Properties of Gases Chpt. 10

Particles slide over each other A Quick Review Matter is anything that occupies space and has mass There are three states of matter Particles slide over each other Particles vibrate about a fixed position Particles have almost complete freedom of movement

In this chapter we will be looking at the third state of matter - GAS. Gases have distinct properties that distinguish them from solids and liquids. These properties may be explained in terms of the particles (atoms, molecules, ions) of a gas having more freedom of movement than the particles of a solid or liquid.

Some Properties of Gases: Gases DO NOT have a definite shape or size and will spread throughout any container they are placed in – DIFFUSION Diffusion: is the movement of particles from an area of high concentration to an area of low concentration. Example: NH3 and HCl Ammonium Chloride Smoke particles travelling throughout the air Example liquids (much slower): Spreading of ink throughout a beaker of water

A gas is defined as a substance that has no well-defined boundaries but diffuses rapidly to fill any container in which it is placed.

2. Gases do not have a fixed volume – they fill any space into which they are put, therefore the volume of the gas is the volume of the container in which they are placed. The volume of a gas is influenced by two factors: - temperature - pressure Increasing Temperature – gas expands and occupies greater volume Increasing Pressure – gas becomes compressed and occupies a smaller volume

Charles (volume & temperature) Boyle (volume & pressure) Jacques Charles and Robert Boyle were two scientists who investigated how the volume of a gas changes with temperature and how the volume of a gas changes with pressure respectively. Charles (volume & temperature) Boyle (volume & pressure)

In this chapter we shall be studying the laws that gases obey and why they obey these laws. This also involves a study of the work of Charles and Boyle

3 Main properties of a fixed amount of gas Temperature Pressure Volume Note: Before studying the laws that gases obey we must first understand how to measure the above three properties

Temperature: Temperature is a measure of the degree of hotness of an object. Two Scales Celsius (centigrade) scale Kelvin (absolute) scale Two fixed points: - 0oC – freezing point of water - 100OC – boiling point of - 0 K – absolute zero (temperature at which a gas would occupy no volume)

Relationship between Celsius Scale and Kelvin Scale O0C 10O0C -273O C 0 K 273 K 373 K Absolute Zero

Temperature can be converted from the Celsius scale to the Kelvin scale by adding 273 Celsius Kelvin *0oC = 0 + 273 = 273 K 30oC = 30 + 273 = 303 K 50oC = 80oC = 100oC = 273oC =

*Note: - size of a degree on the Celsius scale is the same as that on the Kelvin scale i.e. rise in temperature of 10oC is same as rise in temperature of 10 K - SI unit of temperature – Kelvin*

Pressure: Pressure of a gas is the force it exerts on each unit area of its container SI unit of pressure is N/m2 (Nm-2) or *Pascal (Pa) We will be dealing with pressure in terms of atmospheric pressure: Normal atmospheric pressure: 1.013 x 105 N/m2 1.013 x 105 Pa 101,325 Pa 101kPa (*1kPa – 1000 Pa)

Note: Old method of expressing pressure of gases used millimetres of mercury or atmospheres: Normal Atmospheric Pressure: 760 mm Hg = 1 atm = 1.013 x 105Pa

Volume: The volume of a sample of gas is the same as the volume of the container in which the sample is held SI unit of volume is m3 Laboratory units: cm3 Litres (L) A litre is also called a cubic decimetre (dm3= 1/10 of metre) 1L = 1000cm3 = 1dm3

Relationship between m3, cm3 and Litres 1m3 = 1 x 106 cm3 *N.B. To change cm3 to m3 multiply by 10-6 To change litres to m3 multiply by 10-3

Summary of measuring three main properties of gases Temperature – unit Kelvin ( convert from celsius) Pressure – unit Pascal Volume – unit cubic metre (convert from cm3 and litres)

Standard Temperature and Pressure (s.t.p.) As previously noted the volume of a gas varies with temperature and pressure. Thus in order to compare volumes occupied by gases, it is necessary to measure all volumes at the same temperature and pressure: Standard Temperature = 273 K (0OC) Standard Pressure = 1.013 x 105 Pa or 101,325 Pa 101kPa

Five Main Gas Laws Boyles Law Charles Law The Combined Gas Law Gay-Lussac’s Law of combing Volumes Avogadro’s Law

Boyles Law Irish scientist Robert Boyle experimented with the relationship between pressure and volume of gases. He set up a J-shaped tube and added mercury to see what it did to the volume of a trapped gas, kept at a constant temperature

As pressure increases, volume decreases

Boyles Experimental Results *This relationship is inversely proportional, when one increases the other decreases.

