Problems Related To Avogadro’s Law

Amedeo Avogadro made a hypothesis in the evolution of atomic theory in 1811. The law itself is named after an Italian Scientist, Amedeo Carlo Avogadro. He expressed that the equivalent volumes of all gases at a particular temperature and pressure contain equivalent quantities of molecules. So Avogadro’s Law expresses that the volume of a gas is relative to the quantity of moles of the gas present when the temperature and pressure are held consistently.

The Avogadro’s number is the number of units in any one mole of a matter that is equal to 6.02214076 ✕ 1023 . For example, the molar mass of carbon dioxide gas is 44.01, so the one gram mole of carbon has a mass of 44.01g and contains 6.02214076 ✕ 1023 molecules.

Equation of Avogadro’s Law

There are different ways of writing Avogadro’s equation in Mathematical terms

k = V/n or  V=k X n

V is the volume of the gas, n is the number of moles of a gas, and K is constant. Avogadro’s Law states that the ideal gas constant is the same value for all the gases. 

Therefore:

k=p1V1/T1n1= P2V2/T2n2

V1/n1=V2/n2

V1n2=V2n1

Where p is pressure, V is volume, T is temperature, and n is a number of moles.

Derivation

This law is derived from the ideal gas equation.

PV=nRT

Here, P is the pressure exerted by a gas 

V is the volume 

n is the total number of moles 

R is the universal constant

T is the temperature 

n2Vn=(RT)P [since the pressure and the temperature are kept constant hence (RT)P is constant]

Therefore, k=Vn 

Limitations of Avogadro’s Law

• It can only be used for real gases.  

• The deviation of the gases tends to increase at lower temperatures and higher pressures.
• The molecules that have low mass, such as helium and hydrogen, act in accordance with Avogadro’s Law to a better extent than molecules with higher mass. 

Problems related to Avogadro’s Law

Example 1: A 7.0 L sample at 300C and 2.00 atm of pressure contain 0.8 moles of a gas. Then adding 0.30 moles of gas at the same pressure and temperature are added, what will be the final total volume of the gas?

Solution:

Formula of Avogadro’s Law

  Vini=Vfnf

Here , 

Vi = initial volume 

ni = initial number of moles 

Vf= final volume 

nf = final number of moles 

Therefore, Vi = 7.0 L and ni = 0.8 mole. when 0.30 mole is added:

nf= ni +0.30

nf= 1.1 mole

Now, Vf = Vi nf/ni

Vf =(7.0L ✕ 1.1mole)/0.8 mole

Vf =7.7L/0.8

Vf = 9.625 L

To check whether the answer is right or not. The final volume should be greater than the initial volume because we added more gas. 

Hence, the final volume of the gas is 9.625

Example 2: A balloon was filled to a volume of  2.25 L with 0.0820 moles of helium gas. Suppose 0.015 moles of helium is added to the balloon with constant pressure and temperature. What will be the new volume of the balloon?

Given: 

V1 = 2.25 L

n1 = 0.0820 mol

n2 = 0.0820 +0.015 =0.097 mol

V2= ? L

Solution:

Formula is V2= V1 X  n2 n1

Putting the values into the formula 

V2= 2.25 X  0.0970.0820=2.66 L

Example 3: A flexible container at an initial volume of 5.00 L contains 6.500 mol of has. More gas is added to the flexible container until it reaches a final volume of 18.30 L. The pressure and the temperature of the gas remain constant. How many moles were added to the container? 

Given:

V1 = 5.00 L

n1 = 6.500 mol

n2 = ?

V2= 18.30 L

Solution:

The Formula is V1/n1=V2/n2

5.00 L6.500 mol= 18.30 Ln2

n2= 23.79 mol (n2 is the total number of moles)

Therefore  the number of moles added were 23.79-6.50=17.29

Notes for Avogadro’s Law

• Avogadro’s Law is also mentioned as Avogadro’s Hypothesis or Avogadro’s Principle.  
• The mathematical relation used for Avogadro’s law is:

             V=k X n

            V is the volume of the gas, K is constant, and n is the number of moles.

•  The quantity or the amount of gas in a container is increased, then the volume also increases
• The quantity or the amount of the gas in a container is decreased, then the volume of the gas decreases. 
• Avogadro Law is only used for gases
• Chemical engineers mostly use it to get the value. 

Conclusion 

Avogadro’s Law, also known as Avogadro’s Hypothesis or Avogadro’s principle, is widely used in chemical and process engineering. Using this Law, you can find any value such as volume of the gas or number of moles if the other values of the problems are given, as we solved in the problems related to Avogadro’s Law. We have mentioned some key points under the heading “Notes for Avogadro’s Law” that you should go through after completing this topic. Also, solve the given examples to understand Avogadro’s Law better.