Weight Ratio Percentage Concentration

Key Concepts

• Weight Ratio Percentage is a way of expressing the concentration of a solution.
• Solubilities are often expressed as a weight ratio:

  Units of solubility: grams of solute per 100 g of water
  Solubility of sodium chloride is 36 g/100 g water at 25° C

• Weight Ratio concentration = mass solute ÷ mass solvent
• Weight Ratio Percentage concentration = weight ratio × 100

  OR
  Weight Ratio Percentage concentration	=	mass solute   mass solvent	× 100

• Any units of mass (weight) can be used for the calculation but the mass of solute and the mass of solvent must be in the same units.

  If the mass of solute is in grams, the mass of solvent must also be in grams.
  If the mass of solvent is in kilograms, the mass of solute must also be in kilograms.

• Weight Ratio Percentage concentration must NOT be confused with Weight (Mass) Percentage concentration (w/w).

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Example : Weight Ratio Percentage Concentration Calculation

Solution:

1. Identify the solute and solvent making up the solution:
   

   solute: sodium chloride
   solvent: water

2. Identify the weights (masses) of solute and solvent and convert to the same units if necessary:
   

   mass solute (sodium chloride) = 10 g
   mass solvent (water) = 90 g

3. Calculate the weight ratio:
   

   weight ratio = mass solute ÷ mass solvent
   weight ratio = 10 ÷ 90 = 0.11

4. Calculate the weight ratio percentage:
   

   weight ratio percentage = weight ratio × 100
   weight ratio percentage concentration = 0.11 × 100 = 11%

Question 2. 250 mg of sodium carbonate is dissolved in 5 g of water.
Calculate the weight ratio percentage concentration of the solution.

Solution:

1. Identify the solute and solvent making up the solution:
   

   solute: sodium carbonate
   solvent: water

2. Identify the masses of solute and solvent and convert to the same units if necessary:
   

   mass solute (sodium carbonate) = 250 mg
   Convert mass in milligrams (mg) to a mass in grams (g):
   mass solute (sodium carbonate)= 250 ÷ 1000 = 0.250 g

   mass solvent (water) = 5 g

3. Calculate the weight ratio:
   

   weight ratio = mass solute ÷ mass solvent
   weight ratio = 0.250 ÷ 5 = 0.05

4. Calculate the weight ratio percentage:
   

   weight ratio percentage = weight ratio × 100
   weight ratio percentage concentration = 0.05 × 100 = 5%

Example : Mass of Solute or Solvent Calculation

Question 1. An aqueous sucrose solution contains 200 g water and has a weight ratio percentage concentration of 4.2%.
What is the mass of sucrose in grams?

Solution:

1. Identify the solute and solvent making up the solution:
   

   solute: sucrose
   solvent: water

2. Identify the known quantities:
   

   mass solute (sucrose) = ? g
   mass solvent (water) = 200 g
   weight ratio percentage = 4.2%

3. Convert the weight ratio percentage to a weight ratio by dividing by 100 :

   Weight Ratio Percentage concentration	=	weight ratio	× 100
   Weight Ratio Percentage concentration 100	=	weight ratio

   
   

   weight ratio = 4.2 ÷ 100 = 0.042

4. Re-arrange the weight ratio equation to find the mass of solute:
   

   weight ratio = mass solute ÷ mass solvent
   mass solute = weight ratio × mass solvent

5. Substitute in the values and solve:
   

   mass solute = 0.042 × 200 = 8.4 g

Question 2. An aqueous potassium chloride solution with a weight ratio percentage concentration of 7.5% contains 312 mg of potassium chloride.
What mass of water in grams is present?

Solution:

1. Identify the solute and solvent making up the solution:
   

   solute: potassium chloride
   solvent: water

2. Identify the known quantities:
   

   mass solute (sucrose) = 312 mg
   Convert mass in milligrams (mg) to a mass in grams (g)
   mass solute (sucrose)= 312 ÷ 1000 = 0.312 g

   mass solvent (water) = ? g

   weight ratio percentage = 7.5%

3. Convert the weight ratio percentage to a weight ratio by dividing by 100 :

   Weight Ratio Percentage concentration	=	weight ratio	× 100
   Weight Ratio Percentage concentration 100	=	weight ratio

   
   weight ratio = 7.5 ÷ 100 = 0.075
4. Re-arrange the weight ratio equation to find the mass of solvent:
   

   weight ratio = mass solute ÷ mass solvent
   mass solvent = mass solute ÷ weight ratio

5. Substitute in the values and solve:
   mass solvent = 0.312 ÷ 0.075 = 4.16 g