Properties of Gases & Mixtures
1) State & Explain Avogadro's Law
Statement: “Equal Volume of all Perfect gases at same Pressure & Temperature contains the same number of molecules”
(Perfect Gas means an Ideal Gas)
The law can be written as:
OR
Where,
V is the volume of the gas,
n is the amount of substance of the gas (unit: moles),
k is the constant for a given temperature & pressure
Example: The process of respiration is a great example of Avogadro’s law. When humans inhale, the increase in the molar quantity of air in the lungs is accompanied by an increase in the volume of the lungs (expansion of the lungs).
Avogadro’s Law is in evidence whenever you blow up a balloon. The volume of the balloon increases as you add moles of gas to the balloon by blowing it up.
If the container holding the gas is rigid rather than flexible, pressure can be substituted for volume in Avogadro’s Law. Adding gas to a rigid container makes the pressure increase.
Sum: 2 moles of helium gas fills up an empty balloon to a volume of 3 litres. What would be the volume of the balloon if an additional 5 moles of helium gas is added? (Assume that the temperature and the pressure are kept constant)
Given,
The initial amount of helium (n1) = 2 moles
The initial volume of the balloon (V1) = 3 L
The final amount of helium (n2) = 2 moles + 5 moles = 7 moles
As per Avogadro’s law, V1/n1 = V2/n2
Therefore, the final volume of the balloon (V2) = (V1n2)/n1 = (3L*7mol)/2mol = 10.5 L
The balloon would occupy a volume of 10.5 litres when it contains 7 moles of helium gas.
2) State & explain Gibbs - Dalton Law of partial pressure
Statement: “Total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture”
For example, let’s assume there is a mixture of 3 gases P1, P2 & P3 having pressure 2 pa, 10 pa & 3 pa respectively. Now according to Dalton’s Law, total pressure P = P1+P2+P3 which is 15 pa.
Partial pressure in terms of mole fraction: The mole fraction of a specific gas in a mixture of gases is equal to the ratio of the partial pressure of that gas to the total pressure exerted by the gaseous mixture.
Example: This example assumes that only two gases exist in the mixture. One consequence of this law is that oxygen accounts for 21 percent of the atmosphere’s total pressure because it makes up 21 percent of the atmosphere. People who ascend to high altitudes experience Dalton’s law when they try to breathe. As they climb higher, oxygen’s partial pressure decreases as total atmospheric pressure decreases in accordance with Dalton’s law. Oxygen has a difficult time making it into the bloodstream when the gas’s partial pressure decreases.
Sum: A mixture of hydrogen gas and oxygen gas exerts a total pressure of 1.5 atm on the walls of its container. If the partial pressure of hydrogen is 1 atm, find the mole fraction of oxygen in the mixture.
Given, Phydrogen = 1 atm, Ptotal = 1.5 atm
Applying Dalton’s law formula, Ptotal = Phydrogen + Poxygen
Therefore, Poxygen = 0.5 atm
Now, the mole fraction of oxygen, Xoxygen = (Poxygen/Ptotal) = 0.5/1.5 = 0.33
Therefore, the mole fraction of oxygen in the mixture is 0.33
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