REVISION: GAS LAWS & MOLE CALCULATIONS 18 JUNE 2013

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Marvin Bruce Weaver
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1 REVISION: GAS LAWS & MOLE CALCULATIONS 18 JUNE 2013 Lesson Description In this lesson we revise how to: apply the gas laws to perform calculations apply the mole concept to perform calculations Key Concepts States of Matter Matter exists in different phases depending on the temperature. The different states of matter have different characteristics. Solid Solids have their own shape and volume. Liquid Liquids have their own volume but take the shape of the container in which they are placed Gas Gases take the shape and volume of the container in which they are placed When studying gases we observe four physical properties: Temperature In every day life measure the temperature of a gas in degrees Celsius ( 0 C), e.g. air temperature. This temperature scale has the zero point as the freezing / melting point of water and C is set as the boiling point of water at sea level. Scientists use the Kelvin temperature scale, where zero is the absolute zero and the freezing / melting point of water is 273K. The boiling point of water at sea level is 373K. The standard temperature of a gas is 273K (0 0 C) Volume There are many different units of volume. The standard SI unit is metres cubed (m 3 ). It is common to measure volume in decimetres cubed or litres too. (1 dm 3 = 1l). You must know how to convert from different units of volume. Pressure Pressure is the force applied per unit surface area. The SI unit for pressure is the Pascal where 1Pa = 1N.m 2. In everyday life we measure pressure of gases in kilopascals. Standard pressure is taken as 101,3kPa. This standard is equal to air pressure at sea level when water boils at C and may be called 1 atmosphere (1atm). Quantity of a gas The quantity of the gas is measure in terms of the number of moles of gas present. We can also measure the mass of gas or talk about the number of molecules.

2 To explain the behaviour of gases and how the physical quantities are related to each other we use different models. The microscopic model of gases is called the kinetic theory of gases. A macroscopic model which relates pressure, volume, temperature and number of moles of gas to each other is called the Ideal gas model The Kinetic Theory of Gases The kinetic theory of gases provides an explanation on how gas molecules behave. According to this model, the following assumptions are made about the particles of a gas: The molecules of a gas are very small compared to the spaces between them. This observation is based on the fact that gases molecules are compressible. To show that air is compressible, a tyre can be pumped up by forcing or compressing gas into it. The molecules are in constant motion. We observe this when the smells diffuse through a room. The molecules fill the container and spread out evenly leaving huge spaces between them. The volume of the gas is taken as the volume of the container. We can say that the forces of attraction between the gas molecules are very small. There are collisions between the molecules and also between the molecules and the sides of the container. These collisions explain why gases exert pressure. The molecules of the same sample of a gas move at different speeds. It is therefore necessary to speak of the average velocity of the gas particles and therefore, average kinetic energy. The speed at which the molecules of the gas move depends on the temperature of the gas. The average kinetic energy of a sample of molecules depends entirely on the temperature of the gas. Gas Laws Gas laws show the relationships between temperature, pressure, volume and the number of moles (quantity) of gas in a given sample. When a relationship between any two variables amongst temperature, pressure and volume is investigated, the other variables must be kept constant. In scientific terms, the variables that are kept constant during an investigation are called the controlled variables. Boyle s Law The pressure of a fixed amount of gas is inversely proportional to the volume provided the temperature remains constant. Boyle s Law is represented as follows mathematically: When multiplied by a constant, k, the equation becomes: Therefore pv = k. When a graph of pressure versus 1/volume is drawn, a straight line is obtained. The gradient of the straight line equals to the constant k. Thus the value of pv throughout the graph is constant or the same at any given point. Thus, the following equation results from Boyle s Law: p 1 V 1 = p 2 V 2 The SI units of measurement for pressure and volume are the pascals (Pa) and cubic metres (m 3 ) respectively. However, other units of measurements can be used but you need to ensure that the same units of measurements are used for both readings of pressure and volume. For real gases in every day scenarios, a compression (reduction in volume) or an expansion (increase in volume) always results in a change in temperature too.

