School Science Lessons
Gas laws, ideal gas
2009-06-22
Please send comments to: J.Elfick@uq.edu.au
See also: Interesting websites
Table of contents
20.0.0 Gas laws
20.1.0 Constant pressure, Charles' law (Gay-Lussac's law) V1 / T1 = V2 / T2, V / T = constant
20.2.0 Constant temperature, Boyle's law (Mariotte's law) P1V1 = P2V2, pV = constant
20.3.0 Constant volume, pressure law p / T = constant
20.4.0 Thermodynamics, isothermal change and adiabatic change
20.0.0 Gas laws
20.0.1 Gas pressure
20.0.2 Boyle's law (Mariotte's law)
20.0.3 Charles' law (Gay-Lussac's law)
20.0.4 Pressure law
20.0.5 Combined gas equation
20.0.6 Standard temperature and pressure, S.T.P, density of gases
20.0.7 Universal gas equation
20.0.8 Dalton's law of partial pressures
20.0.9 Henry's law and decompression sickness, the bends
20.1.0 Constant pressure, Charles' law (Gay-Lussac's law) V1 / T1 = V2 / T2, V / T = constant
4.8 Expansion of air
4.243 Cold air is heavier than warm air
37.12 Cold air is heavier than warm air, inverted paper bag balance
5.42 Heated air expands (Primary)
6.35 Burn candle over water (Primary)
20.1.01 Use oil instead of mercury for school Charles' law experiments
20.1.03 Gas-filled bulb and U-tube manometer
20.1.1 Expansion of air when heated, expansion of air in a flask
20.1.2 Heating air and cooling air, heating a flask with hands / water
20.1.3 Heating a flask with hands 
20.2.0 Avogadro's law (Avogadro's hypothesis), air pumps, absolute zero Kelvin (K)
20.2.1 Lift weight by blowing
20.2.2 How an air pump works
9.241 Volume of air in a breath
20.3.0 Constant volume, pressure law, pressure-temperature graph, p / T = constant
2.316 Volume and pressure of air
2.316A Pressure affects boiling point of water
2.317 Make a model of the lungs
2.318 Oxidation and air pressure, steel wool over water
4.243 Cold air is heavier than warm air
12.3.3 Air has mass, air has weight, balance balloons, weigh a basketball, coal gas has weight
12.3.4 Aneroid barometer
12.3.5 Air exerts pressure in all directions
12.3.5.1 Drinking straw, finger on drinking straw, glass tube
20.4.0 Thermodynamics, isothermal change and adiabatic change
20.4.01 Ice cubes in boiling water, second law of thermodynamics
20.4.1 Heat cycles, Carnot cycle
23.11.0 Adiabatic processes
20.0.0 Gas laws
Universal gas equation, P1V1 / T1 = P2V2 / T2, pV = nRT, ideal gas, statics of fluids, static pressure, real gas behaviour, kinetic theory of gases, computer simulation of kinetic model
PV = nRT, n = number of moles of gas
R = gas constant, 0.08206 litres X atmospheres X mol-1 X K-1
Find the weight of chlorine gas in a 5 litre flask at 21oC and 0.79 atmospheres.
PV = nRT, n = PV/RT, n = 0.79 X 5 / 0.08206 X (21 + 273) = 0.164 mol = 0.164 X 70.9 g /mol Cl2 = 11.6 g
20.0.1 Gas pressure
Gases are made up of molecules moving randomly at high speeds, in straight lines, in all directions. Pressure is a measure of the force per unit area on a surface. Pressure = Force / Area where force is in newton, N, and area in square metres, m2. 1 newton / metre2 = 1 pascal, Pa. The pressure of a gas = number of collisions per second per unit area X the average impulse per collision for the molecules.
20.0.2 Boyle's law (Mariotte's law)
Robert Boyle (1627-1691) (E. Mariotte 1620-1684) For a given mass of gas at constant temperature, the volume is inversely proportional to the pressure, PV = constant.
20.0.3 Charles' law (Gay-Lussac's law)
(Jacques Charles 1746-1823) (Joseph Louis Gay-Lussac 1778-1850) For a given mass of gas at constant pressure, the volume, V, is proportional to the absolute or Kelvin temperature of the gas, T, Volume = constant X T.
20.0.4 Pressure law, constant volume, pressure law p / T = constant
The pressure law states for a gas with constant volume the pressure is proportional to the Kelvin temperature of the gas.
20.0.5 Combined gas equation
P1 X V1 / T1 = P2 X V2 / T2
20.0.6 Standard temperature and pressure, STP, density of gases
See also 5.1.3: Molar volume
S.T.P refers to the standard conditions used in calculations of the effects of changing temperature and pressure. They are STP = 0oC or 273.15 K, and 760 mm Hg or 101325 pascals, Pa. (101.325 Nm-2)
Density of gases at STP
Carbon dioxide 0.0019769 g / mL
Hydrogen gas 0.00008988 g / mL
Oxygen gas 0.0014290 g / mL
A standard atmosphere (International Standard Atmosphere), atm, is a hypothetical atmosphere used as a basis of comparing altimeters. It is a pressure of  101.325 Nm-2, equivalent to the pressure exerted by a column of mercury 760 cm high at 0oC.
20.0.7 Universal gas equation
The universal gas equation combines the three gas laws as pV = nRT, n = amount of gas and R is the gas constant (universal molar gas constant) = 8.314 JK-1 mol-1.
20.0.8 Dalton's law of partial pressures
See also: Saturation vapour pressure over water
The total pressure of a mixture of gases or vapours in a closed container is equal to the sum of the partial pressures of each gas or vapour, i.e. the sum of the pressures if each gas or vapour alone occupied the space in the closed container. So each gas or vapour exerts its own pressure regardless of the presence of any other gas or vapour. When a gas is collected over water, the water molecules in the water vapour contribute to the total pressure over the water.
Total pressure = pressure of gas produced + pressure of water vapour.
20.0.9 Henry's law and decompression sickness, the bends
If the temperature is constant, the mass of gas doissolved at equilibrium is directly proportional to the partial pressure of the gas. The solubility of a gas depends directly on the gas pressure. The concentration of dissolved gas depends on the partial pressure of the gas. If the pressure is doubled the concentration of the dissolved gas double. If the temperature remains constant increasing the pressure will increase the amount of dissolved gas.
O2 (g) <-->O2 (aq)
Pgas = KC, at constant temperature, where P = pressure, C = concentration and K = the Henry's law constant that is different for every gas, temperature and solvent.
The concentration to pressure ratio is the same when the pressure changes.
C1/P1 =C2/P2
Decompression sickness occurs when a person experiences a sudden change in atmospheric pressure. Nitrogen has a  low solubility in body fluids at normal atmospheric pressure but at higher than normal pressure, additional nitrogen molecules diffuse across the alveolar surfaces of the lungs and into the bloodstream and tissues. If the atmospheric pressure then decreases slowly, the excess nitrogen can diffuse out of the tissues, into the blood, and across the alveolar surfaces without discomfort to the person. However, if the atmospheric pressure decreases suddenly, the nitrogen leaves solution and forms bubbles of nitrogen gas in the blood, tissues, and body fluids. Small bubbles fuse to form larger bubbles that twist tissues and produce severe pain in joint capsules and causing the person to bend over, "the bends". Treatment by recompression forces the nitrogen in the tissues back into solution to alleviate the problem. Then a gradual reduction in pressure allows the nitrogen to diffuse slowly out of the tissues without forming bubbles. The bends still occurs to scuba divers who have dived too deep or stayed too long at depth, to construction crews working in pressurized surroundings and even to passengers experiencing a sudden loss of cabin pressure in a commercial aeroplane, where a pressure experienced at 2000 metres height is normally maintained.
