Question

An ideal gas occupies a volume of 0.60 m3 at 5.0 atm and 400. K. What volume does it occupy at 4.0 atm and a temperature of 200. K?

What is the known and unknown when using P1V1/T1=P2V2/T2

Answer 1

It is given that P1=5atm
V1=0,6m3
T1=400K
And
P2=4atm
T2=200K
Therefore the unknown is V2
From now on you put all the known in the formula P1xV1/T1=P2xV2/T2 and with the help of algebra find what the unknown is ☺️

Answer 2

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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