Gas Laws

and breathing is the most common application of this.

Here are some questions for you to think about...

Why does pumping a tyre become more difficult as the tyre becomes more inflated?

Why does the balloon lift upwards into the air after the flame heats up the air inside it?

Why does soda eventually go flat when it is left exposed to the atmosphere?

By the end of this module, you'll figure out the answers...and be able to

• visualize a gas at the atomic level
• state Boyle's Law and work problems using Boyle's Law
• state Charles' Law and work problems using Charles' Law
• state Dalton’s Law of Partial Pressure and work problems using Dalton’s Law
• calculate pressures and partial pressures in gas mixtures
• state the basic assumptions of the kinetic theory as applied to an ideal gas
• explain qualitatively in terms of intermolecular forces and molecular size:

(i) the conditions necessary for a gas to approach ideal behaviour

(ii) the limitations of ideality at very high pressures and very low temperatures

• state and use the general gas equation PV = nRT in calculations, including the determination of Mr

Ready to start?

Kinetic Theory of Matter

Three distinct states of matter:

and the Kinetic Theory of Matter describes the arrangement of the particles in solids, liquids and gases and the movement of these particles.

and now we have...

Boyle's Law

which states that at a constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

or rather, two letters and a number...

which can be expressed in the following graphs

The two straw figures have pockets of air trapped within them. When the bottle is squeezed, the pressure of the water in the bottle increases. By Boyle's Law, the air in the straw must decrease in volume to increase its pressure to that of the water. This will draw water into the straw and the density of the straw figures increase and they start to sink. By varying the strength used in squeezing the bottle, one can adjust the density of the straw figures.

and next we have...

Charles' Law

which states that at constant pressure, the volume of a fixed mass of a given gas is directly proportional to its absolute temperature (expressed in Kelvins, K).

and is more elegantly shown as

Graphically, this can be expressed as

When liquid nitrogen is poured onto the balloon, the temperature of the air inside the balloon decreases. By Charles' Law, V=kT, volume of the air therefore decreases, and hence the balloon deflates.

Theoretically, a gas can reach zero volume when the temperature is -273.15 degrees Celsius or 0 K (ie. absolute zero). Absolute zero is the lowest possible temperature. In practice, however, gases will not actually reach zero volume as they will liquefy well above that temperature!!

and then we have...

Avogadro's Law

which states that under conditions of constant temperature and pressure, equal volumes of gas contain equal number of molecules.

otherwise known as

When the film of soap covered the basin, the carbon dioxide formed from the sublimation of the dry ice is trapped inside. By Avogadro's Law, as the number of moles of carbon dioxide increases, the volume will increase, hence the bubble expanded.

and we also have...

Dalton's Law

The total pressure exerted by a mixture of gases which do not react is equal to the sum of the partial pressures of the constituent gases at the same temperature.

also expressed as

Gas Laws

Neither Boyle’s Law nor Charles’ Law depends on the identity of the gas being studied. These laws describe the behaviour of any gasesous substance, regardless of its identity.

Ideal Gas Equation

which is written as...

After the can is heated, the water inside vapourizes and forces out the air originally in the can. When the can is placed upside down into the water, the water vapour is unable to escape and condenses. There is a drastic reduction in the number of moles of gases (mainly water vapour) and temperature. Since P = nRT / V, the pressure inside the can suddenly decreases, and the atmospheric pressure will crush the can.

Theoretically, we have the concept of ideal gases, but in practice, we have...

Real Gases

Considering real gases, there are two scenarios of deviation from ideality...

Negative Deviation

Real gases tend to exhibit negative deviation when the temperature is low

At high temperature, the gas molecules are moving fast, and can overcome attractive forces between them. Intermolecular forces of attraction are insignificant, and the molecules hit the vessel wall to result in a measured pressure relatively closer to the expected (ideal) pressure. Therefore, at high temperature, the basic assumptions of the Kinetic Theory can be considered valid.

At low temperature, the gas molecules are moving very slowly and hence are not able to overcome attractive forces between them. Intermolecular forces of attraction become significant and the force with which a gas molecule strikes the wall is reduced. Hence, the measured pressure of the gas (arising from molecular impact with the wall) will also be lower. As a result the product of PV is less than we expect on the basis of the ideal gas equation.

At low pressure, NH3 shows the greatest negative deviation.

(Note: boiling point of NH3 is higher than the other two gases, so 273 K is relatively a lower temperature than for the other gases.

Positive Deviation

Real gases tend to exhibit positive deviation when the pressure is high.