20.1.0 Gas expansion, Constant pressure, Charles' law (Gay-Lussac's law) V1 / T1 = V2 / T2, V / T = constant
The effect of temperature on the volume of a gas
See diagram 20.1.1
V1 / T1 = V2 / T2 Constant Pressure, volume / temperature graph, V / T = constant, PVT relationship, Quantitative treatment of ideal gases. Boltzman's Constant, approximations used for real gases
Put a drop of oil into the capillarity tube to seal a column of air. Measure the length of the trapped column of air rather than its volume. Use a spring band to fix a capillarity tube and a thermometer together, put them into a beaker. Use the scale intervals on a thermometer to measure length. To read easily, the lowest level of a column of air trapped in a capillarity tube is better to meet at 0oC on the thermometer. Then record the length of the column of air by using the scale nearest to top of the column of air. Measure a set of values of length of a column of air and temperature between 0oC and 100oC. Before the experiment, mix crushed ice and water in a bottle of mineral water, put them into a beaker. Record your temperature readings in a suitable position of set up the table. Then pour tap water into the beaker, heat it by an alcohol burner. As the temperature reaches 40oC, 60oC, 80oC, record the length of the column of air trapped in a capillarity tube each. Remove the alcohol burner before taking records. As water boils, record the last reading. Draw a graph of temperature t and length of the column of air L so your graph can show how of volume of air varies with temperature.
20.1.01 Use oil instead of mercury for school Charles' law experiments
After Geoff Snowdon, The Australian Science Teachers Journal, Vol. 33 No. 2
Coloured oil can be put into a 30 centimetre length of capillary tubing by using the following procedure: Leave both ends open. Heat the tube strongly at one third the length. Dip an end into the oil. The oil rises into the tube. Manipulate the tube to get a 5 cm length of oil. Seal an end or heat to seal.
20.1.03 Gas-filled bulb and U-tube manometer.
Connect a glass bulb containing air or other gases to one arm of a manometer. Place your hand over the bulb and observe the change in levels of the liquid in the manometer.
20.1.1 Expansion of air when heated, expansion of air in a flask
See diagram 20.1.1 Heated air expands | See diagram 23.4.5 | See diagram 2.110
1. Use a small bottle or flask fitted with a stopper and inserted glass tube that extends into the bottle. Put a small amount of oil in the glass tube to trap air in the flask. Hold the flask in your hands. The oil moves up the tube because the heat from your hands has expanded the air. The bottle will change size first before you heat, or cooled the gas because the glass of the bottle will expand. Cool the flask. The oil moves down.
2. Fit a hard-glass test-tube with a one hole stopper that has a length of glass tubing through it. Invert the test-tube so that the end of the tubing is in a beaker of water. Clamp the test-tube in that inverted position and heat it with a Bunsen burner. Heat the test-tube and observe the bubbles from the end of the tube in the beaker of water. Heat has caused the air to expand. Cool the test-tube by pouring cold water over it. Water moves up the glass tubing as the cooling air contracts. Fit a toy balloon over the neck of a small flask. Put the flask in a container of water. Heat the water. The balloon expands as the heated air in the flask expands.
3. Use a piece of thick cardboard on a table as a base. Paste another piece of cardboard vertically at the side of the base and mark it as a scale. Stretch tight a rubber film over the mouth of a bottle to air proof the bottle. Flatten one end of a drinking straw then paste it at the middle of the rubber film. Cut the other end of the drinking straw into a sharp needle to act as an indicator. Place the bottle on the base. Adjust the position of the bottle so that the indicator points to half way up the scale. Observe the movement of the indicator during the day. When heated the air in the bottle expands to press the rubber film so that the indicator moves up.
20.1.2 Heating air and cooling air
See diagram 23.4.6
Use a 100 mL taper flask; a rubber stopper; a N-shape capillary of 250 mL length and a straight capillary longer than the height of the flask; a 400 mL beaker of coloured water. Add ink to the water.
20.1.3 Heating a flask with hands
See diagram 2.110
Seal the flask with the rubber stopper. On the stopper insert the N-shape capillary. Insert the other end of the N-shape capillary into the coloured water at the beaker. Cover the flask with your hands to heating the air in the flask. Observe the end of the capillary under the coloured water. Leave your hands off the flask then hold the capillary. Observe the end of the capillary under the coloured water again. While you heat the air in the flask, its volume expands and pressure increases. So air bubbles appear at the end of the capillary until the pressure inside the flask is equal to the outside pressure. The amount of the air in the flask decreases at the process. While the air in the flask becomes cold, the air pressure decreases to less than the outside pressure so that the coloured water in the beaker under the atmosphere pressure, enters the capillary to contract the air volume to make the inside and outside pressures balance.
