deduce gas law with the help of kinetic gas equation
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Answer:
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Explanation:
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Answer:
Deduction of Gas Laws with the help of Kinetic Gas Equation is explained below
Explanation:
What are Gas Laws?
Gas Laws in basic terms define the properties of gases or the laws that relate to the gas's pressure, volume, and temperature.
Anglo-Irish physicist Robert Boyle produced the first credible measurement of gas characteristics in 1662. Boyles law is the name of the law he created. Jacques Charles and Joseph Lewis Gay Lussac later drew inspiration from hot air balloons to develop new gas laws.
What is the Kinetic Gas equation?
Gas, according to the kinetic theory, is made up of a vast number of submicroscopic constituents such as atoms or molecules that are all moving at random and in a continuous manner. The collisions of the particles with one other and the container walls produce unpredictability.
P= 1/3mNV²
Here, mN= molecular mass of the gas
The root mean square velocity and density of gas molecules are calculated using the kinetic gas equation, which is derived from the kinetic theory of gases.
P=1/3mNCRMS²
Boyle's law
Boyle's Law, also known as Mariotte's Law, is a relationship that describes how a gas compresses and expands at a constant temperature. The pressure of a given quantity of gas changes inversely with its volume at a constant temperature, according to this empirical relationship proposed by the scientist Robert Boyle in 1662.
Calculation based on the Kinetic Gas Equation
According to the kinetic gas equation, we know that,
PV = 1/3 mnv²
PV = 2/3 × 1/2 (Mv²)
But 1/2 Mv² = Kinetic energy of the gas
PV = 2 K.E/ 3
As
K.E. ∝ T
we know,
K.E. = kT
So, ,
PV = 2kT/3
Since 2/3 and k are constant
Hence PV = constant
Charles law
If the pressure remains constant, Charles' law states that the volume occupied by a certain amount of gas is exactly proportional to its absolute temperature.
Calculation based on the Kinetic Gas Equation
We Know,
PV = 1/3 mnv²
PV = 2/3 × 1/2 (Mv²)
But 1/2 Mv² = Kinetic energy of the gas
PV = 2 K.E/ 3
K.E. ∝ T
K.E. = kT
PV = 2kT/3
we can write it as,
V/T = 2k / 3P
Since 2/3 and k are constant
So, P is kept constant,
V/T =constant.
That is what Charles's law defines.
Dalton's the law of partial pressure
The total pressure exerted by a gas mixture is equal to the sum of the partial pressures of each individual gas present, according to Dalton's Law of Partial Pressures.
Calculation based on the Kinetic Gas Equation
We know,
PV = 1/3 (mnv²)
we can write it as,
P= mnv² / 3V
If only the first gas is enclosed in the vessel of volume V, the pressure exerted would be,
P1 = m₁n₁v₁² / 3V
If the second gas is enclosed in the same vessel, then the pressure exerted would be
P2 = m₁n₂v₂² /3V
Therefore
P= m₁n₁v₁² / 3V + m₁n₂v₂² /3V + …
P =P₁ + P₂
Hence, it proves Dalton's law of partial pressure.