Properties of Gases PDF

Properties of Gases **Definition: A gas is a substance that has no well-defined boundaries but diffuses rapidly to fill any container in which it is placed.** The gaseous state is often referred to as one of the states of matter. All substances exist as either liquids, gases or solids and these are...

Properties of Gases **Definition: A gas is a substance that has no well-defined boundaries but diffuses rapidly to fill any container in which it is placed.** The gaseous state is often referred to as one of the states of matter. All substances exist as either liquids, gases or solids and these are known as the three states of matter. The Gas Laws Temperature - Temperature is the measure of the degree of hotness of an object. - Two scales: Kelvin has -273oC as absolute zero (0K) Celsius: Freezing point of water is 0oC and the boiling point of water is 100oC (1) Temperature can be converted from the Celsius scale to the Kelvin scale by adding 273. Pressure - The pressure of a gas is the force that the gas exerts on a unit area of its container. Pressure is measured in Newtons per metre squared (Nm-2). This is called the pascal. - Normal atmospheric pressure is 1 x 105 Nm-2 (1 x 105Pa or 100,000Pa) - The kilopascal (kPa) is 1000 Pa - The hectopascal (hPa) is 100 Pa 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 the cubic metre (m3) - Normally measures in cubic centimetres (cm3) or litres (L) - A litre is also called a cubic decimetre (dm3) - 1 litre = 1000cm3 = 1 cubic decimetre (dm3) Standard Temperature and Pressure (s.t.p) Standard temperature = 273 K Standard pressure = 100,000 Pa 1 Boyle’s Law Irish chemist, Robert Boyle, built an air pump in order to study the properties of gases. **Definition: Boyle’s Law states that, at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.** - He used this pump to investigate how the volume of a fixed mass pf gas, kept at constant temperature, varied with changes in pressure. - He found that as the pressure increased, the volume decreased and that in fact the volume is inversely proportional to the pressure. Pressure (Pa) Volume cm3 Pressure (Pa) 1/volume (cm-3) - The straight line graph passing through the origin showed that the pressure and the volume of the gas were inversely proportional. - Boyle found that this relationship was true for all the gases he studied, regardless of their different properties. The apparatus on the left can be used to verify Boyle’s Law. Using a pump, the pressure on the air trapped in the glass tube is varied. The pressure is read on the pressure gauge. For each pressure value, the corresponding volume of air is read. (2) pV = k is the mathematical expression for Boyle’s Law. P = Pressure in Pa, V= Volume in litres, k = temperature in Kelvins 2 Charles’ Law Jacques Charles, a French scientist, investigated the relationship between the volume and temperature of a fixed mass of gas at constant temperature. **Definition: Charles’ Law states that, at constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature measured on the Kelvin scale.** 60 50 Volume (cm3) 40 30 20 10 0 0 20 40 60 80 100 120 Temperature oC - The straight line does not pass through the origin. Therefore, the volume of gas is not directly proportional to the temperature. However, if the line is continued backwards, it cuts the X axis at -273oC. 60 50 Volume (cm3) 40 30 20 10 0 -300 -200 -100 0 100 200 Temperature oC Using the above scale of temperature there is now a direct relationship between volume and temperature. V/T = k is the mathematical expression of Charles’ Law. 3 The Combined Gas Law We have seen from Boyle’s Law that pV = k If the volume of gas is allowed to change from V1 to V2 and its pressure changes from an initial value of p1 to a final of p2, while keeping the temperature constant, we say: p1V1 = p2V2 Similarly, from Charles’ Law: V1/T1 = V2/T2 Combining Boyle’s Law and Charles’ Law we get The Combined Gas Law: 𝑝1 𝑉1 𝑝2 𝑉2 = 𝑇1 𝑇2 This equation is used when the initial conditions of Pressure, Volume and Temperature of a gas are given. Also given are two final conditions. You are asked to find the missing 3rd final condition (either a P, V or T) A sample of nitrogen gas has a volume of 75cm3 at a temperature of 27oC and a pressure of 95 kPa. Find the volume that the gas would have at s.t.p. Given: s.t.p V1 = 75cm3 V2 = ? p1 = 95 kPa p2 = 100 kPa T1 = 27oC + 273 = 300K T2 = 0oC + 273 = 273 K 𝑝1 𝑉1 𝑝2 𝑉2 95 𝑥 75 100 𝑥 𝑉2 = = 𝑇1 𝑇2 300 273 95 𝑥 75 𝑥 273 V2 = 300 𝑥 400 V2 = 64.84 cm3 Gay – Lussac’s Law of Combining Volumes Joseph Gay-Lussac, a French chemist, confirmed that when hydrogen reacts with oxygen, two volumes of hydrogen always react with one volume of oxygen to form two volumes of steam. 1 Volume Hydrogen + 1 Volume Oxygen → 2 Volumes Steam From studying further gases the following Law was confirmed. **Definition: Gay-Lussac’s Law of Combining Volumes states that, in a reaction between gases, the volumes of 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.** 4 Avogadro’s Law **Definition: Avogadro’s Law states that equal volumes of gases contain equal numbers of molecules under the same conditions of temperature and pressure.** From Avogadro’s Law we can confirm that at s.t.p. one mole of any gas occupies a volume of 22.4 litres. This is called the molar volume. The molar volume at room temperature and pressure is 24.0 litres. The Kinetic Theory of Gases **Definition: An ideal gas is one that perfectly obeys all the assumptions of the kinetic theory of gases under all conditions of temperature and pressure.