20.2.0 Constant Temperature, Boyle's law (Mariotte's law), pressure / volume graph, pV = constant, pressure effect on gas volume of syringe, P1V1 = P2V2
See diagram 20.1.3
Use a calibrated syringe mounted on a block of wood and with a platform securely attached to the top of the plunger. Measure the masses of platform and plunger, the outer diameter of the plunger or the inner diameter of a syringe. Put light oil on the plunger to lubricate it. Lift the plunger, record the original position of it. Seal the outlet with a piece of rubber tube. Put weights on the platform and record volume of air in the cylinder using the scale on the syringe. Change the weights on the platform, record the volume of the air in the syringe under different case, but maintain the temperature constant in this process. Calculate the air pressure. The pressure acted on air in the syringe = atmospheric pressure + the pressure produced by weights of plunger and platform + the pressure produced by weights added on the platform. Observe and test according to measured volume and pressure calculated. As the temperature is constant and the gas has a definite mass, when its pressure increases its volume decreases, and vice versa. The product of pressure and volume of the gas remains the same, i.e. PV = C. Finally, graph the relationship between volume and pressure of air in the syringe.
Air pumps
20.2.1 Lifting a weight by blowing, the work done by gas pressure
See diagram 20.2.1
20.2.2 How an air pump works
Use of a syringe needle may be not allowed in some school systems.
is forbidden for use in schools!. If temperature is constant, when you compress gas and reduce its volume, its pressure will increase, and vice versa. Insert a piston covered with some glycerine into a 100 mL pump with a valve. Rotate the piston inside the pump several times to make the glycerine distributed evenly. This can insulate the air inside the pump from outside completely. Open the valve and suck up 60 mL air into the pump. Measure the volume of the air with the scale on the pump. Close the valve to insulate the air in the pump from outside. Push the piston to compress the air volume to about 2 / 3 of the original, i.e. about 40 mL. Release the piston that will come back to the original position. Pull the piston out with effort to expand the air volume in the pump to about 80 mL. Release the piston that will come back to the original position. The reason of coming back of the piston is the pressure difference between two sides of the piston. At constant temperature, the more the air volume inside the pump is compressed, the more pressure it has. As the air volume expands, the pressure decreases. When the piston is compressed, as the air pressure inside the pump is higher than that of outside, the air inside the pump will push the piston back to its original position. When you pull out the piston, the air pressure inside the pump becomes less, the atmospheric pressure outside pushes the piston back. You can do the experiment with a large glass syringe instead of a pump. Close the hole with the fingers used as a valve.
20.4.0 Thermodynamics, isothermal change and adiabatic change
See diagram 20.4.0: Thermodynamics | See also 2.0.5: Conic sections, hyperbola
An isolated system contains a certain quantity of energy called the internal energy of the system = total kinetic energy and potential energy of all the atoms and molecules in the system that can be transferred as heat. Internal energy does not include chemical energy or nuclear energy. Thermodynamics is about how energy changes from one form to another, the direction of heat flow and how energy does work.
The value of the internal energy of a system can be changed by the following:
1. transfer of mass,
2. transfer of heat,
3. work done on or by the system.
In an isothermal change the temperature remains constant, and PV = a constant. On a pressure / volume graph an isothermal change is shown as a rectangular hyperbola.
In an adiabatic change no heat is is received or lost from the surroundings. For an adiabatic system with constant mass, the transfer of heat = 0, the change in internal energy = work done and a change in temperature occurs. For example, if a piston is raised in a cylinder containing a gas, the volume of the cylinder increases and the temperature of the gas falls as work is done against the rising piston. On a pressure / volume graph an adiabatic change is always steeper than a rectangular hyperbola because adiabatic expansion is accompanied by a fall in temperature.
