CHEM110 Worksheet - Gases Chem 110 General Principles of Chemistry Chapter 9 Gases (pages 337-373) In this chapter we - first contrast gases with liquids and solids and then discuss gas pressure. - review the mass laws, which describe the gas behaviour. - examine the ideal gas law, which encompasses the other mass laws, and apply it to reaction stoichiometry. - find that real gas behaviour, especially under extreme conditions, requires refinements of the gas law and the model. LEARNING OBJECTIVES In this chapter, you should keep in mind the following goals. 1. You must be able to contrast gases with liquids and solids and know the properties that affect how gases behave. 2. You must know the concept of pressure, it s various units of measurement, how it is measured and be able to carry out calculations involving pressure. 3. Go through Sample Exercise 9.1. 4. You must know the gas laws: Boyles law, Charles s law and understand how pressure, temperature and volume are related and affect each other and be able to carry out calculations involving these laws. 5. You must know the conditions for standard temperature and pressure of gases. 6. You must know Avogadro s law and be able to carry out calculations involving this law. 7. You must know and understand the Ideal and General gas equations and be able to carry out appropriate calculations using these equations. 8. Go through Sample Exercises 9.3 to 9.5 including the Practice Exercises for these problems. 1
9. You must be able to apply the ideal gas equation to determine molar mass and gas densities. 10. Go through Sample Exercises 9.6 and 9.7 including the Practice Exercises for both these problems. 11. You must be able to carry out calculations in gas chemical reactions and apply the law of combining volumes. 12. Go through Sample Exercise 9.8 including the Practice Exercise. 13. You must understand how gases behave when they mix together, Dalton s law of partial pressures and the concept of mole fraction. 14. You must be able to carry out calculations involving these concepts. 15. Go through Sample Exercises 9.9 and 9.10 including the Practice Exercises for each of these problems. 16. You must understand how real gases differ from ideal gases and be able to carry out calculations using the van der Waals equation. 17. Go though Example Sample Exercises 9.15 including the Practice Exercise. Terms: kinetic theory of gases (see glossary at the back of the book) atmospheric pressure pascal (pa) barometric pressure manometer standard atmosphere (atm) manometer, closed end torr manometer, open end absolute zero Volume-Pressure law (Boyle s Law) Volume temperature (Charles's Law) Volume no. of particles Avogadros Principle Ideal Gas combined gas law Ideal Gas Law (equation of state of an ideal gas) Standard temperature and pressure (STP) Standard Molar Volume Universal Gas Constant, R Partial pressure Dalton s Law of partial pressure Vapour pressure 2
Difference between gases, liquids and solids. (page 338) The volume of a gas can be altered significantly by changing the applied external force or the temperature. The corresponding volume changes for liquids and solids are much smaller. Gases flow more freely and have lower densities than either liquids or solids, and they mix in any proportion to form solutions. Of the four important variables of a sample of a gas-pressure, volume, temperature, and mass (or moles) cannot be changed without changing one or more of the others. Liquids or solid samples do not display this feature. You will study how P, V, T, and n are interrelated by the gas laws. Pressure (page 339) - Gases exert pressure (force/area) on all surfaces with which they make contact. - A barometer measures atmospheric pressure in terms of height of the mercury column that the atmosphere can support. (760 mmhg at sea level and o C). - Both closed end and open end manometers are used to measure the pressure of a gas sample. - Chemists measure pressure in units of atmospheres (atm), torr (equivalent to mmhg) or pascals (Pa - the SI unit). Conversion between the different units of pressure 1 atm = 760 mmhg = 760 torr = 101 325 Pa 3
THE GAS LAWS (page 341) Four variables define the physical behaviour of an ideal gas: Volume (V), pressure (P) temperature (T) and amount (number of moles n). Most simple gases display nearly ideal behaviour at ordinary temperatures and pressures. Pressure-Volume-Temperature Relationships for a Fixed Amount of Gas Boyle's Law (pressure-volume law) Gases generally obey the rule that their volumes are inversely proportional to their pressures, provided that the temperature and the amount of gas are kept constant. 1 V α (constant T and n) P The hypothetical gas that would obey this relationship exactly is called an ideal gas. Charles's Law (temperature-volume law) Provided we express the temperature of a gas in kelvins, the volume of a fixed amount of gas is directly proportional to the temperature if the pressure is kept constant. V α T (constant P and n) Gay-Lussac's Law (pressure-temperature law) Provided that the volume is held constant, the pressure of a fixed quantity of gas is directly proportional to its kelvin temperature. P α T (constant V and n) Combined Gas Law. For a fixed mass of gas the combined gas law tells us that PV 1 T 1 1 P2V = T 2 2 4