3 Charles Law The absolute temperature is directly proportional to the volume of a fixed amount of gas provided the pressure of the gas remains constant. When we plot a graph of volume and temperature readings, the graph is a straight line but it does not pass through the origin if the temperature of the gas is measured in degrees Celsius. We need to change the scale of the temperature reading. The zero cannot be the freezing point of water but the point where the average kinetic energy of the gas molecules is zero. We call this point absolute zero. When we extrapolate to find where the straight line will cut the temperature axis you will see that the reading is -273 C. This point is taken as zero Kelvin (0 K). When we draw a volume versus temperature (measured in Kelvin), we get a straight line passing through the origin. Now we can state Charles Law mathematically as follows: V α T K When a constant, k, is introduced, the equation becomes V = kt K where T K is the absolute temperature measured in Kelvin. From the equation V = kt K we can change the subject of the equation to get, k. But k is a constant which equals the gradient of the graph and since the gradient of the graph is constant, we can write the equation: Gay-Lussac s Law The pressure of a fixed amount of gas is directly proportional to the absolute temperature provided the volume is kept constant. A graph of pressure versus absolute temperature will be a straight line passing through the origin showing that pressure is directly proportional to temperature (K). This relationship can be shown mathematically as follows: p α T. Multiplying by a constant, k, gives; p = kt. Therefore = k. p/t is the gradient of the pressure versus temperature graph and therefore it is constant at any point along the graph since it is a straight line. Thus p 1 /T 1 = p 2 /T 2. The Combined Gas Equation The combined gas equation is also known as the general gas equation. To arrive at the general gas equation, Boyles s Law and Gay-Lussac s Law are used. From Boyle s Law; p α 1/V. From Gay- Lussac s Law; p α T. Combining the two yield; p α T/V. when the proportionality is multiplied by a constant, k, the following equation is arrived at;. Therefore. Since k is a constant which remains the same for the conditions of temperature, pressure and volume of any fixed amount of gas; p 1 V 1 /T 1 = p 2 V 2 /T 2. This is known as the general gas equation. The Molar Volume It has been found experimentally that one mole of any given gas will occupy a volume of 22,4 dm 3 at Standard Temperature and Pressure (STP). A temperature of 0 0 C (273 K) and pressure of 101,3 kpa are the STP values. Thus the number of moles occupying a particular volume at STP can be found by using the formula: where n is the number of moles, v is the volume of the gas and M v is the molar volume at STP equal to 22,4 dm 3. You must be reminded that if the quantity of the gas at STP is given in mass, the number of moles of the gas would be found by using the formula; is the number of moles, m is the given mass of the gas and M is the molar mass of the given gas. where n

4 Converting Temperature Converting from degrees Celsius to Kelvin: K = T( C) Converting from Kelvin to degrees Celsius: C = T(K) Ideal Gases In reality there is no such thing as an ideal gas. In this model we recognise the following assumptions related to the kinetic theory: Ideal gas molecules have mass but occupy no volume There are no intermolecular forces between ideal gas molecules Collisions between ideal gas molecules and the sides of the container are completely elastic. Kinetic energy is conserved in all collisions. A real gas deviates from the behaviour of an ideal gas under low temperatures and high pressures. When the pressure of a gas is very high, its particles are very close to each other and the forces of attraction between the molecules (intermolecular forces) become greater. The volume of the molecules gets closer to the volume of the gas. Under these conditions real gases change state and become liquids. An ideal gas never changes state. At low temperatures the average speed of the particles is low and the forces between the molecules increase. At low temperatures real gases liquefy. Real gases behave like an ideal gas at room temperature and pressure. The Ideal Gas Equation To arrive at the ideal gad law, Boyle s Law and Charles Law are used. From Boyle s Law we know that p α 1/V. therefore pv = k. From Charles Law; V α T. Thus V/T = k. From the molar volume formula at STP; n = V/V o where V o is the molar volume. Thus V α n. therefore V = kn. Therefore V/n = k. Combining all the three formulae above results in the following expression:. In this case, k is a special gas constant called the Universal Gas Constant with a symbol R = 8,31 J.K -1 mol -1. So the expression above can be written as pv = nrt where p = pressure in Pa V = volume (m 3 ) n = number of moles (mols) R = Universal Gas Constant (8.31 J.K -1 mol -1 ) T = Kelvin temperature (K). This is normally written as:

