentage Purity Calculation: Formula & Examples

Percentage purity tells you how much of a sample is actually the desired substance, expressed as a percentage of the total mass. To calculate it, divide the mass of the pure substance by the total mass of the sample, then multiply by 100. This article explains the formula, shows a worked example, and covers common pitfalls and practical uses.

Formula

The percentage purity is calculated using the basic formula:

Percentage Purity (%) = (Mass of Pure Substance / Total Mass of Sample) × 100

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

This formula assumes the impurity is something other than the desired substance. In chemistry, purity is often expressed as a percentage by mass, but it can also be by volume or by mole fraction depending on the context.

Worked Example

Using the default values from the calculator: a sample has a total mass of 5.0 g, and analysis shows it contains 4.5 g of the pure substance. The calculation is:

1. Write the formula: purity = (mass of pure / total mass) × 100
2. Plug in the numbers: (4.5 g / 5.0 g) × 100
3. Divide: 4.5 ÷ 5.0 = 0.9
4. Multiply by 100: 0.9 × 100 = 90%

The sample is 90% pure. The calculator rounds to two decimal places, so it shows 90.00%.

When to Use Percentage Purity

Percentage purity is widely used in chemistry and manufacturing to assess the quality of a substance. Common applications include:

• Pharmaceuticals – ensuring active ingredients meet specified purity standards.
• Analytical chemistry – determining the purity of a synthesized compound.
• Food and beverage – checking the purity of additives or flavorings.
• Metallurgy – measuring the purity of metals like gold or silver.

It is also used in stoichiometry to adjust reaction yields when starting materials are not 100% pure. For example, if you need 10 g of a reactant but it is only 80% pure, you must weigh out 12.5 g of the impure sample to get the required amount.

How to Determine the Mass of Pure Substance

In practice, you rarely weigh the pure substance directly. Instead, you determine it through analysis. Common methods include:

• Titration – reacting the sample with a known concentration of reagent to find the amount of active substance.
• Gravimetric analysis – precipitating the substance and weighing the dried precipitate.
• Spectroscopy – using absorbance or other signals to quantify concentration.
• Chromatography – separating the desired compound and measuring its peak area.

Each method has its own assumptions and errors, so the calculated purity is only as accurate as the analytical technique used.

Common Mistakes and Misconceptions

One frequent error is confusing percentage purity with percentage yield. Yield refers to how much product you obtained compared to the theoretical maximum, while purity refers to how much of your sample is the desired substance. Another mistake is using the wrong mass – for example, using the mass of a hydrate instead of the anhydrous compound, or forgetting to account for water of crystallization.

Also, be careful with units. The formula works with any mass unit as long as both masses are in the same unit. If you mix grams and kilograms, the result will be wrong. Finally, rounding too early in the calculation can introduce errors, especially when the purity is close to 100%.

Limitations of the Formula

The simple formula assumes that the impurity is inert and that the sample is homogeneous. In reality, impurities can react, or the sample may not be uniform. For gases or liquids, purity is often expressed by volume or mole fraction, which requires different formulas. Also, the formula gives a mass-based purity; if the substance has a different molar mass than the impurity, mole-based purity will differ.

For very high purity samples (e.g., 99.999%), the measurement uncertainty of the analytical method becomes significant. Always report purity with an appropriate number of significant figures based on the precision of the analysis.

Frequently Asked Questions

What is the difference between purity and assay?

Purity refers to the fraction of the sample that is the desired substance, while assay is a broader term that often includes the measurement of the active ingredient’s concentration, which may be expressed as a percentage of the label claim. In many contexts, they are used interchangeably, but assay can also refer to the analytical procedure itself.

Can percentage purity exceed 100%?

No, by definition purity cannot exceed 100%. If you get a value above 100%, it usually indicates an error in measurement, such as including water or solvent in the pure mass, or a calculation mistake. In rare cases, it could be due to the presence of a heavier impurity that is counted as the pure substance.

How do you calculate purity from titration data?

From titration, you first calculate the moles of the substance that reacted using the volume and concentration of the titrant. Then convert moles to mass using the molar mass. Finally, divide that mass by the mass of the sample taken and multiply by 100 to get the percentage purity.

Does purity affect the melting point?

Yes, impurities generally lower the melting point and broaden the melting range. A pure substance has a sharp melting point, so measuring the melting point is a quick way to assess purity, though it is not quantitative. For a precise purity percentage, you need a quantitative method like chromatography.

What is the purity of a substance after recrystallization?

Recrystallization typically increases purity, but the exact percentage depends on the substance, solvent, and procedure. It is not a fixed value; you must analyze the recrystallized product to determine its purity. Often, one recrystallization is not enough to reach high purity, and repeated cycles may be needed.

Is percentage purity the same as percentage composition?

No. Percentage composition refers to the mass percentage of each element in a compound (e.g., water is 11.2% hydrogen by mass). Percentage purity refers to how much of a sample is the compound itself, regardless of its elemental makeup. They are different concepts.

Related

• Create Picture-in-Picture Video on Any Device
• Note 10 Plus Live Focus Video Test and Setup
• Five Paths Astrology: How 386 Fixed Rules Work

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