When P 1 = P 2, the equation reduces to that of Charles's Law (the temperature-volume law). T 1 = T 2, the combined gas law equation expresses Boyle's Law (the pressure-volume law). V 1 = V 2, the combined gas law equation reduces to Gay-Lussac's Law (the pressure - temperature law). Avogadro s Law The volume of a gas is directly proportional to the amount of substance at constant pressure and temperature. (Equal volumes of gases, at constant temperature and pressure, contain the same number of particles). Standard temperature and pressure (STP) Standard temperature is zero degrees Celsius or 273 K (kelvin). Standard pressure is 1 atm or 101.325 kpa (kilopascals) A mole of ANY gas at standard temperature and pressure (STP) occupies 22.14 L. This is one of the ways that the moles of a gas are linked to its volume. If the quantity of gas is expressed in terms of grams then Moles of gas = mass of gas in grams molar mass in g / mol Similarly If the quantity of gas is expressed in terms of volume then Moles of gas = 3 Volume of gas in dm at STP 3 Volume of 1 mol of gas in dm at STP 3 Volume of gas in dm at STP i.e. Moles of gas = 3 22.14 dm / mol of gas at STP obviously volume of a gas (in L) at STP = moles of gas 22.14 L mol -1 It follows from the above that equal volumes of gases at the same temperature and pressure have the same number of molecules. 5
THE IDEAL GAS EQUATION (page 344) Ideal Gas Law A summary of the three gas law described above is represented below: V P 1 α (Boyles law - n, T constant) V α T (Charles law - n, P constant) V α n (Avogadros law - P,T constant) Combining the three gas laws above gives the relationship V or nt α P V = expresses an equality which when rearranged gives rise to PV = nrt The ideal gas law incorporates the individual gas laws into one equation PV = nrt, where R is the universal gas constant, P is the pressure of the gas (appropriate units); V is the volume of the gas n is the number of moles of gas, T is the kelvin temperature of the gas, and R is the "universal gas constant". Use the gas constant R = 0.08206 atm. L mol -1 K -1 when pressure is expressed in atm and volume is expressed in L (litres). The equation above can be expressed as PV moles (n) = RT which can be used to calculate the moles of gas at STP or non STP conditions. 6
Application of the Ideal Gas Equation (Page 349) Density and Molar mass of a gas The ideal gas equation can be rearranged to calculate the density and molar mass of a gas. In a mixture of gases, each component contributes its own partial pressure to the total pressure Remember moles = mass molar mass therefore the ideal gas equation becomes mass molar mass = PV RT rearranging the equation in terms of density mass volume = P x molar mass RT mass note that volume = density density = P x molar mass RT rearranging the equation in terms of molar mass molar mass = density x RT P Note that R is a constant and that the variables of pressure, temperature and density of a gas can be measured in the laboratory. It is thus possible to measure the molar mass of an unknown gas in this way this information is useful for empirical formula calculations. 7
VOLUMES OF GASES IN CHEMICAL REACTIONS (page 351). By expressing the amount (mol) of gaseous reactant or product in terms of the other gas variables. We can solve stoichiometric problems for reactions involving gases. Stoichiometry and Gas Volume Remember that the requirements of a stoichiometry problem are: There must be a balanced equation to represent the reaction that occurs. You must know the amount of one material and you are asked to calculate the amount of another material in the same equation. The principles are the same as that applied in earlier calculations except that we find moles of a gas by using the ideal gas equation GAS MIXTURES AND PARTIAL PRESSURES (page 352) Dalton's Law of Partial Pressures This law specifies that the total pressure of a mixture of gases is the sum of the partial pressures of the individual gases in the mixture P total = P A + P B + P C +.. Where A, B and C are gases This law is useful for calculations that involve the collection of gases over water and as a result have water vapour as one of the gases present. P dry gas = P total - P water The partial pressure of water vapor when it is in the presence of liquid water is called the vapour pressure of the liquid water. It depends only on the temperature of the water. All liquids, including water, have their own vapour pressures. For any given liquid the value of its vapor pressure increases with increasing temperature. 8
