Weight/Volume Percentage Concentration (w/v %)

Key Concepts

• Weight/Volume Percentage Concentration is a measurement of the concentration of a soluton.
• weight/volume percentage concentration is usually abbreviated as w/v (%)
• To calculate w/v % concentration:
  

  w/v (%) =

  mass of solute (g)     volume of solution (mL)

  × 100

• Common units for w/v% concentration are g/100mL (%)

  Solubilities are sometimes given in units of grams of solute per 100 mL of water, that is, as a weight/volume percentage concentration.

• weight/volume is a useful concentration measure when dispensing reagents.
• Note that weight/volume is also referred to as mass/volume.

  mass/volume can be abbreviated as m/v
  mass/volume percentage concentration is abbeviated as m/v %

Please do not block ads on this website.
No ads = no money for us = no free stuff for you!

Weight/Volume Percentage Concentration Calculations

Question 1. What is the weight/volume percentage concentration of 250 mL of aqueous sodium chloride solution containing 5 g NaCl?

1. Write the equation used to calculate the weight/volume (%) :

   weight/volume (%) = (mass solute ÷ volume of solution) × 100

2. Identify the solute:

   solute = sodium chloride = NaCl

3. Extract the data from the question:

   mass solute (NaCl) = 5 g
   volume of solution = 250 mL

4. Substitute the values into the equation and solve:

   w/v (%) = (5g ÷ 250 mL) × 100 = 2g/100mL (%)

Question 2. 10.00 g BaCl₂ is dissolved in 90.00 g of water.
The density of the solution is 1.09 g/mL.
Calculate the weight/volume percentage concentration of the solution.

1. Identify the solute and solvent:

   solute = barium chloride = BaCl₂
   solvent = water = H₂O_(l)

2. Calculate the volume of the solution:

   density = mass(solution) ÷ volume(solution)

   mass(solution) = mass(solute) + mass(solvent)
   mass(solution) = 10 g BaCl₂ + 90 g water = 100.00 g

   volume solution = mass ÷ density
   volume solution = 100 g ÷ 1.09 g/mL = 91.74 mL

3. Calculate w/v (%)

   w/v (%) = (mass solute ÷ volume solution) × 100
   mass solute (BaCl₂) = 10.00 g
   volume solution = 91.74 mL

   Substitute the values into the equation and solve:
   w/v (%) = (10.00 g ÷ 91.74 mL) × 100
   w/v (%) = 10.90 g/100 mL (%)

Conversion from Other Units to w/v %

Question 1. 2.0 L of an aqueous solution of potassium chloride contains 45.0 g of KCl.
What is the weight/volume percentage concentration of this solution in g/100mL?

1. Convert the units (mass in grams, volume in mL):

   mass KCl = 45.0g
   volume of solution = 2.0 L = 2.0 L × 10³ mL/L = 2000 mL

2. Calculate w/v (%)

   w/v (%) = [mass solute (g) ÷ volume solution (mL)] × 100

   Substitute in the values and solve:
   w/v (%) = [45.0 ÷ 2000 mL] × 100 = 2.25 g/100mL (%)

Question 2. 15 mL of an aqueous solution of sucrose contains 750 mg sucrose.
What is the weight/volume percentage concentration of this solution in g/100 mL?

1. Convert the units (mass to grams, volume to mL)

   mass solute (sucrose) = 750 mg = 750 mg ÷ 1000 mg/g = 0.750 g
   volume solution = 15 mL

2. Calculate w/v (%)

   w/v (%) = [mass solute (g) ÷ volume solution (mL)] × 100

   Substitute the values into the equation and solve:
   w/v (%) = (0.750 g ÷ 15 mL) × 100 = 5.0 g/100mL (%)

Question 3. 186.4 L of aqueous sodium hydroxide solution contains 1.15 kg NaOH.
What is the weight/volume percentage concentration of this solution in g/100 mL?

1. Convert the units (mass to grams, volume to mL)

   mass solute (NaOH) = 1.15 kg = 1.15 kg × 1000 g/kg = 1,150 g
   volume solution = 186.4 L = 186.4 L × 1000 mL/L = 186,400 mL

2. Calculate w/v (%)

   w/v (%) = [mass solute (g) ÷ volume solution (mL)] × 100

   Substitute in the values and solve the equation:
   w/v (%) = (1,150 g ÷ 186,400 mL) × 100
   w/v (%) = 0.62 g/100mL (%)

Reagent Volume-Mass Calculations

Question 1. A student must add 1.22 g of sodium chloride to a reaction vessel.
The student is provided with an 11.78 g/100 mL (%) aqueous sodium chloride solution.
What volume of this solution must be added to the reaction vessel?

1. Extract the data from the question:

   mass of solute required = mass(NaCl) = 1.22 g
   concentration of NaCl_(aq) provided = w/v (%) = 11.78 g/100 mL
   volume of solution needed = ? mL

2. Re-arrange the w/v % equation to find the volume of solution:

   
   

   w/v (%) =

   mass of solute (g)     volume of solution (mL)

   × 100

   
   Multiply both sides of the equation by volume of solution (mL)
   

   w/v (%) × volume of solution (mL) =

   mass of solute (g)

   × 100

   
   Divide both sides of equation by w/v (%):
   

   volume of solution (mL) =

   mass of solute (g) w/v (%)

   × 100

3. Subsitutue the values into the equation and solve for volume of solution:
   

   volume of solution (mL)	=	mass of solute (g) w/v (%)	× 100
   	=	1.22 g       11.78 g/100 mL	× 100
   	=	10.36 mL

Question 2. What is the mass in grams of potassium iodide in 14.86 mL of a 32.44 g/100 mL aqueous potassium iodide solution?

1. Extract the data from the question:

   mass solute = mass(KI) = ? g
   volume(KI_(aq)) = 14.86 mL
   concentration of KI_(aq) = 32.44 g/100 mL

2. Re-arrange the w/v (%) equation to find mass(solute):

   w/v(%) = mass solute (g) ÷ volume solution (mL) × 100

   Divide both sides of the equation by 100
   w/v(%) ÷ 100 = mass solute (g) ÷ volume solution (mL)

   Multiple both sides of the equation by volume solution (mL)
   mass solute (g) = (w/v (%) ÷ 100) × volume solution (mL)

3. Substitutue the values into the equation and solve:

   mass solute (g) = (w/v (%) ÷ 100) × volume solution (mL)
   mass(KI) = (32.44 ÷ 100) × 14.86 = 4.82 g