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Equation to Find Volume of a Solution

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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(1) for w/v% concentration are g/100 mL :

    • w/v% (m/v%) is a useful concentration measure when dispensing reagents.

  • Note that weight/volume is also referred to as mass/volume.

    • (i) mass/volume can be abbreviated as m/v

    (ii) mass/volume percentage concentration is abbeviated as m/v %

  • Rearrange the equation for w/v% concentration to find:

    • (i) mass of solute

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

    (ii) volume of solution

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

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Weight/Volume Percentage Concentration Calculations

Weight/Volume percentage concentration (w/v% or m/v%) is a measure of the concentration of a solution.
w/v% or m/v% is calculated by dividing the mass of the solute in grams by the volume of solution in millilitres then multiplying this by 100 as shown below.

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

A percentage concentration tells us how many parts of solute are present per 100 parts of solution. In weight per volume terms (mass per volume terms), this means a percentage concentration tells us the parts of solute by mass per 100 parts by volume of solution.

In SI units, w/v% concentration would be given in kg/100 L, but these units are far too large to be useful to Chemists in the lab, grams and milliltres are more convenient units for us.
Recall that 1 kg = 1 000 g
Recall that 1 L = 1 000 mL
so kg/100 L = 1000 g/100 000 mL = g/100 mL
so the units for w/v% concentration are most often given as g/100 mL.

Therefore the units for w/v% (m/v%) concentration are grams of solute per 100 mL of solution (g/100 mL).

To prepare a solution with a particular concentration, you will weigh out the solid and then dissolve it enough solvent to make a known volume of solution. Therefore you know two quantities:

  • mass of solute
  • volume of solution

which you can use to calculate the weight/volume percentage concentration.

To calculate a weight/volume percentage concentration (mass/volume percentage concentration:

  1. Step 1 Write the equation: w/v% = w/v × 100
  2. Step 2 Identify the solute and solvent (by name or chemical formula)
  3. Step 3 Extract the data from the question (mass of solute, volume of solution)
  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)
  5. Step 5 Substitute these values into the equation and solve.

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

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100

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

  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = sodium chloride = NaCl

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass solute (NaCl) = 5 g

    volume of solution = 250 mL

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. mass solute (NaCl) = 5 g (no unit conversion needed)

    volume of solution = 250 mL (no unit conversion needed)

  5. Step 5 Substitute these values into the equation and solve.

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

    (Note: only 1 significant figure is justified)

Question 2. 10.00 g BaCl2 is dissolved in 90.00 g of water.

The density of the solution is 1.090 g/mL.

Calculate the weight/volume percentage concentration of the solution.

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100

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

  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = barium chloride = BaCl2

    solvent = water = H2O(l)

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass of solute = mass(BaCl2) = 10.00 g

    mass of solvent = mass(H2O) = 90.00 g

    density of solution = 1.090 g/mL

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. mass of solute = mass(BaCl2) = 10.00 g (no unit conversion needed)

    volume of solution is unknown and needs to be calculated using the density of solution and the masses of solute and solvent:

    density = mass(solution) ÷ volume(solution)

    mass(solution) = mass(solute) + mass(solvent)

    mass(solution) = 10.00 g BaCl2 + 90.00 g water = 100.0 g

    volume(solution) = mass(solution) ÷ density(solution)

    volume(solution) = 100.0 g ÷ 1.090 g/mL = 91.74 mL

  5. Step 5 Substitute these values into the equation and solve.

    6. w/v (%) = (mass solute ÷ volume solution) × 100

    w/v (%) = (10.00 g ÷ 91.74 mL) × 100

    w/v (%) = 10.90 g/100 mL

    (Note: only 4 significant figures are justified)

Conversion from Other Units to w/v %

The most common units for w/v% (m/v%) concentration are g/100 mL.
If the mass of the solute is not given in grams then you will need to convert the units to grams.
If the volume of the solution is not given in millilitres then you will need to convert the units to millilitres.

Question 1. 2.00 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/100 mL?

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100
  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = potassium chloride = KCl

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass KCl = 45.0 g

    volume of solution = 2.00 L

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. mass KCl = 45.0 g (mass in g, no unit conversion needed)

    volume of solution = 2.00 L (need to convert to mL)
    V(solution) = 2.00 L × 103 mL/L = 2000 mL

  5. Step 5 Substitute these values into the equation and solve.

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

    w/v (%) = [45.0 g ÷ 2000 mL] × 100 = 2.25 g/100 mL

    (Note: only 3 significant figures are justified)

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?

