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Physics Lesson 9.1.5 - Density of a Mixture

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Welcome to our Physics lesson on Density of a Mixture, this is the fifth lesson of our suite of physics lessons covering the topic of Fluids. Density of Fluids, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Density of a Mixture

In most cases, materials we use in daily life are not made of pure substances but by mixing two or more substances. As an example in this regard, we can mention beverages we drink every day. Thus, alcoholic beverages are not made of pure alcohol as people could not consume them in such a state, but they are mixed with water instead. The percentage of alcohol contained in a certain beverage is usually written in the etiquette stamped on the bottle. Thus, if a 333 ml bottle of beer contains 10% of alcohol, this means there are 333 / 10 = 33.3 mL of alcohol and 333 - 33.3 = 299.7 mL of water in that bottle.

To calculate the density of a mixture, we use the formula

ρmix = mtot/Vtot

Thus, for two substances (1) and (2), we can write

ρmix = m1 + m2/V1 + V2

For three substances (1), (2) and (3), we can write

ρmix = m1 + m2 + m3/V1 + V2 + V3

and so on.

Example 4

  1. How much space does a mixture made of 24 g water and 40 g alcohol occupy if the density of water is 1 g/cm3 and that of alcohol is 0.8 g/cm3.
  2. What is the density of this mixture in g/cm3?

Solution 4

a) We have

Vwater = mwater/ρwater
= 24 g/1 g/cm3
= 24 cm3
Valcohol = malcohol/ρalcohol
= 40 g/0.8 g/cm3
= 50 cm3

Therefore, the total volume of the mixture is

Vtot = Vwater + Valcohol
= 24 cm3 + 50 cm3
= 74 cm3

This result means the mixture occupies 74 cm3 of space in the container.

b) The density of the given mixture is

ρmix = mwater + malcohol/Vwater + Valcohol
= 24 g + 40 g/24 cm3 + 50 cm3
= 64 g/74 cm3
= 0.865 g/cm3

Now, let's consider an example with gases.

Example 5

The atmosphere contains 78% nitrogen, 21% oxygen and 1% carbon dioxide. If densities of the above gases in certain conditions are 1.25 kg/m3 for nitrogen, 1.40 kg/m3 for oxygen and 1.98 kg/m3 for carbon dioxide respectively, calculate:

  1. The total mass of air inside a 60 m3 room
  2. The density of air in the given conditions

Solution 5

a) First, let's calculate the volumes of each gas in the room. We have:

Vnitrogen = 78% of Vtot
= 0.78 × 60 m3
= 46.8 m3
Voxygen = 21% of Vtot
= 0.21 × 60 m3
= 12.6 m3
Vcarbon dioxide = 1% of Vtot
= 0.01 × 60 m3
= 0.6 m3

Now, let's calculate the mass of each gas inside the room. We have

mnitrogen = ρnitrogen × Vnitrogen
= 1.25 kg/m3 × 46.8 m3
= 58.5 kg
moxygen = ρoxygen × Voxygen
= 1.40 kg/m3 × 12.6 m3
= 17.64 kg
mcarbon dioxide = ρcarbon dioxide × Vcarbon dioxide
= 1.98 kg/m3 × 0.6 m3
= 1.12 kg

Therefore, the total mass of air inside the room is

mair = mnitrogen + moxygen + mcarbon dioxide
= 58.5 kg + 17.64 kg + 1.12 kg
= 77.26 kg

b) Since the volume of air is equal to the volume of room (air fills up the entire space of the room), we obtain for the density of air

ρair = mair/Vair
= 77.26 kg/60 m3
= 1.29 kg/m3

You have reached the end of Physics lesson 9.1.5 Density of a Mixture. There are 5 lessons in this physics tutorial covering Fluids. Density of Fluids, you can access all the lessons from this tutorial below.

More Fluids. Density of Fluids Lessons and Learning Resources

Density and Pressure Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
9.1Fluids. Density of Fluids
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
9.1.1The Definition of Matter. States of Matter and their Features
9.1.2What Are Fluids?
9.1.3What is Density?
9.1.4Auxiliary Units of Volume
9.1.5Density of a Mixture

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  3. Density and Pressure Revision Notes: Fluids. Density of Fluids. Print the notes so you can revise the key points covered in the physics tutorial for Fluids. Density of Fluids
  4. Density and Pressure Practice Questions: Fluids. Density of Fluids. Test and improve your knowledge of Fluids. Density of Fluids with example questins and answers
  5. Check your calculations for Density and Pressure questions with our excellent Density and Pressure calculators which contain full equations and calculations clearly displayed line by line. See the Density and Pressure Calculators by iCalculator™ below.
  6. Continuing learning density and pressure - read our next physics tutorial: Pressure. Solid Pressure

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