The volume is inversely proportional to the pressure *Note: see fig. 10.8(a) and fig. 10.8(b) pg. 120

Boyles Law: At a constant temperature , the volume of a fixed mass of gas is inversely proportional to its pressure V α 1 P The proportionality symbol can be replaced by a constant k which gives us a mathematical equation: V = k1 pV = k p = pressure V = volume k = proportionality constant

Knowing that the pressure of a gas multiplied by its volume is always a constant value gives another way of expressing Boyle’s Law: p1V1 = p2V2 Thus, it is possible to calculate the volume of a gas at one pressure when its volume at another pressure is known. *Note: see pg. 120 table 10.1 and fig. 10.11 for further explanation

Boyle’s Air Pump

Boyles Law Summary V α 1 P pV = k p1V1 = p2V2 Must also be familiar with associated graphs (3)!!!!! (pg 120 – Fig 10.8 & pg 121 – Fig 10.11)

Charles Law French scientist, Jacques Charles, investigated the relationship between the volume and temperature of a fixed mass of gas at constant pressure

Charles Law French physicist Jacques Charles was the first to fill a balloon with hydrogen gas and make a solo flight. He showed that the volume of a gas increases when the temperature increases (at a constant pressure)

Charles Law Experiment

Charles Law Experimental results *Note: see figure 10.14 pg. 122

In previous graph straight line does not go through the origin therefore one cannot say that the volume of the gas is directly proportional to the temperature measured in O C. However, if the line is continued backwards, it cuts the x-axis at -273oC i.e. absolute zero in terms of the Kelvin Scale

-273oC O K *Note: see figure 10.15 pg. 122 Using the Kelvin scale of temperature a direct relationship between volume and temperature can be seen i.e. volume is directly proportional to temperature

Charles Law: At constant pressure , the volume of a fixed mass of gas is directly proportional to its temperature measured on the Kelvin scale V α T V = kt V = k T The proportionality symbol can be replaced by a constant k which gives us a mathematical equation: V = volume k = proportionality constant T = temperature (Kelvin)

Knowing that volume divided by temperature always gives a constant value allows the volume of a gas at any given temperature to be calculated provided that its volume at some other temperature is known: V1 = V2 T1 T2 *Note: see pg. 122 table 10.2 and fig. 10.17 for further explanation

Charles Law Summary V α T V = k T V1 = V2 T1 T2 Must also be familiar with associated graphs (3)!!!!! (pg 121-122 – Fig. 10.14, 10.15, 10.17)

T1 T2 The Combined Gas Law (The General Gas Law) The results of Boyle’s and Charles’ law can be combined into a single expression which takes the form: p1 V1 = p2 V2 T1 T2 Using this equation, the volume of a gas at any temperature and pressure can be calculated provided that its volume at some other given temperature and pressure is known.

*Points to Note: Since combined gas law derived from Charle’s law MUST convert all temperatures to the KELVIN SCALE Units on both sides of equation must be consistent e.g. if using kPa on left side must use kPa on right side

Example 1: A certain mass of gas was found to occupy a volume of 269cm3 when the temperature was 17o C and the pressure 99.7kPa. What volume would the gas occupy at s.t.p.?

Example 2: A sample of hydrogen of volume 100cm3 at a pressure of 1 x 105 Pa is compressed to 55cm3 at constant temperature. What is the new pressure of the gas?

Gay-Lussac’s Law of Combining Volumes Following on from work done by Henry Cavendish on the composition of water (electrolysis), Joesph Gay-Lussac confirmed that when hydrogen reacts with oxygen, 2 volumes of hydrogen always react with 1 volume of oxygen 1808 – Gay-Lussac stated his law of combining volumes

*Note: Please read through experiment outline pg’s 123-124 He studied the reactions of other gases to further investigate whether they also reacted in simple ratios Hydrogen + Oxygen Steam 2 volumes 1 volume 2 volumes Hydrogen + Chlorine Hydrogen Chloride 1 volume 1 volume 2 volumes Nitrogen + Oxygen Nitrogen Dioxide Monoxide 2 volumes 1 volume 2 Volumes *Note: Please read through experiment outline pg’s 123-124

Gay-Lussac’s Law of Combining Volumes In 1808, Gay-Lussac was able to state his law of combining volumes: Gay-Lussac’s Law of Combining Volumes In a reaction between gases, the volumes of the reacting gases and the volumes of any gaseous products are in the ratio of small whole numbers provided the volumes are measured at the same temperature and pressure.

