# 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 %

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## 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 (%)

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## 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 (%)

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## 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

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