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100
  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = sucrose

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass solute (sucrose) = 750 mg

    volume solution = 15 mL

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. mass solute (sucrose) = 750 mg (need to convert to grams)
    mass solute = 750 mg ÷ 1000 mg/g = 0.750 g

    volume solution = 15 mL (no conversion needed)

  5. Step 5 Substitute these values into the equation and solve.

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

    w/v (%) = (0.750 g ÷ 15 mL) × 100 = 5.0 g/100 mL

    (Note: only 2 significant figures are justified)

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?

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100
  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = sodium hydroxide = NaOH

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass solute (NaOH) = 1.15 kg

    volume solution = 186.4 L

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)(2)

    5. mass solute (NaOH) = 1.15 kg (convert units to g)

    mass solute (NaOH) = 1.15 kg = 1.15 kg × 1000 g/kg = 1 150 g

    volume solution = 186.4 L (convert units to mL)

    volume solution = 186.4 L = 186.4 L × 1000 mL/L = 186 400 mL

  5. Step 5 Substitute these values into the equation and solve.

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

    w/v (%) = (1 150 g ÷ 186 400 mL) × 100

    w/v (%) = 0.617 g/100 mL

    (Note: only 3 significant figures are justified)

Reagent Volume and Mass Calculations

In the sections above we calculated the w/v% concentration of solutions using the known mass of solute and volume of solution.

When we come to use this solution in the lab, we are most likely to use a pipette or burette to deliver a volume of solution.

If we know the volume of solution used, we can calculate the mass of solute present.

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

If we know the mass of solute we want to use, we can calculate the volume of solution we will need to use.

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

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?

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100

    2. Rearrange the equation to find volume of solution:

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

    Multiply both sides of the equation by volume

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

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

    Divide both sides of the equation by w/v%

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

    volume of solution (mL) = mass of solute (g)
    w/v (%)     		× 100
  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = sodium chloride = NaCl

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. 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

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. mass of solute required = mass(NaCl) = 1.22 g (no unit conversion needed)

    concentration of NaCl(aq) provided = w/v (%) = 11.78 g/100 mL (no unit conversion needed)

    volume of solution needed = ? mL

  5. Step 5 Substitute these values into the equation and solve.
    6. volume of solution (mL) = mass of solute (g)
    w/v (%)     		× 100
    = 1.22 g
    11.78 g/100 mL     		× 100
    = 10.36 mL
    = 10.4 mL

    (Note: only 3 significant figures are justified)

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?

Solution:

  1. Step 1 Write the equation: w/v% = w/v × 100

    2. Rearrange the equation to find volume of solution:

    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)

  2. Step 2 Identify the solute and solvent (by name or chemical formula)

    3. solute = potassium iodide = KCl

    solvent is water, H2O, because this is an aqueous solution.

  3. Step 3 Extract the data from the question (mass of solute, volume of solution)

    4. mass solute = mass(KI) = ? g

    volume(KI(aq)) = 14.86 mL

    concentration of solution = w/v%(KI(aq)) = 32.44 g/100 mL

  4. Step 4 Check the units for consistency and convert if necessary (mass in grams, volume in millilitres)

    5. volume(KI(aq)) = 14.86 mL (no unit conversion needed)

    w/v%(KI(aq)) = 32.44 g/100 mL (no unit conversion needed)

  5. Step 5 Substitute these values into the equation and solve.

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

    mass(KI) = (32.44 ÷ 100) × 14.86 = 4.821 g

    (Note: 4 significant figures are justified)

Footnotes:

(1) Common units for w/v% (m/v%) are g/100 mL but other units are also possible, for example, kg/100 L, mg/100 μL
We will restrict the following discussion to g/100 mL but you can apply the same logic and equations using other appropriate units.
Note that solubilities are most often given as weight ratio percentage concentration.

(2) You don't really need to convert these units because both the mass and volume are given in SI units, that is
w/v% = (1.15 kg/186.4 L) × 100 = 0.617 kg/100 L = 617 g/100 000 mL = 0.617 g/100 mL
but it's probably best to practice doing the unit conversions, at least until you have full appreciation of what a w/v% concentration means.

Equation to Find Volume of a Solution

Source: https://www.ausetute.com.au/wtvol.html