If the pressure of a sample of gas is doubled at constant temperature, what happens to the volume of the gas? A) The volume doubles. B) The volume is halved. C) The volume quadruples. D) The volume remains the same.

its B on USATestPrep

according to ideal gas equation, we have

PV = n RT

where P = pressure, V = Volume, n = number of moles, R = gas constant and

T = temperature

the formula can be rearranged as

T = PV / (nR)

at constant temperature, the formula can be reformed as

T₁ = T₂

P₁V₁ / (nR) = P₂V₂ / (nR)

hence

P₁V₁ = P₂V₂

where

P₁ = initial pressure

P₂ = final pressure = 2 P₁

V₁ = initial volume

V₂ = final volume

P₁V₁ = (2 P₁) V₂

V₁ = (2) V₂

V₂ = V₁ / 2

hence the Volume is halved