What is the percent-by-weight formula

Percent-by-Weight Formula (w/w%)

The percent-by-weight formula (also called weight percent or mass percent) is used to express the concentration of a substance in a mixture or solution. It is calculated using the following formula:

Percent by weight=(Mass of soluteMass of solution)×100\text{Percent by weight} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100Percent by weight=(Mass of solutionMass of solute​)×100

Where:

• Mass of solute = The mass of the substance (solute) in the solution.
• Mass of solution = The total mass of the solution (solute + solvent).
• 100 = Converts the fraction to a percentage.

Example Calculation

🔹 Suppose you dissolve 5 g of salt (NaCl) in 95 g of water. What is the percent-by-weight of salt in the solution?

Step 1: Calculate the total mass of the solution

$$\text{Mass of solution}=\text{Mass of solute}+\text{Mass of solvent}=5g+95g=100g$$

Step 2: Apply the formula

Percent by weight=(5g100g)×100=5%\text{Percent by weight} = \left( \frac{5g}{100g} \right) \times 100 = 5\%Percent by weight=(100g5g​)×100=5%✅ Answer: The salt solution is 5% w/w (weight/weight).

Applications of Percent-by-Weight

• Chemistry: Used in laboratory solutions and chemical formulations.
• Pharmacy: Expressing the concentration of active ingredients in medications.
• Food Industry: Calculating nutritional content (e.g., salt or sugar content in food).
• Cosmetics & Skincare: Determining ingredient concentrations in lotions and creams.