A gas has a pressure of 2.92 atm and occupies a volume of 5.5 L. If the gas is compressed to a volume of 2.61 L, what will its pressure be, assuming constant temperature? Answer in units of atm.

Question

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Answer 1

The ideal gas law is PV = nRT. Solving this for nR we get PV/T = nR. n is the number of moles of the gas and R is the ideal gas constant so, since this is a sealed container, neither of those will change. So we can say that PV/T (at time 1) = PV/T at time 2) or

P₁V₁/T₁ = P₂V₂/T₂

In this particular case, we are told that temp remains constant, so we can cancel out the T₁ and T₂ to get:

P₁V₁ = P₂V₂

P₁ = 2.92 atm

V₁ = 5.5 L

V₂ = 2.61 L

We are trying to find P2 so solving the equation for P2 we get:

P₂ = P₁V₁/V₂

so P₂ = (2.92)(5.5)/(2.61)

P₂ = 6.15 atm

Answer 2

Boyle's law states: the pressure of a gas is inversely proportional to its volume, given its temperature remains constant.

This is a situation where Boyle's law is applicable because the temperature remains constant.

Mathematically, Boyle's law is written as

p₁V₁ = p₂V₂

Substitute the given values

2.92(5.5) = p₂(2.61)

p₂ = 6.15 atm