Ideal Gases K Warne

The Gas Phase Covered in this presentation  Kinetic Theory of Matter - solids, liquids & gasses Boyle's law Kelvin & Celsius Temperatures Ideal Gas Model pV=nRT Molar gas volume Calculations p1v1/T1 = p2V2/T2 Non ideal behavior - graphs

Gas Problems – Aerosol cans Question: Pressurized containers (aerosol cans) carry warnings to avoid heating the container. Why is this? – describe a gas law that relates to this problem and explain it’s relevance in terms of the Kinetic Theory of Gases.

Gas Problems – Aerosol cans Question: Pressurised containers (aerosol cans) carry warnings to avoid heating the container. Why is this – describe a gas law that relates to this problem and explain it’s relevance in terms of the Kinetic Theory of Gases. ANS: Heating a gas will increase the pressure this could lead to an explosion – that is the reason for the warning. The gas law relating to this is Guy Lussac’s law which states that the pressure of a gas is directly proportional to its temperature. (at a constant volume) According to the kinetic theory of gases – increasing temperature of the gas increases the average kinetic energy of the particles (move faster) which increases the rate and energy of collisions with the sides of the container and therefore increases the pressure.

Gas Problems Question: Weather balloons are not fully inflated prior to being released. There are two conflicting factors relating to atmospheric conditions at high altitude which are involved in this scenario. Identify these factors as well as the gas laws which relate to these conditions and explain which of the factors is responsible for the under inflation of the balloons.

Gas Problems Question: Weather balloons are not fully inflated prior to being released. There are two conflicting factors relating to atmospheric conditions at high altitude which are involved in this scenario. Identify these factors as well as the gas laws which relate to these conditions and explain which of the factors is responsible for the under inflation of the balloons. ANS: At high altitude the temperature and pressure decrease. According to Guy Lussac’s law as the temperature decreases the pressure of the gas in the balloon will decrease. (if the volume is constant the balloon volume is not constantso this law does not apply.) According to Charles’ law the volume is directly proportional to the temperature so the volume should decrease. (at const P) According to these two laws the volume of the balloon should decrease. However according to Boyle’s law the volume is inversly proportional to the pressure – so as the pressure decreases the volume should increase. The decrease in pressure has a larger effect in this case than the temperature so the volume of the balloon INCREASES. If the balloon was fully inflated it would burst!

Gas Problems Explain how and why real gases differ from the behaviour of an ‘ideal gas’.

Gas Problems Explain how and why real gases differ from the behavior of an ‘ideal gas’. Real gases deviate from the ideal gas model - this occurs at high pressure and low temperature. 1. At high pressure the particles are forced close together and their volume adds to the total volume of the gas. The volume of the real gas is larger than that of an ideal gas at high pressure. 2. At low temperature the forces between the particles pull them closer together. The volume of the real gas is therefore lower than that of an ideal gas.

Gas Problems 1. If a car tyre has a pressure of 280 kPa at 25 o C, what would the pressure be if the tyre temperature heats up to 38 o C on a long journey? (Assuming the volume stays constant.)

Gas Problems 1. If a car tyre has a pressure of 280 kPa at 25 o C, what would the pressure be if the tyre temperature heats up to 38 o C on a long journey? (Assuming the volume stays constant.) P1=P2 T1T =P P2=260906Pa  =292.21kPa (4)

Gas Problems 2. Calculate the volume of a hot air balloon which has a volume of 1m 3 at the surface of the earth where the temperature is 20 o C and the pressure is Pa if it rises to an altitude of 2.5 km where the temperature is 10 o C and the pressure 40 Pa.

Gas Problems 2. Calculate the volume of a hot air balloon which has a volume of 1m 3 at the surface of the earth where the temperature is 20 o C and the pressure is Pa if it rises to an altitude of 2.5 km where the temperature is 10 o C and the pressure 40 Pa. P1 V1=P2 V2 T1T2 (101300)(1.00)  =(40)V2 (293.00)(283) V2= m3  (5)

Gas Equation Poblems If 2.5 g of methane (CH 4 ) gas are placed in a 2.5 dm 3 container at room temperature (25 o C), what will the pressure in the container be?