First law of thermodynamics: Heat can be changed into mechanical energy and mechanical energy can be changed into heat energy but the total energy of the system remains constant, i.e. the law of conservation of energy always holds true.
Second law of thermodynamics: Heat cannot pass from a body at lower temperature to a body at high temperature, heat always flows from hot bodies to cold bodies, a machine unaided by an external agent cannot transfer heat from a body at lower temperature to a body at higher temperature.
Third law thermodynamics: The entropy of a substance approaches zero as is temperature approaches absolute zero. Entropy measure the unavailability of the energy of a system to do work. In any closed system an irreversible change is associated with an increase in entropy. For an adiabatic process no heat transfer occurs and the entropy remains constant during the process. Increase in entropy is another way of stating the second law of thermodynamics.
Isothermal change and adiabatic change
For an ideal gas, i.e. no attractive forces between its molecules, the volume decreases with temperature down to -273oC, called absolute zero or 0o Kelvin, K. For monatomic gases, the molar heat capacity cp = 12.5 joule / mole K, so you need 12.5 joules to raise the temperature of a mole of a monatomic gas by 1K. In an isothermal change the temperature remains constant. In an adiabatic change no heat is received from or lost to the surroundings. Adiabatic expansion occurs when a gas expands quickly, or when a gas is insulated from the surroundings. The gas does work and the temperature drops, as in refrigeration. Adiabatic compression occurs when you compress a gas quickly, or insulate a gas from the surroundings. The temperature rises, as in igniting the fuel in a diesel engine.
20.4.01 Ice cubes in boiling water, second law of thermodynamics
Heat a pot of water until it is boiling steadily. Add several ice cubes to the pot. The boiling action stops almost immediately as heat is transferred from the burner to the lower temperature ice rather than to the higher temperature water. When all the ice is melted the boiling action starts again.
20.4.1 Heat cycles, Carnot cycle
The working of an ideal reversible engine is shown as the Carnot cycle. A gas is contained in a cylinder with a conducting base and non-conductiong walls and friction-less piston.
Stage 1: A constant heat source, temperature T1, heats the conducting base and the load on the piston is decreased. Heat is taken in. Isothermal expansion of the gas at temperature T1 occurs.
Stage 2: The heat source is removed, the conducting base of the cylinder is insulated and the load on the piston is decreased. Adiabatic expansion of the gas occurs as the temperature of the gas falls to T2. Work is done by the gas.
Stage 3: The conducting base of the cylinder is no longer insulated, it is heated by a constant heat source, temperature T2 and the load on the piston is increased. Heat is given out. Isothermal compression of the gas at temperature T2 occurs. Work is being done on the gas.
Stage 4: The heat source is removed, the conducting base of the cylinder is insulated and the load on the piston is increased. Adiabatic compression of the gas occurs until the temperature returns to T1. Work is done on the gas
No engine can be more efficient than the theoretical reversible engine working between the same temperature limits, (T2 - T1).
23.11.0 Adiabatic processes
See also 20.4.0 Thermodynamics
In an isothermal change the temperature remains constant. In an adiabatic change no heat is received from or lost to the surroundings.
1. Light the cotton
A piece of cotton in a glass tube will ignite when a plunger is used to quickly compress the air match lighter A match head placed in a cylinder lights when a tight fitting piston is. Quickly compressed match lighter. Push down hard on a piston in a close fitting tube to light a match head at the bottom light a match head.
2. Expansion cloud chamber
Put some smoke and alcohol in a stoppered flask and shake. When the stopper is released a fog forms.
3. Cloud chambers
Pump a one gallon jug with a bicycle pump until the cork pops out.
4. Adiabatic cooling
Pressurize a one gallon jar with a bicycle pump until the cork blows. Measure the temperature adiabatic heating and cooling An air cylinder moves a piston back and forth. Use a thermocouple to measure the temperature adiabatic heating and cooling.
5. Expansion chamber
Make a temperature detector to insert into a flask that will be warmed and cooled by compression and expansion.
6. Joule-Kelvin coefficients
A thermocouple measures the temperature change as cools on expansion and heats on expansion.