Page 364 - Physics Coursebook 2015 (A level)

352
Cambridge International A Level Physics
WORKED EXAMPLE
3 A car tyre contains 0.020 m3 of air at 27 °C and at a pressure of 3.0 × 105 Pa. Calculate the mass of the air in the tyre. (Molar mass of air = 28.8 g mol−1.)
Step1 Here,weneedfirsttocalculatethenumber of moles of air using the equation of state. We have:
p=3.0×105Pa V =0.02m3 T=27°C=300K
Hint: Don’t forget to convert the temperature to kelvin.
So, from the equation of state: n= pV = 30×105 ×0.02
RT 8.31 × 300 n=2.41mol
Step2 Nowwecancalculatethemassofair: mass = number of moles × molar mass mass=2.41×28.8=69.4g≈69g
QUESTIONS
For the questions which follow, you will need the following value:
R=8.31Jmol−1K−1
11 At what temperature (in K) will 1.0 mol of a gas
occupy 1.0 m3 at a pressure of 1.0 × 104 Pa?
QUESTION
16 A cylinder of hydrogen has a volume of 0.10 m3. Its pressure is found to be 20 atmospheres at 20 °C.
a Calculate the mass of hydrogen in the cylinder.
b If it were instead filled with oxygen to the same pressure, how much oxygen would it contain?
(Molar mass of H2 = 2.0 g mol−1, molar mass of O2 = 32 g mol−1; 1 atmosphere = 1.01 × 105 Pa.)
Modelling gases – the kinetic model
In this chapter, we are concentrating on the macroscopic properties of gases (pressure, volume, temperature). These can all be readily measured in the laboratory. The equation:
pV = constant T
is an empirical relationship. In other words, it has been deduced from the results of experiments. It gives a good description of gases in many different situations. However, an empirical equation does not explain why gases behave in this way. An explanation requires us to think about the underlying nature of a gas and how this gives rise to our observations.
A gas is made of particles (atoms or molecules). Its pressure arises from collisions of the particles with the walls of the container; more frequent or harder collisions give rise to greater pressure. Its temperature indicates the average kinetic energy of its particles; the faster they move, the greater their average kinetic energy and the higher the temperature.
The kinetic theory of gases is a theory which links these microscopic properties of particles (atoms or molecules) to the macroscopic properties of a gas. Table 22.1 shows the assumptions on which the theory is based.
On the basis of these assumptions, it is possible to use Newtonian mechanics to show that pressure is inversely proportional to volume (Boyle’s law), volume is directly proportional to thermodynamic (kelvin) temperature (Charles’s law), and so on. The theory also shows that the particles of a gas have a range of speeds – some move faster than others.
12 Nitrogen consists of molecules N . The molar −1 2
massofnitrogenis28gmol .For100gof nitrogen, calculate:
a the number of moles
b the volume occupied at room temperature
and pressure. (r.t.p. = 20 °C, 1.01 × 105 Pa.)
13 Calculate the volume of 5.0 mol of an ideal gas at a pressure of 1.0 × 105 Pa and a temperature of 200 °C.
14 A sample of gas contains 3.0 × 1024 atoms. Calculate the volume of the gas at a temperature of 300 K and a pressure of 120 kPa.
15 At what temperature would 1.0 kg of oxygen occupy 1.0 m3 at a pressure of 1.0 × 105 Pa? (Molar mass of O2 = 32 g mol−1.)