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Percent Solutions
Mass percent solutions
Are defined based on the grams of solute per 100 grams of solution.
Example: 20 g of sodium chloride in 100 g of solution is a 20% by mass solution.
Volume percent solutions
Are defined as milliliters of solute per 100 mL of solution.
Example: 10 mL of ethyl alcohol plus 90 mL of H2O (making approx. 100 mL of solution) is a 10% by volume solution.
Mass-volume percent solutions
Are also very common. These solutions are indicated by w/v% and are defined as the grams of solute per 100 milliliters of solution.
Example: 1 g of phenolphthalein in 100 mL of 95% ethyl alcohol is a 1 w/v% solution
Conversion between Percent Solutions
You may wish to convert mass percent to volume percent or vice versa. If so, follow this procedure:
A 10% by mass solution of ethyl alcohol in water contains 10 g of ethyl alcohol and 90 g of water.
- The formula for determining the volume of the component (ethyl alcohol in our example) is:
Mass of ethyl alcohol
Volume = ——————————
Density of ethyl alcohol
- Determine the volume of the total solution by dividing the mass of the solution by the density of the solution
- Determine the percent by volume by dividing the volume of the component by the volume of the solution.
Let`s solve 1, 2, and 3 above as follows:
- Mass of ethyl alcohol = 10 g(given density of ethyl alcohol = 0.794 g/mL (from handbook)
Mass
Volume = ———
Density
10 g
Volume of ethyl alcohol = ——— = 12.594 ml
0.794 g/mL
- Mass of solution = 100 g (given)
Density of solution (10% ethyl alcohol) = 0.794 g/mL (from handbook)
100 g
Volume of solution = ———— =125.94ml
0.794 g/mL
- Volume percent of solution
Percent = volume of ethyl alcohol
Total volume of solution
12.594
= ———
125.94 = 10%
Calculating Molarity from Percent Solution
To determine the molarity of a mass percent solution, the density of the solution is required. Use the following procedure:
- Determine the mass of solution by multiplying the volume of the solution by the density of the solution
Mass = volume x density
- Determine concentration in percent by mass of the solute in solution. Change to the decimal equivalent.
- Calculate the molar mass of the compound, MM.
- Multiply mass (step 1) by mass % (step 2) and divide by molecular mass
(step 3) to find the number of moles present in the whole solution.
- Divide the number of moles (step 4) by the volume in liters of the solution to find the molarity of the solution.
Example: Determine molarity of 37.2% hydrochloric acid (density 1.19 g/mL)
Mass of solution = 1,000 mL x 1.19 g/mL = 1,190
Mass % = 37.2 % = 0.372
Molar mass of hydrochloric acid = 36.4 g/mol
=mass x mass %
MMHCl
1,190 g x 0.372
= ————————
36.4 g/mol = 12.1 moles
Molarity = moles/liters
= 12.1
moles/1 liter = 12.1 M