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# Avogadro’s Law: Statement, Representation, Application, Practice Problems and FAQs

What will you observe when you start filling the air in a balloon? Yes, it will inflate slowly! When air is filled inside there is a significant increase in the size/volume of the balloon. In 1811, Italian scientist Amedeo Carlo Avogadro explained the relationship between the volume of the gas and the amount of gaseous substances in the form of a law known as Avogadro’s law or Avogadro’s hypothesis.

Table of content

• Mathematical representation of Avogadro’s law
• Graphical representation of Avogadro’s law
• Practice problems

According to this law “ At a constant temperature and pressure, the volume of the gas is directly proportional to the amount of gas present in the container”

## Mathematical representation of Avogadro’s law

At constant temperature and pressure,

Constant

Where represents the volume occupied by the gas, denotes the number of moles of gas, represents the proportionality constant.

Now, consider two different conditions. The volume and no. of moles of the gas are changed keeping the pressure and temperature constant.

Using Avogadro’s law for both Case and Case we get;

From equation and , we get;

Constant

Where , represent volume occupied by the gas and , represent the number of moles of gas in Case and Case respectively.

## Graphical Representation of Avogadro’s law

The volume vs number of moles curve at a constant temperature and pressure is represented as:

We know the general equation of a straight line is

Where, and represent the co-ordinate axis, represents the slope of the curve and represents the intercept on axis.

If we compare the equation and , we can say;

Intercept and Solpe

Therefore, the above curve between volume and no. of moles is a straight line with a constant slope.

Avogadro’s law has a wide range of applications which includes:

• Breathing
• Blowing up the balloons
• Inflating tyres

## Practice problems

Question 1. If argon present in a movable cylindrical piston occupies a volume of at some pressure and temperature, What will be the volume occupied when of argon is added at the same temperature and pressure?

Answer: According to the given data;

Initial no. of moles of argon

Initial volume occupied by the argon gas

Final no. of moles of argon Initial no. of moles of argon No. of moles of argon added

Final no. of moles of argon

Final volume occupied by argon gas =

Question 2. If of oxygen gas occupies a volume of at some pressure and temperature. What volume will be occupied by g oxygen gas under the same temperature and pressure conditions?

a. 2 L
b. 4 L
c. 6 L
d. 4.5 L

According to the given data;

Initial no. of moles of oxygen gas

Initial volume occupied by oxygen gas =

Final no. of moles of oxygen gas

Final volume occupied by oxygen gas =

Question 3. Volume occupied by of an ideal gas at temperature and pressure is . When of another ideal gas is introduced in the same cylinder (having one wall flexible) at same temperature and pressure conditions, the volume of the cylinder is found to be . What will be the relationship between the molar mass of and molar mass of ?

a.
b.
c.
d.

Initial no. of moles of gas =

Initial volume occupied by gas

Final no. of moles of the gas and No. of moles of gas No. of moles of gas

Final volume of the gas occupied by and

Solving the above expression we get,

Question 4. A flexible container containing of nitrogen gas at and occupies the volume of . Some more oxygen gas is added at the same temperature and pressure until the volume becomes. Calculate the no. of moles of oxygen gas added to the container.

According to the given data,

Initial no. of moles of oxygen gas

Initial volume occupied by the oxygen gas

Final no. of moles of nitrogen gas present Initial mole of nitrogen gas present + No. of moles of nitrogen gas added

Final no. of moles of nitrogen gas present

Final volume occupied by nitrogen gas

So, No. of moles of nitrogen gas added

Question 1. How Avogadro’s law can be used in stoichiometry?
Answer: Avogadro’s law can be used to compare the number of molecules of gas present in a given volume at a given temperature and pressure. According to Avogadro's law, the volume occupied by the gas is proportional to the number of molecules of gas at constant temperature and pressure.

Question 2. What are the limitations of Avogadro’s law?
Answer: Avogadro’s law is valid for ideal gases but it provides an approximate relationship for real gases. Gases having relatively lower molecular mass obey Avogadro’s law to a higher extent as compared with the gas having higher molecular mass.

Question 3. What is the relation between the number of molecules of two different gases occupying the same volume at a certain temperature and pressure?
Answer: According to Avogadro’s law “volume occupied by a gas is directly proportional to the number of moles of gas present at a constant temperature and pressure”. So, the same volume of two different gases will contain the same number of molecules if temperature and pressure are constant.

Question 4. Why a flat tyre takes up less space as compared to inflated tyres?
Answer: The flat tyre takes up less space as compared to inflated tyres as it follows Avogadro’s law which states that “volume occupied by a gas is directly proportional to the number of moles of gas present at a constant temperature and pressure”. So when the tyre is inflated it contains more no. of molecules of air which results in increase in volume of the tyre as compared with the flat tyre.

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