## Percent by Weight Formula

In addition to molarity, normality, or molality, the solution can also be described in other concentrations. A solution may be expressed as a relative percentage concentration of solute in the solution. To determine the weight percent of a solution, divide the mass of the solute by the mass of the solution (the solute plus the solvent) and multiply by 100 to get the percentage.

**Formula**

Per cent by weight = gram of solute/100 g of solution

## Solved Examples

**Q1: Calculate the number of grams of NaOH needed to make a 30.0% solution using deionized water as the solvent.**

**Solution:**

Substitute the value of the weight percent known in the basic formula

X g of solute in 100g of solution = 30.00.0g of NaOH = X

Therefore, dissolve 30g of NaOH in 70g of deionized water. A 30% solution of NaOH in water should be produced. In addition, any amount of NaOH can be dissolved in deionized water in a 3:7 ratio to form a 30% NaOH solution.

**Q2: Determine the percentage of a solution containing 25.0 g NaCl dissolved in 100 mL deionized water.**

**Solution:**

Given,

Solute mass (NaCl) = 25 g

Solvent mass (deionized water) = 100 g (1 ml deionized water weighs about 1 g)

Therefore, solution mass = solute Mass + mass of solvent = 100 g + 25 g = 125 g

Mass% of NaCl in this solution = (25 g / 125 g) 100% = 20%

Therefore, the mass% of NaCl in solution is 20%.