What is Combined Gas Law?
The combined gas law is the law which combines Charles’s law, Gay-Lussac’s law and Boyle’s law. It’s an amalgamation of the three previously discovered laws. These laws relate one thermodynamic variable to another holding everything else constant. The interdependence of these variables represents combined gas law which states that the ratio between the product of pressure-volume and temperature of a system remains constant.
Combined Gas Law Formula
Combined gas law can be mathematically expressed as
k = PV/T
Where,
P = pressure
T = temperature in kelvin
V = volume
KÂ = constant (units of energy divided by temperature)
When two substances are compared in two different conditions, the law can be stated as,
PiVi/Ti = PfVf/Tf
Where,
Pi = initial pressure
Vi = initial volume
Ti = initial temperature
Pf = final pressure
Vf= final volume
Tf = final temperature
Example 1
The initial volume of the gas is 5L and final volume is 3L Calculate the final pressure of the gas, given that the initial temperature is 273 K, the final temperature is 200 K, and initial pressure is 25 kPa.
Solution
According to the given parameters,
Pi= 25 kPa
Vi = 5L
Vf = 3L
Ti = 273K
Tf = 200K
According to combined gas law,
PiVi/Ti = PfVf/Tf
Substituting in the formula, we get
25 x 5 / 273 =  Pf x 3 / 200
Therefore, Pf = 30.525 kPa
Example 2
Determine the volume of a gas given Vi = 3L, Ti = 300K, Tf = 250K, Pi = 35 kPa and Pf= 50 kPa
Solution
Given Parameters are
Pi = 35 kPa
Vi = 3L
Ti = 300K
Pf= 50 kPa
Tf = 250K
According to given parameters, we have an equation
PiVi/Ti = PfVf/Tf
Substituting in the above equation, we get
35 x 3 / 300 = 50 x Vf / 250
Therefore, Vf = 1.75 L
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