 # The Gas Laws

### What the curriculum thinks you need to know:

PC_BK_19 Physics of gases. Gas Laws: kinetic theory of gases, Boyles, Henry’s, Dalton, Charles, Gay-Lussac

### What you need to know (The theory):

The gas laws describe the way a perfect gas will behave given a certain set of conditions. This meaning under a certain Pressure, volume and temperature. Remember all of the following are done with a set amount of gas, by this we mean a set number of molecules. Remember from your GCSE/A-Level physics/chemistry: One mole of a substance = 6.02 x 1023molecules, this is Avagandro’s number.

Also remember STP, Standard temperature and pressure. This is at 0oC (or 273.15K) and atmospheric pressure or 101.325 kPa (760 mmHg, 1 Bar).

#### Perfect Gases

‘A gas which obeys all of the three gas laws completely.’

Firstly, there is no actual ‘perfect’ gas. A perfect gas would need to have infinitely small particles to enable it to be indefinitely compressed. All molecules take up space, but the smallest ones obey the laws most closely. Hence why hydrogen is the most ‘perfect gas’.

#### Law 1: Boyle’s Law

‘At a constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure.’

Remember, Water ‘boyles’ at a constant temperature.

In equation form:

V ∝ 1/P   Or   P x V = K (constant)

So, as you squeeze your gas into a smaller volume, the pressure increases and visa versa. Think of a syringe with a bung on the end and squeezing the plunger.

#### Law 2: Charles’ Law

‘At a constant pressure, Volume of a fixed amount of gas is proportional to its absolute temperature.’

Remember, Charles is under constant pressure to be king.

In equation form:

V ∝ T   Or   V / T = K (constant)

So, as you heat your gas, the volume will increase if the pressure stays the same. Think of a balloon full of gas, if we heat it up, it gets bigger and more tense. If we put it in the freezer, it shrivels up.

#### Law 3: Gay Lussac’s Law

‘At constant volume, Pressure of a fixed volume of gas will increase in proportion to absolute temperature.’

I don’t know of a decent way to remember this from the name, buts it is the odd one out!

In equation form:

P ∝ T   Or   P / T = K (constant)

So, If you heat a gas in an enclosed, fixed volume space, the pressure will rise and visa versa. We all know if you heat a gas filled cylinder enough it goes…. BANG (as the pressure increases above what the cylinder can contain) – Just think of all those action movies with cylinders exploding…

#### Law 1+2+3: The Universal Gas Equation

So those are the 3 common gas laws, they can also be combined into one equation to rule them all (‘Lord of the Rings’ style):

As we know that P ∝ T and V ∝ T , we can then say that PV ∝ T

We also need to add in a constant to make this all work in practice. This constant is the molar gas constant (R = 8.31 J/K/Mol, don’t worry about this, just accept its needed!).

PV =nRT

Where:

P = Pressure in Pascals (NOT kPa!!)
V = Volume in m3
n = number of moles
R = Molar gas constant
T = Temperature (in Kelvin!)

This can then be rearranged to find any remaining value (P,V or T) if the molar amount of gas and two other values are known.

Get to know this and work though some examples as it makes a very good MCQ/SBA question!

The college also specifies two further laws you need to know:

#### Henry’s Law

This describes the partial pressure exerted by gases which are dissolved in a liquid.

‘At constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of this gas in equilibrium with it.’

The typical example is that of a glass of fizzy drink. The gas dissolved in the drink is carbon dioxide. The drink has CO2 mixed with it at high pressure. The drink then appears fizzy as the carbon dioxide comes out of solution to become in equilibrium with the atmosphere (<0.04% CO2). If we think of how we make fizzy drinks we need to put high pressure on the gas in contact with the liquid drink (think of a soda-stream machine). This then dissolves much more carbon dioxide than would normally happen at atmospheric pressure.

Notice the constant pressure bit in the law above. Now, this is due to the fact that solubility of gases in liquid decreases as temperature increases. This is easy to get the wrong way round as we all know solids dissolve in hot liquids easier. But, think of it this way, more temperature means more energy for those gas particles which are then going to bounce around and try and get out of solution.

When we then take a bottle of fizzy pop out into the sun where the temperature increases, the pop froths when you pour it, releasing large amounts of CO2 quickly as its solubility is low, but then goes horrid and flat. But if we pour cold pop, it slowly releases its CO2 (it will always release this as remember its trying to get into equilibrium with the atmosphere at <0.04% concentration!). Because this release is slow, it appears to be fizzy for longer.

#### Dalton’s Law

This is also known as the law of partial pressures. Each of the gases in a gas mixture (think air), exert a pressure. The total pressure exerted by the gas mixture is simply the sum of all these pressures.

So, if we take the example of atmospheric air, the pressure of room air is 101.325 kPa. Air is made up of the following:

78% nitrogen
21% oxygen
0.93% argon
<0.04% carbon dioxide
And a few other small print things.

The pressure a sample of this gas exerts in the atmosphere is, as we said 101.325 kPa, so each gas will be responsible for exerting its fair share of this pressure, so for example nitrogen will exert 78% of that 101.325 kPa, or, roughly 79 kPa. The same goes for all the other gases.

### What you need to know (How it works in practice):

So what does this mean in practice? Well these equations have many day to day applications:

#### Breathing

When we take a breath in, we increase our intrathoracic volume, and hence decrease our intrathoracic pressure to draw gas into the lungs to equilibrate with atmospheric pressure. Volume and pressure at a constant temperature? Boyles law!

V ∝ 1/P

As your volume increases, your pressure drops. See, you do this stuff 12-16 times a minute without thinking about it!

This also works for using a breathing circuit (doesn’t matter which, as long as you have a bag on it)…

You or your ventilator squeeze the bag or bellows to make your patient breath. Squeezing the bag decreases the circuit volume, hence increasing the circuits pressure. Boyle’s Law.

The pressure eventually (over a fraction of a second) equilibrates with the patients lungs which expand due to their elastic nature. The volume of the circuit then increases with the increase in lung volume and the pressure in the circuit decreases. Boyle’s law again.

#### Oxygen canisters

So oxygen canisters are a set volume and for the most part operate at a fairly set temperature. See that gauge on the side of the cylinder that says how ‘full’ it is? that is actually a pressure gauge, A bourdon gauge if we’re being picky.

So constant temperature, constant volume…. Lets discount those then.

PV =nRT

So we’re left with P = nR

Well R is a constant, So we’re left with P = n

So pressure is proportional to the number of moles of gas. So when that pressure gauge shows half maximum pressure (a typical cylinder can hold 137 bar), it has half the volume of gas as a full cylinder. All they do is change the pressure readings for full, 1/2 full, 1/4 full etc at the appropriate pressures.

### Random Exam factoids (i.e. the things the college like asking):

1. The college quite like questions to test you knowledge of the 3 main gas laws. So they may ask something like a gas sample is 4L, its pressure is doubled, the resultant volume is….
2. Remember your definitions of STP. The college seem to like asking it, a lot.

© Sam Beckett and Physics4FRCA, 2017. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited.