1. Could 131 g of xenon gas in a vessel of volume 1.0 dm3 exert a pressure of 20 atm at
25°C if it behaved as a perfect gas? If not, what pressure would it exert? (b) What
pressure would it exert
if it behaved as a van der Waals
gas?
2. A perfect gas undergoes isothermal compression, which reduces its volume by 2.20 dm3.
The final pressure and volume
of the gas are 5.04 bar and 4.65 dm3, respectively.
Calculate the original
pressure
of the gas in (a) bar, (b) atm.
3. A car tyre (i.e. an automobile tire)
was inflated to a pressure of 24 lb in−2 (1.00 atm =
14.7 lb in−2) on a winter’s day when the temperature was –5°C. What pressure will be found,
assuming no leaks have
occurred and that the volume is constant, on a subsequent summer’s day when the temperature is 35°C? What complications should be taken into account
in practice?
4. A homeowner uses 4.00 × 103 m3 of natural gas in a year to heat a home. Assume that
natural gas is all methane, CH4, and that methane is a perfect gas for the conditions of this problem, which are
1.00 atm and 20°C. What is
the mass of gas used?
5. What pressure
difference must be generated across
the
length
of
a
15
cm
vertical
drinking straw in order to drink a water-like liquid of density 1.0 g cm−3?
6. A manometer consists of a U-shaped tube containing a liquid. One side is connected to
the apparatus and the other is open to the atmosphere. The pressure inside the apparatus
is then determined from the difference in heights of the liquid. Suppose the liquid is water,
the external pressure is 770 Torr, and the
open side is 10.0 cm lower
than the side connected to the apparatus. What is the pressure in the apparatus? (The density of water
at 25°C is 0.997 07 g cm−3.)
7. At 100°C and 1.60 kPa, the mass density of
phosphorus vapour is 0.6388 kg m−3. What is the molecular formula of
phosphorus under these conditions?
8. Calculate the mass of water vapour present in a room of volume 250 m3 that contains air
at
23°C on a day when the relative humidity is 53%.
9. Given
that the density of air at 0.987 bar and 27°C is 1.146 kg m−3, calculate
the mole fraction and partial pressure of nitrogen and oxygen assuming
that (a) air consists only of
these two gases, (b) air also contains 1.0 mole per cent Ar.
10.
The density of a gaseous compound was found to be 1.23 kg m−3 at 330 K and 20 kPa.
What is the molar mass
of the compound?
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