Avogadro’s Law An explanation of Gay-Lussac’s law depends on the idea that gases consist of particles. Gay-Lussac’s and Daltons Atomic Theory were published at the same time (1808). However attempts to explain Gay-Lussac’s theory using Dalton’s atomic theory failed. Amedeo Avogadro, (Professor of Physics in 19th century Italy) put forward a hypothesis, which explained Gay-Lussac’s law, relating molecules and volumes.

Avogadro showed experimentally that 100 cm3 of hydrogen react exactly with 100 cm3 of chlorine. This indicates that there must be the same number of molecules of hydrogen and chlorine in each volume: Hydrogen + Chlorine Hydrogen Chloride 1 volume 1 volume 2 volumes Applying Avogadro’s Law: n molecules + n molecules 2n molecules Hydrogen Chlorine Hydrogen 1 molecule + 1 molecule 2 molecules H2 Cl2 2HCl

Two volumes of hydrogen contain twice as many molecules ……… …. as one volume of oxygen Each oxygen atom bonds with two hydrogen atoms to form a molecule of water

Similarly, 2H2 + O2 2H2O 2NO + O2 2NO The ratio in which the volumes of gases combine is the same as the ratio in which the molecules of gases combine. Thus, when dealing with gaseous reactions the words volume and molecule can always be interchanged.

Avogadro’s Law Equal volumes of gases, under the same temperature and pressure contain equal numbers of molecules

Molar Volume Leading on from Avogadro’s study of gaseous reactions and the words volume and molecule being interchangeable a definition of molar volume was formed Remember: 1 mole = 6 x 1023 particles By experiment it was found that: 1 mole O2 occupies 22.4L at s.t.p.

Since 1 mole of any gas contains 6 x 1023 molecules then according to Avogadro’s Law: At s.t.p. one mole of any gas occupies a volume of 22.4 L Molar Volume: the volume occupied by one mole of any gas is called its molar volume *Note: at r.t.p. (room temperature, pressure) one mole occupies a volume of 24 L

Calculations involving Molar Volume 1. Moles → Litres 2. Litres → Moles 3. Litres → Number of particles 4. Litres → Grams 5. General Questions

Converting moles to litres Volume (Litres) = moles x Molar Volume (22.4L) Example 1: What is the volume of 2 moles of H2 at s.t.p.? Litres = 2 x 22.4 Litres = 44.8L

2. Converting litres to moles Moles = Volume Molar Volume Note: 22.4L = 22,400cm3 Example 1: How many moles of SO2 are there in 3L of the gas at s.t.p.? Moles = 3 22.4 Moles = 0.13 moles

Example 2: How many moles of NO2 are there in 175cm3 of the gas at s.t.p.? Moles = Volume Molar Volume Moles = 175 22,400 Moles = 0.0078125 moles

3. Converting litres to number of particles (molecules/atoms) Step 1. Change litres/cm3 to moles Step 2. Change moles to molecules/atoms Example 1: How many molecules are there in 560cm3 of chlorine gas at STP?

Example 1 Solution:

Example 2: How many atoms are there in 840cm3 of butane gas,C4H10, at STP?

4. Converting Litres to Grams Step 1: Change Litres/cm3 to moles Step 2: Change moles to grams Example 1: What is the mass in g of 140cm3 of oxygen gas at STP?

Example 1 Solution:

5. General Questions This section involves taking what you know from the previous chapter on the Mole and incorporating this into answering the question Example 1: Calculate the volume occupied by 20g of sulphur dioxide gas at s.t.p.?

Example 2: 200 cm3 of a certain gas at s.t.p. Have a mass of 0.25g. Calculate the relative molecular mass of the gas.

Example 3: Calculate the density of carbon dioxide at s.t.p.

Try the following question: What is i) the volume at s.t.p. and ii) the number of molecules in 24g of sulphur dioxide (SO2)

Please complete the following questions on the mole and molar volume Book: 10.5, 10.6, 10.7 pg. 137-138 Workbook: W10.4, W10.5 pg. 22

Mandatory Experiment: To measure the relative molecular mass of a volatile liquid *Note: A volatile liquid is a liquid that is easily vaporised

The Kinetic Theory of Gases This theory was developed to explain the five gas laws discussed previously. It was based on the idea that all matter is made up of tiny particles in constant motion i.e. Solids – particles vibrate Liquids – particles can move freely around each other Gases – particles have complete freedom of movement Robert Brown, a botanist, was the first to find evidence to support the idea of particles in motion.

