How to Find Mass Percent
In general chemistry, mass percent (also called percent by mass, weight percent, or \(m/m\%\)) describes how much solute is present in a solution based on masses. It is a common form of percent concentration for solutions.
The definition used for how to find mass percent is:
\[ \text{mass percent} = \frac{m_{\text{solute}}}{m_{\text{solution}}}\times 100\% \]
For a two-component solution: \(m_{\text{solution}} = m_{\text{solute}} + m_{\text{solvent}}\). For mixtures with several components, \(m_{\text{solution}}\) is the sum of all component masses.
Step-by-step method
- Identify the solute and the solution total. Confirm that all masses are in the same unit (g, kg, etc.).
- Compute the total mass of the solution: \[ m_{\text{solution}} = \sum m_i \] (often \(m_{\text{solute}} + m_{\text{solvent}}\)).
- Divide solute mass by total solution mass and multiply by \(100\%\): \[ \text{mass percent} = \frac{m_{\text{solute}}}{m_{\text{solution}}}\times 100\% \]
| Quantity | Meaning | Typical unit |
|---|---|---|
| \(m_{\text{solute}}\) | Mass of dissolved substance (solute) | g or kg |
| \(m_{\text{solvent}}\) | Mass of the solvent (e.g., water) | g or kg |
| \(m_{\text{solution}}\) | Total mass of the final mixture | g or kg |
| \(\text{mass percent}\) | Percent concentration by mass (\(m/m\%\)) | % |
Worked example (forward calculation)
A solution is prepared by dissolving \(12.5\ \text{g}\) of NaCl in \(187.5\ \text{g}\) of water. Find the mass percent of NaCl.
\[ m_{\text{solution}} = 12.5\ \text{g} + 187.5\ \text{g} = 200.0\ \text{g} \]
\[ \text{mass percent} = \frac{12.5\ \text{g}}{200.0\ \text{g}}\times 100\% = 6.25\% \]
Reverse (common exam format): find solute mass from mass percent
If a solution is \(8.0\%\) (by mass) NaCl and the total solution mass is \(250\ \text{g}\), then
\[ 8.0\% = \frac{m_{\text{solute}}}{250\ \text{g}}\times 100\% \quad\Rightarrow\quad m_{\text{solute}} = \frac{8.0}{100}\times 250\ \text{g} = 20\ \text{g} \]
Frequent mistakes to avoid
- Using the solvent mass in the denominator instead of the solution mass. The denominator is \(m_{\text{solution}}\), not \(m_{\text{solvent}}\).
- Mixing units (e.g., grams for solute and kilograms for solvent). Convert first so the ratio is unit-consistent.
- Forgetting the factor of \(100\%\). The fraction \(m_{\text{solute}}/m_{\text{solution}}\) is a mass fraction; multiplying by \(100\%\) converts it to percent.