The partial pressure of any gas (A) in the mixture is that fraction of the total pressure that equals the mole fraction of the gas (X A ). The mole fraction of any one gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of all gases. P A = X A x P total REAL GASES (NON IDEAL) (Page 362) At very high pressures or low temperatures all gases deviate from ideal gas behaviour. As pressure increases, most real gases exhibit first a lower and then a higher PV/RT ratio then the value for the same amount (1 mol) of an ideal gas. These deviations are due to attraction between molecules, which lower the pressure and the ratio) and to the larger fraction of the container volume occupied by the molecules, which increase the ratio. By including parameters characteristic of each gases, the van der Waals equation corrects these deviations. NOTE: To simplify the theoretical treatment and its calculation, those who first postulated the kinetic theory simply ignored the fact that gas particles themselves do occupy some space and they assumed that ideal gas particles exert no forces on each other. For most practical purposes, these assumptions work very well, and we can use the ideal gas law (PV = nrt) in most ordinary situations, especially when the gas is at a relatively low pressure and relatively high temperature. To correct for the real volume of just the gas particles, van der Waals subtracted a term, nb (where n moles and b = a correction factor that differs for each gas), from the measured volume of the gas. In other words, he substituted the term (V - nb) for V in the ideal gas law. To correct for the real forces of attraction between gas particles, van der Waals added the term n 2 a/v 2 (where n = moles, a = a correction factor that is different for each gas, and V = volume) to the measured pressure of the gas. In other words, he 9
substituted the expression (P + n 2 a/v 2 ) for P in the ideal gas law. The final equation is called the van der Waals' equation of state: Problems from your textbook: Chapter 9, Pages 369-372 Nos: 9.11, 9.17, 9.24, 9.26, 9.32, 9.35, 9.39, 9.42, 9.60. Questions on gases from past exam papers. Multiple Choice Questions 1.A pressure of 3.00 atm is the same as a pressure of torr. A) 253 B) 33.7 C) 2280 D) 33775 (1) 2. Which one of the following statements about gases is FALSE? A) Gases are highly compressible. B) Distances between molecules of gas are very large compared to bond distances within molecules. C) Gases expand spontaneously to fill the container they are placed in. D) All gases are colorless and odourless at room temperature. (1) 10
3. Which statement about ideal behavior of gases is FALSE? A) At low densities all gases have similar properties. B) Gas ideality assumes that there are no interactions between gas particles. C) All particles in the ideal gas behave independently of each other. D) Low pressures and high temperatures typically cause deviations from the ideal gas behavior. (1) 4. The van der Waals equation for real gases recognizes that: A) gas particles have non-zero volumes and interact with each other. B) the non-zero volumes of gas particles effectively decrease the amount of "empty space" between them. C) the molecular attractions between particles of gas decreases the pressure exerted by the gas. D) all of the above statements are true. (1) 5. i) What is the density, in g L -1, of a sample of Cl 2 gas at 1124 torr and 24.0 C? (Note: The molar mass of Cl 2 is 70.90 g mol -1 ). (2) ii) What is the mass of Cl 2, in grams, if the volume is 9.22 L? (1) 6. Ammonium sulfate is prepared by reacting ammonia with sulfuric acid as shown in the following reaction, 2NH 3 (g) + H 2 SO 4 (aq) (NH 4 ) 2 SO 4 (aq) If 1774 moles of NH 3 reacts with sulfuric acid at 315.15 K and 15.6 atm, calculate the volume of ammonia required for this reaction in litres. (1) 11
Molar mass of LiOH = 24.0 g mol -1 (5) 7.1 Calculate the volume, in ml, of hydrogen collected over water at 18 0 C and 725 mmhg when 0.840 g of lithium reacts with water? The equation for the reaction is: 2Li(s) + 2H 2 O(l) H 2 (g) + 2LiOH(aq) 7.2 Calculate the density, in g L -1, of H 2 gas at STP. (2) 12
Tools you have learned Tool Combined Gas Law Ideal Gas Law Dalton's law of partial pressures) Function To be used to calculate a particular value of P, V, or T given other values and the quantity of gas as fixed. To be used in applications of Boyle's, Charles' or Gay- Lussac's law To be used when any three of the four variables of the physical state of a gas, P, V, T, or n, are known to calculate the value of the fourth. To calculate the partial pressure of one gas in a mixture of gases from the total pressure and either the partial pressures of the other gases or their mole fractions Given the volume and temperature of a gas collected over water and the atmospheric pressure, to calculate the volume the gas would have when dry Mole fractions To calculate the mole fraction or mole percent of one component of a mixture from other data about the mixture. To calculate the partial pressure of one gas in a mixture from its mole fraction. Deviations from Ideal Behaviour To calculate pressure and volume of a gas Taking into consideration intermolecular forces of attraction and actual gas volumes. 13
Gas equation for real gases 14