A gas sample enclosed in a rigid metal container at room temperature (20.0?C) ha

Question

A gas sample enclosed in a rigid metal container at room temperature (20.0?C) has an absolute pressure p1. The container is immersed in hot water until it warms to 40.0?C. What is the new absolute pressure p2?

Nitrogen gas is introduced into a large deflated plastic bag. No gas is allowed to escape, but as more and more nitrogen is added, the bag inflates to accommodate it. The pressure of the gas within the bag remains at 1.00 atm and its temperature remains at room temperature (20.0?C). How many moles n have been introduced into the bag by the time its volume reaches 22.4 L?

Explanation / Answer

(1) Since the volume is constant because the container is rigid , therefore
P/T = Constant , hence
P2/P1) = (T2 /T1)
P2 = (T2/T1)P1
Where T2 = 40 oC = 40+273 = 313 K
T1 = 20 oC = 20+273 = 293 K
P1 = 1 atm = 1.013*105 Pa
Now Putting all the values in the above equation
P2 = (313/293)*1.013*105 = 1.082*105 Pa
(2)
We know that ideal gas follow
PV = nRT
Where P is pressure = 1 atm = 1.013*105 Pa
V is volume = 22.4 L = 22.4*10-3 m3
n is no. of moles = ?
R is universal characterstic gas constant = 8.314 J/mol-K
T is temperature in K = 20oC = 20+273 = 293 K
now putting all the values in above equation
(1.013*105)*(22.4*10-3) =n*8.314*293
n = 0.931 moles

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