** Assumptions of the Kinetic Theory of Gases - Gases are made up of particles that are in continuous 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 gas. - The volumes of the gas molecules are negligible compared to the distance between the molecules. - Collisions between the molecules are perfectly elastic. - The average kinetic energy of the molecules in a sample of gas is proportional to the temperature measured on the Kelvin scale. Limitations to the Kinetic Theory of Gases - Attractive forces do exist between gas molecules due to Van-der-Waals forces, dipole-dipole forces, and hydrogen bonding. - The volume of the gas molecules is not negligible compared to the distances between them. The Equation of State for an Ideal Gas pV = NRT P = Pressure (Pa) V = Volume (m3 = cm3 ÷ 1,000,000 = L ÷ 1,000) n = number of Moles of gas (mol) R = 8.3 (J K-1 mol-1 ) Universal Gas Constant T = Temperature (K) When substituting into the equation pV = NRT, always ensure that the units of pressure are pascal, the units of volume are cubic metres and the units of temperature are kelvins. 5 Mandatory Experiment – To measure the relative molecular mass of a volatile liquid using a conical flask. 1. Two-thirds fill the beaker with water, place on tripod stand and heat to almost boiling with the Bunsen burner. Control the flame so that the temperature remains at 95 0C. 2. Cut a circle of aluminium foil large enough to cover the mouth of the conical flask and fold down a little around the sides of the flask. 3. Find the total mass of the clean dry conical flask, the aluminium foil and the rubber band. 4. Using a dropping pipette, add 3 – 4 cm3 of the volatile liquid to the flask. You need not worry about the exact quantity at this stage because some of this liquid will be lost as a vapour during the experiment. 5. Cover the mouth of the flask with the aluminium foil. Hold in place tightly with the rubber band so that no vapour can escape between the foil and the glass. With the pin, prick one small hole in the centre of the aluminium foil cap. Attach the clamp to the neck of the flask. 6. Carefully immerse the conical flask into the boiling water. Holding the clamp, move the flask up and down periodically to check the liquid level in the flask. 7. All of the volatile liquid vaporises and some of it will escape out through the hole in the cap until the pressure inside the flask is equal to atmospheric pressure. When the flask appears to be empty (i.e. all the liquid appears to have evaporated), this stage has been reached. Immediately and with care, remove the flask from the beaker. Record the exact temperature of the hot water. 8. Record the value of atmospheric pressure using the barometer. 9. Allow the flask to cool. Then, thoroughly dry the outside of the flask, including the foil. You may now notice that there is a small quantity of liquid in the flask. This is the volatile liquid, which has cooled and condensed. Find the mass of the flask, cap, rubber band and contents. By subtraction of the first mass recorded, the mass of the vapour, which occupied the flask at the temperature of the boiling water, is now known. 6  10. Remove the cap and rubber band. Find the volume of the flask by completely filling it with water, and then, transferring all of the liquid from it to graduated cylinders. Record the volume of the liquid transferred. 11. Calculate the value of the relative molecular mass, Mr, of the volatile liquid. - After heating the conical flask for a while, all of the volatile liquid in the flask will have vaporised. No liquid will then be visible in the flask. - As the flask cools, droplets of liquid are seen forming inside the conical flask. Exam Questions 2012 – HL – Section A – Question 3 3. The relative molecular mass of a volatile liquid can be found by means of a procedure involving the use of either apparatus A or apparatus B shown below. (a) Give an example of a liquid suitable for use in this experiment. Cyclohexane (b) Describe how (i) the mass, (ii) the volume, of the vapour is determined. (i)- Weigh flask and fittings. - Heat until all liquid gone, cool, dry and reweigh. - Find difference between the initial and final mass (ii) Fill flask with water and empty into graduated cylinder. (c) Explain why the pressure of the vapour is the same as atmospheric pressure. The pinhole means that the vapour is exposed to the air. (d) The vapour of 0.63 g of a pure liquid occupies a volume of 330 cm3 at a temperature of 100 °C and at a pressure of 101 kPa. Calculate the number of moles of vapour and hence calculate the relative molecular mass of the volatile liquid. PV = nRT n = 101 × 103 × 330 × 10–6 8.3 x 373 = 0.01076 moles Mass = 0.63 0.01076 = 58.6 Mass = 58.6 (e) Why is this method unsuitable for liquids that are non-volatile? They do not vaporise easily What modern instrumental technique could be used as a more accurate method to measure the relative molecular masses of volatile and non-volatile liquids as well as of solid and gaseous substances? Mass spectrometer 2009 – HL – Section B – Question 10 10. Answer any two of the parts (a), (b) and (c). (a) State Avogadro’s law. Equal volumes of gases contain equal numbers of molecules Give two assumptions of the kinetic theory of gases. Under the same conditions of temperature and pressure. 7 Gases made up of particles in rapid, random, straight-line motion Average kinetic energy of molecules proportional to Kelvin temperature Give two reasons why real gases deviate from ideal gas behaviour. - Forces of attraction between the molecules - Volume is not negligible. How many moles of gas are present in a sample containing 1.8  1024 atoms of chlorine at s.t.p.? 1.8 × 102 = 9 ×1023 molecules 2 9 x 1023 6 x 1023 = 1.5 moles 8  References 1. BYJUs.com 2. Chemistrygod.com 9