Percent By Volume Formula
The percent by volume formula gives the volume of solute present in a given volume of solution. It is used to express the concentration of a solute volumetrically. It calculates the volume percentage of a solute in the solution. The volume of a solution is evaluated by adding the volume of solute as well as the solvent. The unit of measurement of percent by volume is the percentage. Its value is directly proportional to the volume of solute. It means that the value of percent by volume increases/decreases with an increase or decrease in the volume of solute and vice-versa.
Percent By Volume Formula
The percent by volume is equal to the ratio of the volume of a solute to the volume of the solution multiplied by 100. A solution is formed when a solute is dissolved in a solvent. The percent by volume takes the volume of both solute and solvent one by one with the volume of solution and gives their concentration values. Because the volume of a solute or solvent cannot exceed the volume of its solution, the value of percent by volume is always less than 100%. It is a unitless quantity since it offers the volume ratio.
P = (v / V) × 100
Where,
v is the volume of solute or solvent,
V is the volume of solution.
For example,
The deionization reaction of sodium hydroxide (NaOH) with water gives sodium ions and hydroxide ions.
NaOH + H2O → Na+ + OH–
Assume that 6 ml of NaOH is dissolved in 80 ml of water to perform deionization of the basic salt. In this case, NaOH is the solute and water is the solvent.
Volume of solute = 6 ml
Volume of solvent = 80 ml
Volume of solution = (6 + 80) ml = 86 ml
So, the percent volume is calculated as,
Percent volume of solute NaOH = (6/86) × 100
= 600/86
= 6.97 %
Percent volume of solvent water = (80/86) × 100
= 8000/86
= 93.023 %
Sample Problems
Problem 1: Calculate the percent volume of solute if 5 ml of it is dissolved in a solvent of 90 ml.
Solution:
Volume of solute (v) = 5 ml
Volume of solvent = 90 ml
Volume of solution (V) = (5 + 90) ml = 95 ml
Using the formula we get,
P = (v / V) × 100
= (5/95) × 100
= 5.26 %
Problem 2: Calculate the percent volume of solute if 7 ml of it is dissolved in a solvent of 110 ml.
Solution:
Volume of solute (v) = 7 ml
Volume of solvent = 110 ml
Volume of solution (V) = (7 + 110) ml = 117 ml
Using the formula we get,
P = (v / V) × 100
= (7/117) × 100
= 5.98 %
Problem 3: Calculate the percent volume of solvent if 10 ml of solute is dissolved in a solvent of 120 ml.
Solution:
Volume of solute = 10 ml
Volume of solvent (v) = 120 ml
Volume of solution (V) = (10 + 120) ml = 130 ml
Using the formula we get,
P = (v / V) × 100
= (120/130) × 100
= 92.30 %
Problem 4: Calculate the percent volume of solvent if 15 ml of solute is dissolved in a solvent of 45 ml.
Solution:
Volume of solute = 15 ml
Volume of solvent (v) = 45 ml
Volume of solution (V) = (15 + 45) ml = 60 ml
Using the formula we get,
P = (v / V) × 100
= (45/60) × 100
= 75 %
Problem 5: Calculate the percent volume of solvent if 25 ml of solute is present in a solution of 80 ml.
Solution:
Volume of solute = 25 ml
Volume of solution (V) = 80 ml
Volume of solvent (v) = 80 – 25 = 65 ml
Using the formula we get,
P = (v / V) × 100
= (65/80) × 100
= 81.25 %
Problem 6: Calculate the percent volume of solvent if 30 ml of solute is present in a solution of 85 ml.
Solution:
Volume of solute = 30 ml
Volume of solution (V) = 85 ml
Volume of solvent (v) = 85 – 30 = 55 ml
Using the formula we get,
P = (v / V) × 100
= (55/85) × 100
= 64.70 %
Problem 7: Calculate the percent volume of solute if 81 ml of solvent is present in a solution of 110 ml.
Solution:
Volume of solvent = 81 ml
Volume of solution (V) = 110 ml
Volume of solute (v) = 110 – 81 = 29 ml
Using the formula we get,
P = (v / V) × 100
= (29/110) × 100
= 26.36 %
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