The Gas Laws

Question 1

According to the molecular theory of matter, describe a solid, liquid and gas.

Answer 1

Solid - atoms arranged in lattice. Each molecule exerts a force upon its neighbour and is continuously in motion, oscillating about a mean position

Add heat to a solid –> increase vibrations between molecules –> move further apart –> melt

Liquid - Molecules move more freely in relation to each other and the forces of attraction between the molecules are called van der Waals forces

Ad heat to a liquid –> increase kinetic energy of molecules which will eventually be able to overcome the van der waals forces exerted by their neighbours and move about freely in space = a gas or vapour

Question 2

Define vapour pressure

Answer 2

The pressure exerted by a vapour above the surface of a liquid

Question 3

What is saturated vapour pressure

Answer 3

The pressure exerted by a vapour in equilibrium with liquid of the same substance. It is influenced by temperature and pressure

Question 4

Define boiling point

Answer 4

The boiling point temperature is the temperature above which vapour pressure equals atmospheric pressure. A lower atmospheric pressure will result in a lower boiling point temperature.

Question 5

What is critical temperature

Answer 5

the temperature above which it is not possible to liquify a gas by increasing its pressure

Question 6

When is a substance a gas and when is it a vapour

Answer 6

A substance is a gas when it is above its critical temperature

A substance is a vapour when it remains in a gaseous phase below its critical temperature

Question 7

What is Boyles law

Answer 7

This is the 1st of the ideal gas laws

Boyles law states that at constant temperature, the volume of a given mass of gas varies inversely with the absolute pressure (think of halving the volume of a sealed 20 ml syringe at constant temperature)

V ~ 1/P

or VP = k

Question 8

What is Charles’ Law

Answer 8

This is the 2nd of the ideal gas laws

Charles’ Law states that at constant pressure, the volume of a given mass of gas varies in direct proportion to the absolute temperature (think of heating a syringe at constant pressure)

V ~ T

or

V/T = k

Question 9

What is Gay-Lussac’s law

Answer 9

This is the 3rd of the ideal gas laws

Gay-Lussac’s law states that at constant volume, the absolute pressure of a given mass of gas varies in direct proportion to the absolute temperature (think of heating a syringe at constant volume)

Question 10

What is an application of the 3rd ideal gas law

Answer 10

The hydrogen thermometer

A constant volume of hydrogen is heated, the rise in pressure may be accurately recorded and it gives a measure of the absolute temperature increase

Question 11

Define Standard Temperature and Pressure

Answer 11

STP

T = 273.15 K (0 deg C)

P = 101.325 kPa (760 mmHg)

Question 12

What is an adiabatic change. Give an example

Answer 12

The ideal gas laws describe the behaviour of gas when one of three variables is constant (temp, pressure, volume). In order for these conditions to apply, het is required to be added or taken from a gas as the change occurs.

The state of a gas can also be changed without allowing the gas to exchange heat energy with its surroundings
–> this is called an adiabatic change.

Example:
Connect and open gas cylinder to anaesthetic machine –> Gas compressed rapidly –> pressure rises rapidly –> temperature of gas rises rapidly = adiabatic change.

Cryoprobe: Compressed gas expands rapidly –> pressure decreases rapidly –> gas expands adiabatically –> cooling occurs.

Question 13

Explain how a cryoprobe works

Answer 13

Cooling from a cryoprobe is the result of an adiabatic process.Gas is allowed to expand rapidly out of a capillary tube and the cooling is as result of rapid expansion.

The cooling effect results from the fact the energy is required as the gas expands to overcome the van der Waals forces of attraction between the molecules of a gas. Heat exchange does not take place between the gas and its surrounding, the energy required is taken from the kinetic energy of the gas molecules themselves which results in the gas cooling as it expands.

Question 14

What is Dalton’s law of partial pressures

Answer 14

States that in a mixture of gases the pressure exerted by each gas is the same as that which it would exert if it alone occupied the container

Question 15

A cylinder filled with entonox has an absolute pressure of 100 kPa. What would is the partial pressure of both O2 and N2O within this mixture and why

Answer 15

Entonox = 50% O2 with 50% N@O.
According to daltons law the partial pressure a gas within a mixture of gases is the same as what it would be if it were alone in the container. Therefore as the absolute pressure is 100 kPa the partial pressure of both is 50 kPa

Question 16

How do manufacturers fill a cylinder with 90% O2 and 10% CO2 to an absolute pressure of 138 bar

Answer 16

First 13.8 bar CO2. (10% of absolute pressure desired)

Then fill the tank to an absolute pressure of 138 bar

Question 17

What is Avagadro’s hypothesis

Answer 17

Avagadro’s hypothesis states that equal volumes of gases at the same temperature and pressure contain the equal numbers of molecules

Question 18

Why is it more convenient to use a concept related to the number of molecules when referring to quantities of gas? What is this concept?

