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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.
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
Thus, for two substances (1) and (2), we can write
For three substances (1), (2) and (3), we can write
and so on.
a) We have
Therefore, the total volume of the mixture is
This result means the mixture occupies 74 cm3 of space in the container.
b) The density of the given mixture is
Now, let's consider an example with gases.
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:
a) First, let's calculate the volumes of each gas in the room. We have:
Now, let's calculate the mass of each gas inside the room. We have
Therefore, the total mass of air inside the room is
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
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.
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