An ideal gas occupies a volume of 0.60 m3 at 5.0 atm and 400K then the volume occupied by it at 4.0 atm and a temperature of 200K would be 0.375 meter³.
What is an ideal gas?
It is an imaginary gas for which the volume occupies by it is negligible, this gas does not exist in a practical situation and the concept of an ideal gas is only the theoretical one, the real gases approach the behaviors of an ideal gas at a very high temperature and very low pressure.
The mathematical relation representing the ideal gas is
PV = nRT
where P is pressure, V is volume,n is the amount of substance, R is the ideal gas constant and T represents the temperature
By using the Combined gas law equation for the given problem
P₁V₁/T₁=P₂V₂/T₂
Where P₁, V₁, and T₁ are initial pressure volume and the temperature
and P₂, V₂, and T₂ are the final pressure volume and the temperature
By substituting the values in the above equation
P₁ = 5.0 atmospheric pressure
V₁= 0.60 meter³
T₁= 400 Kelvin
P₂ = 4.0 atmospheric pressure
V₂= ? meter³
T₂= 200 Kelvin
The only unknown term which we have to find is the final volume of the gas
5.0 ×0.6/400=4.0×V₂/200
V₂ = 0.375 meter³
Thus, the gas would occupy 0.375 meter³ volume at 4.0 atm and a temperature of 200 Kelvin.
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