Question

A fixed quantity of gas at 21 ∘C exhibits a pressure of 758 torr and occupies a volume of 5.42 L .

A) Calculate the volume the gas will occupy if the pressure is increased to 1.89 atm while the temperature is held constant.

B) Calculate the volume the gas will occupy if the temperature is increased to 185 ∘C while the pressure is held constant.

Answer 1

(A)We know that PV = nRT

Where

T = Temperature ;P = pressure ; n = No . of moles ;R = gas constant ; V= Volume of the gas

As the gas remains the same , n will constant & T held constant PV = constant

So PV = P'V'

Where

P = initial pressure = 758 torr = 758/760 atm                Since 1 atm = 760 torr

                            = 0.997 atm

V = initial volume = 5.42 L

P'= final pressure = 1.89 atm

V' = final volume = ?

Plug the values we get V' = (PV) / P'

                                      = 2.86 L

(B)We know that PV = nRT

Where

T = Temperature ;P = pressure ; n = No . of moles ;R = gas constant ; V= Volume of the gas

As the gas remains the same , n will constant & P held constant , V proportional to T

So V/V' = T/ T'

Where

V = initial volume = 5.42 L

T = initial temperature = 21.0 ^oC = 21.0+273 = 294 K

V' = final volume = ?

T' = final temperature = 185 ^oC =185+273 = 458 K

Plug the values we get

V' = (VT') / T

   = 8.44 L