5. A gas cylinder with a movable piston holds 150 mL of a sample of an ideal gas
ID: 995939 • Letter: 5
Question
5. A gas cylinder with a movable piston holds 150 mL of a sample of an ideal gas sample at 1 atm and 295.15 K. Calculate the effect that the following changes in volume, temperature, or pressure will have in this system.
a. Calculate the final volume if the temperature increases to 300 °C; assume pressure remains constant.
b. Calculate the final pressure if the volume decreases to 12.5 mL; assume temperature remains constant.
c. Calculate the final volume if the pressure increases to 5 atm; assume temperature remains constant.
d. Calculate the concentration (moles) of gas in this system at the initial conditions.
e. Calculate the density of the gas in each case, assume that the mass of the sample is 112 g.
Explanation / Answer
a)
V1/V2 = T1 /T2
150 mL / V2 = 295.15 K /(273.15 + 300) K
V2 = 291 mL
b)
P1 V1 = P2 V2
1 atm x 150 mL = P2 x 12.5 mL
P2 = 12 atm
(c)
P1 V1 = P2 V2
150 mL x 1 atm = V2 x 5 atm
V2 = 30 atm
(d)
Concentration = mol = PV/RT
= 1 atm x 0.150 L /0.082 x 295.15
=0.006 moles
(e) density = mass /volume = 0.112 g / 0.150 x 10-3 m3 == 747 kg/m3
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