We will be looking at gases and
their behaviour under different conditions. The behaviour of ideal
gases is quite easily predictable. However
real gases tend to behave slightly differently, especially those that consist of
molecules. So the ideal gas we will
consider is:
monatomic
at low temperature
at low pressure.
There is no interaction between the molecules of an ideal gas except for collisions, which are always perfectly elastic. Helium is a good example of an ideal gas.
Why is air not an ideal gas? |
Ideal Gas Equation
There are three gas laws:
Boyle's Law
Charles' Law
Pressure Law
You are not expected to know them for the examination, but understanding them is useful. Click HERE to find out more about the Gas Laws.
From the gas laws we can write:
The value of the constant
depends on how much gas is being considered.
If we are looking at one mole of gas (which we will define later), then
the constant is the universal molar gas
constant.
For
n moles of a gas, we can write:
Where:
p - pressure (Pa)
V - volume (m^{3})
n - number of mols
R - molar gas constant ( 8.31 J mol^{-1} K^{-1})
T - Temperature (K)
This is called the equation of state of an ideal gas. In this equation, SI units must be used, i.e. volume in m^{-3}, pressure in Pa. Temperature must be in Kelvin (K). 0 K = -273 ^{o}C.
The temperature quoted in degrees Celsius is commonly set as a bear trap. Make sure you don't fall into it.
Question 2 |
What is the volume of 2 moles of helium atoms at a temperature of 20^{ o}C and a pressure of 100 kPa? |
A more useful version of the ideal gas equation is this:
p_{1}V_{1} = p_{2}V_{2}
T_{1} T_{2}
The term p_{1} stands for pressure in container 1 while p_{2} stands for pressure in container 2.
A
SCUBA* diver is deep underwater at a point where the pressure is 3.03 ×
10^{5} Pa, and the temperature is 10 ^{o}C. The
volume of her lungs is 3 litres. She spots a dangerous animal and
rises very rapidly to the surface where the temperature of the water is
20 ^{o}C and the air pressure is 1.01 × 10^{5} Pa.
What is the volume of air in her lungs now? *SCUBA stands for Self-Contained Underwater Breathing Apparatus. |
The
mole is defined as:
the same number of particles of
a substance as there is in 12 g of ^{12}C.
This
number is called the Avogadro constant,
and is given the codes
L or
N_{A}.
L
= 6.02 x 10^{23} mol^{-1}
The molar mass M_{m} is the mass of 1 mole of the substance. Chemists quote this in grams per mole; for physics we need to convert to kilograms per mole by dividing by 1000 (or multiplying by 10^{-3}).
A sealed container of volume 0.8 × 10^{-3 }m^{3} contains gas at a temperature of 320 K and a pressure of 1.5 × 10^{6} Pa. Calculate: a) The number of moles and molecules of the gas. b) The mass of the gas if its molar mass is 32.0 × 10^{-3 }kg c) The mass of a single molecule of gas. |