Kinetic theory of Matter 1.All Matter is made up of ______________. 2.Forces of ______________________________ exist between particles. 3.The particles are in a state of ___________________ motion. 4.Particles collide with __________________ and _____ ______________________. 5.Particle collisions are ____________________. (Particles not deformed.) 6.Particles in a given sample do not have the same _____________________.

Kinetic theory of Matter 1.All Matter is made up of particles. 2.Forces of attraction and repulsion exist between particles. 3.The particles are in a state of constant random motion. 4.Particles collide with one another and walls of containers. 5.Particle collisions are perfectly elastic. (Particles not deformed. 6.Particles in a given sample do not have the same kinetic energy.

Gases Motion – Rapid random (speed and direction) motion. ________________. Forces – ________________ forces - negligible (can be ____________ in most situations) Energy – very _________ energy - kinetic energy.

Gases Motion – Rapid random (speed and direction) motion. Fill any space. Forces – very weak forces - negligible (can be ignored in most situations) Energy – very high energy - kinetic energy.

Macroscopic / microscopic Kinetic theory relates the ________________ properties of substances to its ___________________ properties. Pressure= force/area Volume =lxb h Temperature = o C or K Pressure: _________________ per unit _________. Temperature: is a measure of the _____________________ of particles. Macroscopic properties: ___________, ___________, ____________ Microscopic properties: ________ & ________ of particles

Macroscopic / microscopic Kinetic theory relates the macroscopic properties of substances to its microscopic properties. Pressure= force/area Volume =lxb h Temperature = o C or K Pressure: Rate of collisions per unit area. Temperature: is a measure of the average kinetic energy of particles. Macroscopic properties: Temperature, Pressure, Volume Microscopic properties: Motion & Forces of particles

Effect of Temperature The temperature of a fixed mass of gas is increased while the volume is kept constant. Explain which macroscopic property will change and how by considering the associated changes in the microscopic properties of the particles.

Effect of Temperature The _____________________________ of a fixed mass of gas is increased while the __________________ is kept constant. The __________________________ will increase. Increasing temperature increases the __________ _______________ _______________ of the particles. The particles will collide ______________________ with the walls of the container and collisions will be _____________________. The increased ____________ and __________________ of collisions increase the _________________. P P  T ( V = const.)

Effect of Temperature The temperature of a fixed mass of gas is increased while the volume is kept constant. The pressure will increase. Increasing temperature increases the average kinetic energy of the particles. The particles will collide more frequently with the walls of the container and collisions will be more energetic. The increased collisions increase the pressure. P P  T ( V = const.) P=k*T P/T = k

Energy Distributions

Effect of Temp

CHARLES’S LAW The volume of a given amount of ideal gas is directly proportional to the (Kelvin) Temperature provided the amount of gas and the pressure remain fixed. V  T V=k.T V / T = k (a constant) or V1 / T1 = V2 / T2 Eg: A hot air balloon 2dm 3 at 273K has air heated to 373K. The air expands and fills the balloon. Calculate the new volume. V (c m 3 ) T (/K) V1/T1 = V2/T2 V2 = (2)(373)/273 = 2.733dm 3

Pressure & Volume If the __________ of a fixed mass of gas is _______ the _________ will increase. (T = const.) The pressure increases because… This happens because there is ________ for the particles to collide with so the ______ of __________ with the sides of the container _____________ increases.

Pressure & Volume If the volume of a fixed mass of gas is reduced the pressure will increase. (temperature constant) This happens because there is less surface area for the particles to collide with so the rate of collisions with the sides of the container per unit area increases.

Boyles Law Spreadsheet T = 298K P  1/V P = k (1/V) pV = k

General Gas Equation P  1/v, T = constant P  T,v=constant P=kT/V p1T1p 2 T 2 = k p1V1/T1 = p 2 V 2 /T 2 = k

PvT Examples If the pressure of a gas in a sealed container is 190kPa at a temperature of 15 o C what will the pressure be if the gas is heated to 40 o C? 1.Write down what you are given and asked: P1 = 190kPa, T1 = 15C, T2 = 40C, P2 = ? (V=C) 2.Write down the equation: P1/T1 = P2/T2 3.Substitute in values given: 190/(15+273) = P2/(40+273) 4. Solve for missing value (Inc. UNITS!!): P2 = 313(190/288) = kPa

Gas Graphs For a fixed mass of gas. pV=_____ pV = ______ T If the amount of gas increased: pV  _____ T n pV T Gradient = ______

