Physics Made Easy

Kinetic Theory and Ideal Gases

Kinetic theory of matter: all matter is composed of tiny, invisible particles. Particles of different substances have different sizes. Increasing temperature increases the kinetic energy of the particles.

Solids: particles have fixed positions close together. Particles can vibrate about these positions but do not have enough energy to overcome the bonds holding them together. Solids have a fixed, definite shape and volume. They are incompressible, so they transmit forces.

Melting: If the temperature is raised, particles in a solid gain kinetic energy. They vibrate more vigorously, and, if enough energy is available, they partially overcome bonds between molecules. When this happens, the solid melts and becomes a liquid. The opposite of melting is freezing.

Liquids: particles are slightly further apart than in solids- they have gained enough energy to partially overcome the bonds holding them together. Particles can move freely, so that even though a liquid has a fixed volume, it can take the shape of its container. Liquids can be compressed very slightly, but generally they are regarded as incompressible. Liquids are fluids- they can flow and transmit pressure.

Boiling: If the temperature is raised, particles in a liquid gain kinetic energy. They begin to move faster and vibrate more vigorously. If enough energy is supplied, the particles will be able to overcome intermolecular bonds and become a gas. This process is boiling; the opposite is condensation. Boiling is not the same as evaporation.

Gases: particles are widely separated and have high energy, leading to weak intermolecular bonds (we often assume there are no intermolecular bonds). Particles can move freely and randomly, so gases take the shape and volume of their container. About 99.99% of a gas’s volume is empty space. Gases are also fluids, they can flow and transmit pressure, even though in everyday terms we only think of liquids as fluids.

Volatile solids and liquids are substances which vaporise easily. Volatile substances usually have small molecules with weak intermolecular bonds that are easily overcome by a small input of energy. I2, CFC’s and other small organic molecules are all volatile. It’s a common mistake to think of volatile as meaning reactive. Don’t fall into that trap!

GAS LAWS

Note: k = a constant

Boyle’s Law: the pressure of a fixed mass of gas is inversely proportional the volume provided the temperature is constant.

p µ 1/V

p = k / V

pV = constant

Charle’s Law: the volume of a fixed mass of gas is directly proportional to its temperature in Kelvin, provided the pressure remains constant.

V µ T

V = kT

Pressure Law: the pressure of a fixed mass of gas is directly proportional to the temperature in Kelvin, provided the volume remains constant.

P µ T

p = kT

Ideal Gas equation: combining the above laws gives this equation.

pV=nRT

p=pressure in Nm-3 or Pascals; V=volume in m3; n= number of moles of gas; R= gas constant, 8.314 J K-1 mol-1; T=temperature in Kelvin. Make sure that all your temperatures are in Kelvin and all your volumes are in m3 and NOT dm3 or you will not get the right answer.

Assumptions made when using the Ideal Gas Equation:

  1. Pressure is the result of molecules colliding with the walls of the container.
  2. Collisions between molecules are perfectly elastic (kinetic energy remains constant).
  3. Intermolecular forces are negligible.
  4. The actual volume of gas molecules is negligible compared to the volume of the container.
  5. The average kinetic energy of the gas molecules is proportional to the temperature in Kelvin. (K.E.=G kT)

Boltzmann constant: Basically, the gas constant for 1 molecule of gas

L = R/NA

L= Boltzmann constant, R=gas constant, NA=Avogadro constant. More useful in Physics.

Determining the molar mass of a gas:

  1. Take the mass of a stoppered flask filled with gas.
  2. Use a vacuum pump to remove the gas. CAREFUL THE FLASK DOESN’T IMPLODE! Now record the mass of the stoppered, empty flask.
  3. Subtract the mass of empty flask from the mass of flask+gas to find the mass of air in the flask.
  4. Fill the flask with water. Either note the volume of water used to fill the flask OR take the mass of flask+water, subtract the mass of empty flask to find mass of water in the flask, then use volume = mass/density where water has a density of 1 g cm-3 or 1000 kg m-3 to find the volume of water in the flask.
  5. Use a thermometer or barometer to determine the current temperature and atmospheric pressure.
  6. Use pV = nRT (V=volume of flask) to find the number of moles of gas in the flask.
  7. Now use no. moles = mass/molar mass to find the molar mass of the gas used in the experiment.

Determining the molar mass of a volatile liquid:

  1. Weigh an empty stoppered flask, then fill with a sample of liquid and re-stopper. Reweigh, and subtract the two values to find the mass of liquid used.
  2. Inject into a gas syringe surrounded by a steam jacket (jacket should include thermometer) to vaporise the sample. Use the gas syringe to take the volume of the sample, and the thermometer to take the temperature.
  3. Use a barometer to note atmospheric pressure.

Once again, use pV = nRT to find the number of moles of liquid present, and then use no. moles = mass/molar mass to find the molar mass of the liquid.

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