Brownian Motion Brownian Motion: the random movement of tiny particles suspended in a liquid or gas

In order to understand the behaviour of gases a number of assumptions were developed – Kinetic Theory of Gases Assumptions of the Kinetic Theory of Gases: Gases are made up of particles that are in constant rapid, random motion, colliding with each other and with the walls of the container. *There are no attractive or repulsive forces between the molecules of a gas *Gas molecules are so small and so widely separated that the actual volume of all the molecules is negligible compared with the space they occupy i.e. they take up very little space.

4. When molecules collide all collisions are perfectly elastic i.e. - If particle collides with wall of its container with a speed of 450 m/s it rebounds with the same speed - No loss of kinetic energy but may be transferred 5. The average Kinetic energy of the molecules is proportional to the Kelvin temperature

Limitations to the Kinetic Theory of Gases: - it is not valid to say that there are no attractive or repulsive forces between the molecules of a gas i.e. dipole-dipole forces between polar molecules and van der Waals forces between non-polar molecules. - it is not always valid to say that the volume of the gases is negligible compared with the space they occupy i.e. under high pressure, when molecules are crowded close together, it is clear that their volume is not negligible.

Ideal Gas Due to these limitations it can be seen that all of the assumptions of the kinetic theory do not hold for real gases but only hold for imaginary or ideal gases An ideal gas is one that obeys all the assumptions of the kinetic theory of gases under all ALL conditions of temperature and pressure

Ideal Gases DO NOT EXIST!!!! A real gas behaves like an ideal gas at: - low pressure – molecules widely spaced and - high temperatures – molecules are moving rapidly and forces between the molecules are small

Reasons why Gases differ from Ideal Gas behaviour At low temperatures and high pressures: - the volume of the particles is not negligible compared with the distances between them - there are attractive and repulsive forces between the particles i.e. molecules are moving slowly and are packed close together resulting in stronger intermolecular forces

*Note: - Under the same conditions of temperature and pressure non-polar molecules come closer to being ideal gases than polar molecules, since the attractive forces are less in the case of non- polar molecules.

Student Question: State which of the following gases you would expect to come closest to ideal behaviour, and which you would expect to deviate most from ideal behaviour: H2, HF, F2 . Explain your answers.

(Equation of State for an Ideal Gas) Ideal Gas Equation (Equation of State for an Ideal Gas) Boyles Law, Charles Law and Avogadro’s law may be combined to form an equation relating volume (V), temperature(T), pressure(p) and number of moles(n) of a gas: Boyle V α 1 constant temperature p Charles V α T constant pressure Avogadro V α n constant temperature & pressure

Combining all three equations: V α (1) Tn (p) Replacing proportionality symbol with R (constant of proportionality – Universal Gas Constant): V = R(1) Tn (p) Rearranging equation: pV = nRT Ideal Gas Equation

The numerical value for R can be found by simply substituting experimental values into the ideal gas equation i.e. we know at s.t.p. I mole of any gas occupies a volume of 22.4L T = 273K P = 1.013 x 105 N/m2 (Pa) n = 1 V = 22.4L – 22.4 x 10-3 = 0.0224m3 pV = nRT R = pV = 1.013 x 105 x .0224 nT 1 mole x 273 R = 8.31 J mol-1 K-1

Units and the Ideal Gas Equation Measure Unit Volume m3 Pressure Pa Temperature K Number of moles mol Universal Gas Constant (R) J mol-1 K-1 (always given to you)

Calculations involving the Ideal Gas Equation Example 1: Calculate the volume occupied by 10g of oxygen gas at 25O C and a pressure of 200kPa (R = 8.31 J mol-1 K-1)

Example 1 Solution:

Example 2: 20g of a gas occupies a volume of 5L at 87OC and 200,000 Pa. i) How many moles of the gas are present? ii) What is the relative molecular mass of the gas?

Example 2 Solution:

Student Question: 2.5kg of carbon dioxide gas are released into the air when a fire extinguisher is discharged. What volume does this gas occupy at a pressure of 100,000 Pa and a temperature of 288K?

Please answer the following questions: Book: 10.9 – 10.12 Workbook: W10.6 – W10.12