Question

# A fixed quantity of gas at 21 ∘C exhibits a pressure of 756 torr and occupies...

A fixed quantity of gas at 21 ∘C exhibits a pressure of 756 torr and occupies a volume of 5.22 L .

Calculate the volume the gas will occupy if the pressure is increased to 1.88 atm while the temperature is held constant.

Calculate the volume the gas will occupy if the temperature is increased to 160∘C while the pressure is held constant.

We know that PV = nRT

Where

T = Temperature : P = pressure : n = No . of moles : R = gas constant = 0.0821 L atm / mol - K

V= Volume of the gas

(1) Since the temperature is kept constant & n is constant & R also kept constant

So PV = constant

PV = P'V'

Where

V = initial volume = 5.22 L

V' = final volume = ?

P = initial pressure = 756 torr

= 756 / 760   atm                       Since 1 atm = 760 atm

= 0.995 atm

P' = final pressure = 1.88 atm

Plug the values we get V = PV / P'

= ( 0.995 x 5.22 ) / 1.88

= 2.76 L

So the volume occupied by gas is 2.76 L

(2) Since the pressure is kept constant & n is constant & R also kept constant

So V/T = constant

V / T = V' / T'

Where

V = initial volume = 5.22 L

V' = final volume = ?

T = initial temperature = 21oC = 21+273 = 294K

T' = final temperature = 160oC = 160+273 = 433 K

Plug the values we get   V / T = V' / T'
V' = VT' / T

= ( 5.22 x 433 ) / 294

= 7.69 L

So the volume occupied by gas is 7.69 L

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