Answer 18

Two syringes: One filled with O2 and one filled with H2 are at equal volume, pressure and temperature. These gases have different masses (molecular masses) but each syringe has the same number of molecules. Therefore the concept of the mole was created.

Question 19

What is a mole

Answer 19

The quantity of a substance containing the same number of particles as there are atoms in 0.012 kg of carbon 12. this is 6.022 x 10^23 atoms and is known as Avagadro’s number

Question 20

What is the point of Avagadros hypothesis

Answer 20

It states that equal volumes of gas at equal pressures contain equal numbers of molecules. Therefore, rather than express a quantity of gas in terms of its mass, it is more convenient to use a concept related to the number of molecules. This is a mole.

Question 21

What volume goes 1 mole of gas occupy

Answer 21

At STP one mole of gas occupies 22.4 L

E.g.
2g of hydrogen –> 1 mole —-> 22.4 Litres
32g of Oxygen —> 1 mole —> 22.4 L
44 g of CO2 ——-> 1 mole —> 22.4 L

n = m/M

Question 22

What important role does Avogadros hypothesis play in the calibration of vaporizers. Provide an example

Answer 22

A steady flow of O2 through a vaporizer converts 18.45 g of isoflurane into 224 L.

MW of isoflurane is 184.5 g/mol

n = m/M = 18.45/184.5 = 0.1 mol

So from above:
0.1 mol of isoflurane has produced 224 L

But: we know that 1 mol isoflurane = 22.4L. therefore 0.1 mol isoflurane should produce 2.24 L so the concentration of isoflurane produeced:

= 2.24 L/ 224 = 1% —-> calibration.

Question 23

What is the tare weight

Answer 23

This is the weight of an empty cylinder. The weight of Nitrous Oxide within the cylinder can be calculated by subtracting the tare weight from the measured weight of the cylinder

Question 24

Combine the gas laws with Avogadro’s hypothesis to explain why the pressure gauge acts as a contents gauge for a gas cylinder provided the cylinder contains gas

Answer 24

1. Boyles: V ~ 1/P or PV = k1
2. Charles: V ~ T or V/T = k2
3. Guy-Lussac: P ~ T or P/T = k3

So PV/T = constant

For 1 mol of gas PV/T equals a unique gas constant called the universal gas constant, R.

Universal gas law: PV = nRT.

If there is only gas in a cylinder:
V is constant
R is constant
T is kept constant

Therefore P ~ n –> so the pressure is proportional to the number of moles left in the cylinder.

Question 25

Define critical temperature

Answer 25

the temperature above which a substance cannot by liquefied however much pressure is applied

Question 26

Define critical pressure

Answer 26

The vapour pressure of a substance at its critical temperature

Question 27

What is the critical temperature for N2O. What are the implications of this in warmer climates

Answer 27

Critical temperature = 36.5 deg C. –> Warmer climates/tropics –> above
Above 36.5 deg C –> N2O is a gas in the cylinder

Filling ratio is the mass of gas in the cylinder divided by the mass of water that would fill the cylinder. 1L water = 1 kg. Filling ratio of N2O is 0.75 but 0.65 in the tropics (also UK and states) as a margin of safety to prevent explosion.

Question 28

Define an isotherm an draw the isotherms for N2O

Answer 28

Isotherms are a series of lines of pressure against volume at various temperatures for the same substance (e.g. N2O) –> see page 48 Kenny and Davis for diagram

Question 29

Differentiate a ‘gas’ from a ‘vapour’

Which of the following is a gas and which a vapour at room temperature and why:

N2O
N2
Isoflurane
CO2
O2

Answer 29

The word gas applies to a substance above its critical temperature. The word ‘ vapour’ applies to a substance below its critical temperature.

Gas (Room temp is above critical temperature)
N2
O2

Vapour (Room temp is below critical temp)
Isoflurane
N2O
CO2

Question 30

What is the critical pressure of N2O

what is the typical gauge pressure of N2O in a cylinder at room temperature

Answer 30

Critical pressure i.e. at 36.5 deg C
73 bar (73 x 100 kPa)

Pressure at 20 deg C
52 bar (52 x 100 kPa) = N@O saturated vapour pressure

Question 31

How are explosions prevented in N2O cylinders

Answer 31

Filling ratio < 0.75

Hypothetical scenario: N2O cylinder filled to FR 1.0 with N2O liquid.

–> Any increase in temperature –> expansion with an exponential increase in pressure as a liquid (unlike a gas) cannot be compressed leading to a considerable risk of explosions.

For this reason N2O cylinders are filled to 75% of the total internal volume. this is referred to as the filling ratio and is the ratio of:

Mass of N2O inside cylinder : Mass of water would completely fill the cylinder