5 Moles and Gases Mole: amount of matter Mass n = number of moles m = mass of sample (g) M m = work out from periodic table (g.mol -1 ) Volume The volume of 1 mole of gas at STP is 22.4 dm 3 Where n = number of moles V = volume of sample of gas (dm 3 ) V m = 22.4 dm 3.mol -1 Converting: 1 dm 3 = 1000 cm 3 and 1 m 3 = 1000 dm 3 In a balanced chemical equation, the number in front of the chemical symbols describes the mole ratio of the reactants and products. Moles and Solutions Concentration The concentration of a solution refers to the number of moles of dissolved substance per dm 3 of solution. c = concentration (mol.dm -3 ) n = number of moles v = volume (dm -3 ) Moles and Reactions Mass Volume Concentration Balanced chemical equation provides the mole ratio of the reactants and products. Take the MOL ROUTE Limiting and Excess A limiting reagent is completely used up in a chemical reaction. An excess reagent is not completely used up in a chemical reaction. Percent yield is calculated using

6 Questions Question 1 A fixed amount of helium gas has a volume of 180 cm 3 at a temperature of 30 C. The pressure of the gas is then adjusted from an initial value of 100kPa to 80kPa whilst the temperature is kept constant. Calculate the volume that the gas will occupy after the adjustments have been made. Question 2 The average global temperature from 1959 to 1999 is taken as 14 C. Scientists are predicting a rising in this average global temperate of 1,4 C by 2050.The average lung capacity of a health young man is 6l. What volume will lungs need to expand to in 2050 compared to today, if the man wants to inhale the same mass of gas? Question 3 The main cause of global warming is the increase in the amount of greenhouse gases in our atmosphere. A sample of 2,5dm 3 of carbon dioxide at a pressure of 100 kpa is produced on the surface of the Earth. What volume will this gas occupy at 45km above the Earth where the temperature is assumed to be the same as on the surface of the Earth but the pressure is only 5 Pa? Question 4 A certain mass of carbon dioxide gas is sealed in a 200 cm 3 container. The gas exerts a pressure of 100 kpa on the sides of the container at a temperature of 0 o C. Calculate; a.) The number of carbon dioxide gas moles present in the container. b.) The mass of the carbon dioxide gas in the container. Question 5 What is the volume of 3 mol of N 2 gas at STP? Question 6 In making up a solution of sodium hydroxide, 17 g of NaOH is dissolved in water and the solution made up to 250cm 3. Calculate the concentration. The following figure highlights the relation between the balanced chemical equation and the number of moles

7 Question 7 (Adapted from DoE Exemplar Paper 2, 2007) Ozone (O 3 ) reacts with nitrogen monoxide gas (NO) to produce NO 2 gas. The NO gas forms largely as a result of emissions from the exhausts of motor vehicles and from certain jet planes. The NO 2 gas also contributes to the brown smog (smoke and fog), which is seen over most urban areas. This gas is also harmful to humans, as it causes breathing (respiratory) problems. The following equation indicates the reaction between ozone and nitrogen monoxide: O 3(g) + NO (g) O 2(g) + NO 2(g) In one such reaction 0,74 g of O 3 reacts with 0,67 g NO. a.) Calculate the number of moles of O 3 and of NO present at the start of the reaction. b.) Identify the limiting reagent in the reaction and justify your answer. c.) Calculate the mass of NO 2 produced from the reaction.

Comparison of Solids, Liquids, and Gases

CHAPTER 8 GASES Comparison of Solids, Liquids, and Gases The density of gases is much less than that of solids or liquids. Densities (g/ml) Solid Liquid Gas H O 0.97 0.998 0.000588 CCl 4.70.59 0.00503