Gas Graphs For a fixed mass of gas. pV= kT pV = k T If the amount of gas increased: pV  n T pV = k n T k = R pV/T = Rn n pV T Gradient = R From the graph n (or R) can be found by calculating the gradient and substituting. Eg: Calculate the value of R using the standard temperature and pressure values and volume of one mole of gas at STP. R = pV/nT = (101.3x10 3 )(22.4x10 -3 )/(1)(273) = 8.31 (N.m.mol -1 K -1 ) J.mol -1 K -1

Ideal Gas Behavior At normal pressures and temperatures all real gases obey Boyle’s law and have behave as an “ideal gas”. An Ideal gas is a __________________________ and Ideal gas particles: 1. are ______________ and exhibit _______________ motion. 2. occupy _______________. 3. exert __________________ on one another 4. have _____________ collisions i.e. no energy is lost.

Ideal Gas Behavior At normal pressures and temperatures all real gases obey Boyle’s law and have behave as an “ideal gas”. An Ideal gas is a useful imaginary model and Ideal gas particles: 1. are identical and exhibit constant random motion. 2. occupy no volume. 3. exert no forces on one another 4. have perfectly elastic collisions i.e. no energy is lost.

Ideal Gas Equation pV = nRT P = pressure of the gas _______ (______) V = volume in m 3 T = Temperature IN _________ n = number of ________ of gas R = ________ gas constant ________ _______ Standard Temperature Standard Pressure (STP) ________ _________ Work out the volume of 1 mole of an ideal gas at S.T.P. ……………………………………………………………………… ……………… …………………………………………………………………… ………………..

Ideal Gas Equation pV = nRT P = pressure of the gas Pa V = volume in m 3 T = Temperature IN KELVIN n = number of moles of gas R = universal gas constant JK -1 mol -1 Standard Temperature Standard Pressure (STP) 273K 101,3 x10 3 Pa The volume of 1 mole of an ideal gas at S.T.P. V = nRT/P = (1)(8.314)(273.15)/(101,3x10 3 )= m 3 M v = 22.4dm 3

Real Gas Deviations Real gases deviate from the ideal gas model - this occurs at __________________ and ___________________. At high ___________________ the particles are _____________ and their _____________ adds to the ____________ of the gas. The volume of the real gas is ______________ than that of an ideal gas at high pressure. P

Real Gas Deviations Real gases deviate from the ideal gas model - this occurs at high pressure and low temperature. At high pressure the particles are forced close together and their volume adds to the total volume of the gas. The volume of the real gas is larger than that of an ideal gas at high pressure. P Volume increased

Ideal Gas Deviations At low ______________ the _____________ between the particles pull them ___________ together. The volume of the real gas is therefore __________ than that of an ideal gas.

Ideal Gas Deviations At low temperature the forces between the particles pull them closer together. The volume of the real gas is therefore lower than that of an ideal gas.

Real Gases - Deviations Real gases deviate from ideal behavior at low __________ and high ____________. Many real gases ___________ under these conditions. At low __ and low ___ Real gas particles are _______ ______ by attractive forces - they therefore exert _____ ___________.

Real Gases - Deviations High P - volume increased Mod T & P High T more Ideal At HIGH PRESSURE real gas particles volume ADDS to the total volume PV is INCREASED. At moderate T & P all gasses almost ideal. At low temperatures and high pressures real gas particles are slowed down by attractive forces - they exert less pressure – many real gases liquefy. Low T – P decreased

Kelvin Temperature pV  T Reference points: Absolute zero Triple point of water (273.16K) At constant V P 1 /P 2 = T 1 /T 2 If “2” = triple point Then P 1 /P tr = T 1 /T tr P T 0 0 T tr P tr

Pressure Measurement Atmospheric Pressure Pressure = force/area Units: Newtons/m 2 = Pa Bourdon gauge - kPa 1kPa = 1000Pa Atmospheric Pressure 760mm Hg = kPa The pressure of the atmosphere is enough to support a column of mercury 760mm high. 760mm

Phases of Matter  Kinetic Theory of Matter - solids, liquids & gasses  Boyle's law  Kelvin & Celsius Temperatures  Ideal Gas Model  pV=nRT Molar gas volume Calculations p1v1/T1 = p2V2/T2 Non ideal behavior - graphs