4.3.4 Ideal Gases

4.3.4 Ideal Gases

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cs Boyle’s Law

Gas has four properties: Pressure (Pa) Temperature (°C or K) Volume (m3) Mass (kg, but more usually in moles)

The Gas Laws relate different properties

Boyle’s Law relates pressure p and volume v

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cs Boyle’s Law

If a gas is compressed, its pressure increases and its volume decreases

Pressure and volume are inversely related

The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of the gas remains constant

pV = constant p 1 V

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cs Boyle’s Law

More usefully, the formula can be written:

p1V1 = p2V2

Attempt SAQ 4 on page 93

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cs Charles’ Law

-273 0 +100

V/m3

θ /°C

0 300 T/K

This graph shows the result of cooling a fixed mass of gas at a constant pressure

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cs Charles’ Law

The relationship between volume V and thermodynamic temperature T is:

V T

or V = constant

T

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cs Charles’ Law

“The volume of a fixed mass of gas is directly proportional to its absolute temperature, provided its pressure remains constant”

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cs Combine the Gas Laws

pV = constant T

or

p1V1 = p2V2

T1 T2

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cs Questions

Now do SAQ’s 5 to 8 on page 94

Objective

(c) state the basic assumptions of the kinetic theory of gases

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cs Kinetic Theory of Gases

A gas contains a very large number of spherical particles

The forces between particles are negligible, except during collisions

The volume of the particles is negligible compared to the volume occupied by the gas

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cs Kinetic Theory of Gases

Most of the time, a particle moves in a straight line at a constant velocity. The time of collision with each other or with the container walls is negligible compared with the time between collisions

The collisions of particles with each other and with the container are perfectly elastic, so that no kinetic energy is lost

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cs Measuring Gases

One mole of any substance contains 6.02 x 1023 particles

6.02 x 1023 mol-1 is the Avogadro constant NA

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cs Questions

Now do SAQ’s 1 and 2 on pages 91 and 92

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cs Ideal Gas Equation

Calculating the number n of moles

number of moles (n) = mass (g) molar mass (g mol-1)

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cs Ideal Gas Equation

For a gas consisting of N particles:

pV = NkT

where k = 1.38 x 10-23 JK-1

N = number of particles

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cs Ideal Gas Equation

For n moles of an ideal gas:

pV = nRT

where R = 8.31 J mol-1 K-1

p = pressure (Pa)V = volume (m3)n = number of moles of gasT = temperature (K)

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cs Questions

Now do SAQ’s 9 to 14 on page 98

Objective

(f) explain that the mean translational kinetic energy of an atom of an ideal gas is directly proportional to the temperature

of the gas in kelvin

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cs Mean Translational Kinetic Energy

‘Mean’Either: add up all the KE’s of each individual

molecules, then calculate the average

or watch one molecule over a period of time and

calculate the average KE over that time

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cs Mean Translational Kinetic Energy

‘Translational’

energy due to the molecule moving along, as opposed to energy due to the molecule spinning around (‘rotational’)

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cs Mean Translational Kinetic Energy gas molecules rush around, colliding place a thermometer in the gas, and the

molecules will collide with it energy from the molecules will be shared with

the thermometer eventually, gas and bulb are at the same

temperature (thermal equilibrium) more energy, higher temperature height of the liquid in the thermometer is related

to the energy of the molecules

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cs Mean Translational Kinetic Energy

therefore:

‘The Mean Translational Kinetic Energy of a molecule of an ideal gas is proportional to the temperature of the gas in kelvin’

Objective

(g) select and apply the equationE = 3/2 kT

for the mean translational kinetic energy of atoms

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cs Mean Translational Kinetic Energy

total kinetic energy of gas T

total internal energy of gas T

therefore:

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cs Mean Translational Kinetic Energy

E = 3/2 kT

where:

E = mean translational KE of an atom in a gask = Boltzmann constant (1.38 x 10-23 JK-1)T = temperature (K)

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cs Questions

Now do SAQ’s 15 to 19 on page 100

and

End of Chapter Questions on pages 101 - 102