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Weight/Volume Percentage Concentration (w/v %)

Key Concepts

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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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