Taller de FQ: Gases ideals II-24
Exercises of the gas perfect
1.2(a) 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.
1.5(a) A diving bell has an air space of 3.0 m3 when on the deck of a boat. What is the volume of the air space
when the bell has been lowered to a depth of 50 m? Take the mean density of sea water to be 1.025 g cm−3
and assume that the temperature is the same as on the surface.
1.6(a) 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.)
1.7(a) In an attempt to determine an accurate value of the gas constant, R, a student heated a container of
volume 20.000 dm3 filled with 0.251 32 g of helium gas to 500°C and measured the pressure as 206.402 cm
of water in a manometer at 25°C. Calculate the value of R from these data. (The density of water at 25°C is
0.997 07 g cm−3; the construction of a manometer is described in Exercise 1.6a.)
1.10(a) 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.
Problema
1.2 Deduce the relation between the pressure and mass density, ρ, of a perfect gas of molar mass M. Confirm
graphically, using the following data on dimethyl ether at 25°C, that perfect behavior is reached at low
pressures and find the molar mass of the gas.
p/kPa 12.223 25.20 36.97 60.37 85.23 101.3
ρ/(kg m−3) 0.225 0.456 0.664 1.062 1.468 1.734
1.3 Charles’s law is sometimes expressed in the form V = V0(1 + αθ), where θ is the Celsius temperature, α
is a constant, and V0 is the volume of the sample at 0°C. The following values for α have been reported for
nitrogen at 0°C:
p/Torr 749.7 599.6 333.1 98.6
103α /(°C) 3.6717 3.6697 3.6665 3.6643
−1
For these data calculate the best value for the absolute zero of temperature on the Celsius scale.
1.5 A constant-volume perfect gas thermometer indicates a pressure of 6.69 kPa at the triple point
temperature of water (273.16 K). (a) What change of pressure indicates a change of 1.00 K at this
temperature? (b) What pressure indicates a temperature of 100.00°C? (c) What change of pressure indicates
a change of 1.00 K at the latter temperature?
