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STATES OF MATTER - properties of gases and liquids (fluids) and solids - the Kelvin temperature scale

17. IDEAL GAS MODEL and IDEAL GAS BEHAVIOUR

Doc Brown's chemistry revision notes: basic school chemistry science GCSE chemistry, IGCSE  chemistry, O level and ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old science students for national examinations in chemistry and also helpful for UK advanced level chemistry students aged ~16-18 and US grades 11-12 K12 honors.

17. Ideal gas behaviour and the gas laws and explaining the origin of the Kelvin scale of temperature and comparing it with the Celsius scale of temperature

Introduction – the kinetic particle model of an ideal gas

• The (advanced) kinetic theory of gases is founded on the following six fundamental postulates:

1. Gases are composed of minute discrete particles (usually molecules) and considered to have zero volume (which isn't true).

2. There are no attractive forces between the gas particles (which isn't true, however weak the intermolecular forces are in gases).

3. The particles are in continuous chaotic motion moving in straight lines between very frequent collisions with each other and the sides of the container (approximately 109/s).

4. The bombardment of the container walls by the particles causes the phenomenon we call pressure (i.e. force of impacts/unit area).

5. The greater the force of collision and the more frequent the collisions the greater the gas pressure exerted by the gas on the container surface.

6. The collisions are perfectly elastic i.e. no energy loss on collision due to friction.

7. At relatively low pressures the average distance between particles is large compared to the diameter of the particles and therefore the inter–molecular forces between the particles is negligible (only ~true at relatively low pressures).

8. The average kinetic energy of the particles is directly proportional to their absolute temperature on the Kelvin scale (K) i.e. average KE(J) T(K)

• This means if you heat up a gas the average thermal kinetic energy of the particles increases, therefore the average speed increases too.

• The Kelvin scale of temperature is explained below.

9. The increase in the average particle kinetic energy with increase in temperature will cause the pressure to increase in fixed volume because the particle-surface impacts will be more forceful and more frequent.

• When a gas behaves according to this model, the gas laws described in sections 18 to 21 are obeyed.

• However in real gases things are not so simple and this so see ...

• non–ideal behaviour is discussed in section 24 (for advanced level students only).

The Kelvin Scale of Temperature

In the past lots of measurements have been made to investigate:

(i) how the pressure and volume of a given mass of vary at constant temperature (left graph above)

(ii) how the pressure and volume gas of a fixed mass of gas varies with temperature (right graph above).

This resulted in the formulation of the laws of gases described in section 17. to 19. along with how to use them in calculations and problem solving.

However, before this, if you look at these two graphs of gas behaviour when changing pressure or volume with temperature, one thing becomes clear, when the graph lines are extrapolated back to the x axis they give a value of –273oC. This gave rise to the idea that there was a minimum possible temperature of –273 oC and further experimentation has confirmed this time and time again. At –273oC all substances are solid and in terms of the kinetic particle theory of matter, at –273 oC the particles have virtually no motion i.e. ~no vibration of the atoms in the solid.

Therefore as well as the established Celsius scale (centigrade scale), a new temperature scale was proposed in which the lowest value was 0 (known as absolute zero) rather than –273. This is called the Kelvin scale of temperature or the absolute temperature scale, denoted by the unit K. Incidentally you don't say degrees Kelvin like you say degrees Celsius, you just say Kelvin. The Kelvin temperature scale was also designed so that a 1 K temperature change or interval, exactly equals 1oC Celsius change or interval. Therefore you can easily convert between the two temperature scale by a simple calculation

K = oC + 273   and  oC = K – 273   and it is the temperature in K that you must use in gas law calculations (4b.)

Some examples are worked out below and a practice in reading a Celsius thermometer, which is what you use in the school or college laboratory!

 –7oC –7 + 273 = 267 K 36oC 36 + 273 = 309 K 77oC 77 + 273 = 350 K 101.5oC 101.5 + 273.0 = 374.5 K 132oC 132 + 273 = 405 K 206oC 206 + 273 = 479 K

Some familiar temperatures are quoted below relating the two temperature scales

 absolute zero Freezing point of water Body temperature Boiling point of water Celsius scale –273 oC 0 oC 37 oC 100 oC Kelvin scale 0 K 273 K 310 K 373 K

It seems a bit weird to say you body has a normal temperature of 310 K, which is why it is always important to state the units too!

Learning objectives for the kinetic particle theory of gases

Be able to outline the particle model of an ideal gas and appreciates and know at least two assumed points on which the ideal kinetic particle theory of gases is incorrect.

Be able to explain why a gas exerts pressure on a containing surface.

Be able to describe (sketch) and interpret volume versus temperature graphs for a fixed pressure..

Be able to describe (sketch) and interpret pressure versus temperature graphs for a fixed volume.

modify x-refs to 18 to 20 (17 to 19 should say 18 to 20

Know what the Celsius and Kelvin scale of temperature are and be able to convert from one to the other.

i.e. K = oC + 273  and  oC = K - 273 (by convention, K does not need the degree o sign)

Know that you must use the Kelvin scale of temperature (K) in gas calculations.

Know how to read a thermometer accurately - making observations by interpolating-interpreting the temperature scale.

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