At high pressure, the basic assumptions of the Kinetic Theory are not entirely true because gas particles do not have negligible volume gas compared to the volume of the container at high pressures.

When the pressure is high, gas molecules are closer, volume of gas molecules become significant and gas molecules takes up space (incompressible). Hence the volume of the gas will be larger than expected. As a result the product PV is larger than it should be, i.e. positive deviation.

designed by Low Kian Seh

Did you know?

And this is Robert Boyle. On a good hair day.

This man, Gay-Lussac, published the first version of this law, but he gave credit to the work of Jacques Charles, and hence the name "Charles' Law". Hmm...if he named it after himself...

John Dalton was an English chemist, meteorologist and physicist. (Actually the delineation of boundaries of subjects is highly arbitrary to begin with.)

A picture says a thousand words...

Food for thought

which can look good even on a t-shirt.

Can a gas shrink to nothing at all?

PV = nRT

Each gas in a mixture exerts the same pressure as when it alone occupies the container at the same temperature.

The man behind the law, Amadeo Avogadro, who in this unflattering portrait seems to resemble a hobbit.

Can you explain why the balloon deflates when liquid nitrogen was poured on it?

Practice 3

Can you explain why the bubble kept expanding till it exploded? Please ignore the bad hairdo.

Practice 4

Practice 1

Can you explain why the marshmallow man expanded when air was pumped out of the container?

To determine relative molecular mass from Ideal Gas Equation

(m = mass of gas)

Practice 5

Can you explain why the coke can crushes after it is placed in the water?

Another two graphical interpretations.

A plot of PV against P or reciprocal of volume 1/V is a straight line of zero slope for a gas that obeys Boyle's Law.

Practice 2

Can you explain how the two straw figures can be controlled to sink or float?

Putting both Boyle’s Law, Charles’ Law and Avogadro’s Law together...

Plotting PV/RT for various gases as a function of pressure

Deviation from Ideal Gas behaviour

An ideal gas (which obeys the ideal gas equation) does not exist in reality.

Real gases do not obey the ideal gas equation.

Deviation from ideal gas behaviour can be shown by plotting PV/nRT against P.

For an ideal gas under all conditions PV = nRT = constant.

PV should be independent of the individual values of P and V and a plot of PV/nRT against P should be a horizontal line.

• The gas consists of particles of negligible volume
• The particles exert no attractive forces on each other
• The particles are in continuous random motion
• The collision between particles are perfectly elastic
• Thus, no kinetic energy is lost on collision
• The average kinetic energy of the particles is directly proportional to the absolute temperature (in Kelvins)

The concept of completely independent gas particles applies to what are called ideal gases. Ideal gases do not actually exist.

Basic Assumptions of the Kinetic Theory (as applied to an ideal gas)

Note that n = 1 mol for each gas

an eLearning module for Temasek Junior College

• The gas consists of particles of negligible volume, compared to the volume of the container it occupies.
• The particles exert no attractive forces on each other.
• The collision between particles are perfectly elastic. Thus, no kinetic energy is lost on collision.
• The particles are in continuous random motion.
• The average kinetic energy of the particles is directly proportional to the absolute temperature (in Kelvins).

The concept of completely independent gas particles applies to what are called ideal gases. Ideal gases do not actually exist.

Factors affecting ideality

Causes of non-ideality

Conditions for ideality

Real gases only tend towards ideal gas behaviour when

i. the pressure is very low

ii. the temperature is very high.

The extent and nature of deviation depends on

i. pressure

ii. temperature

iii. nature of the gas

Deviation from ideal gas behaviour can be attributed to

a. the significant volume occupied by gas molecules

b. the attractive forces between the gas molecules

Learning Objectives

Low Pressure Container

High Pressure Container

The deviation from ideal behaviour of nitrogen gas at different temperatures

Therefore in summary,

pressure of real gas < pressure of ideal gas

PV / nRT of real gas < PV / nRT of ideal gas

PV / nRT of real gas < 1 (Negative Deviation)

Notice that negative deviation is more extensive at lower temperature.

Volume of gas molecule is significant

Volume of gas molecule is insignificant

Plot of PV/RT against P for one mole of gas at 273 K

When is the temperature considered to be low?

Reason:

This is due to the relative stronger intermolecular forces of attraction (hydrogen bond) between NH3 molecules.

The stronger the intermolecular force of attraction the more extensive the negative deviation.

Everything at a glance...

Yay! I'm finally done.