# Percent By Weight Formula

Solutions can be described in other concentration besides molarity, normality or molality. Solutions are sometimes represented in terms of relative per cent concentration of solute in a solution. To determine the weight per cent of a solution, divide the mass of solute by mass of the solution (solute and solvent together) and multiply by 100 to obtain per cent.

The per cent by weight formula can be expressed as

$\dpi{120}&space;\large&space;Percent\;&space;by\;&space;weight=\frac{gram\;&space;of\;solute}{&space;100g\;&space;of\;&space;solution}$

Example 1

Calculate how many grams of NaOH are required to make a 30.0% solution by using De-ionized water as the solvent.

Solution

Substitute the numbers that are known in the basic formula for per cent weight

X g of solute in 100g of solution = 30.0%

30.0 g of NaOH = X

Thus, 30 grams of NaOH must be dissolved in 70 grams of de-ionized water to make a 30% solution of NaOH in water. Furthermore, any amount of NaOH can be dissolved in de-ionized water in a 3:7 ratio to form a 30% solution of NaOH.

Example 2

Determine the % of a solution which has 25.0g of NaCl dissolved in100mL of De-ionized water.

Solution

Given,

Mass of solute (NaCl) = 25g

Mass of solvent (de-ionized water) = 100g (1 mL of de-ionized water roughly weighs 1g)

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

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

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