Answers Set A Module 5 PDF

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MODULE 5 − GASES A5.1

(a) List the physical characteristics of gases. (b) Air is 78 % nitrogen (N2), 21 % oxygen and 1 % other gases including Ar, CO2, NO, SO3, NO2, CO, and many others. (c) There are many different units of pressure in common use. (i) What are the SI units for pressure? pascals, Pa (1 Pa = 1 N m−1 = 1 kg m−1 s−2) (ii) List other common units of pressure. bar, atmospheres (atm), torr, mm Hg. (d) The total air pressure at the summit of Mt Everest is about 0.35 bar (i.e. about 1/3 of the air pressure at sea level). Calculate the air pressure at the summit of Mt Everest in units of (i) torr (ii) mm Hg (iii) Pa (iv) atm

*A5.2 (a) State in both words and as a mathematical expression (i) Boyle’s Law Volume of a gas at constant temperature is inversely proportional to its pressure. V ∝ 1/P i.e. V = k11/P (k1 is a constant) (ii) Charles’ Law Volume of a gas is directly proportional to its temperature. V ∝ T i.e. V = k2T (k2 is a constant) (iii) Avogadro’s Law Volume of a gas is directly proportional to the number of moles of a gas. (i.e. equal volumes of different gases at the same T and P have the same number of molecules. V ∝ n i.e. V = k3n (b) (i) If the initial pressure of a gas in a variable volume flask is 0.53 bar and the initial volume is 0.68 L, what is the final pressure of the gas if the volume is reduced to 0.41 L. (use P1V1 = P2V2) 0.88 bar (ii) A 36.4-L volume of methane gas (CH4) is heated from 25°C to 88°C at constant pressure. What is the final volume of the gas? (use V1/T1 = V2/T2) 44 L *A5.3 (a) What is the “ideal gas equation”? PV = nRT (b) Use words to describe the relationship between pressure, volume, number of moles and temperature for ideal gases. The product of pressure and volume is equal to the product of the number of moles of gas and the temperature multiplied by the gas constant. (c) Show that if pressure is in kPa, temperature is in Kelvin, quantity of gas is in moles and volume is in litres, then the units of the gas constant, R, are L kPa K−1 mol−1. R = PV/nT ∴ has units kPa L K−1 mol−1 (d) What are the conditions known as standard temperature and pressure? 1 bar and 0°C (273 K) (e) Calculate the volume occupied by 1 mol of an ideal gas under conditions of standard temperature and pressure. 22.7 L

*A5.4 (a) A sample of chlorine gas (Cl2) is in a container of volume 2.3 L. At a temperature of 32ºC it exerts a pressure of 4.7 bar. Calculate the number of moles of chlorine gas present. 0.43 mol (b) The Hindenburg was a hydrogen-filled dirigible that exploded in 1937. If the Hindenburg held 2.0 × 105 m3 of hydrogen gas at 23°C and 1 bar, what mass of hydrogen was present? 1.7 × 104 kg of H2 (c) Calculate the number of molecules in a deep breath of air whose volume is 2.50 L at body temperature, 37°C, and a pressure of 0.980 bar. 5.72 × 1022 molecules A5.5

Consider the apparatus shown in the drawing. (a) When the stopcock between the two containers is opened and the gases allowed to mix, how does the volume occupied by the N2 gas change? Increases from 2.0 L to 5.0 L What is the partial pressure of N2 after mixing? p(N2) = 0.41 bar (b) How does the volume of the O2 gas change when the gases mix? Increases from 3.0 L to 5.0 L What is the partial pressure of O2 in the mixture? p(O2) =1.2 bar (c) What is the total pressure in the container after the gases mix? 1.6 bar

*A5.6 (a) State Dalton’s Law in words The total pressure of a mixture gases equals the sum of the of the pressures that each gas would exert if it were present alone. (b) State Dalton’s Law using an equation using an equation (consider a flask containing 3 gases A, B and C) Ptotal = PA + PB + PC (c) A cylinder contains a mixture of two gases, Ar and He. The partial pressure of Argon is 26.3 bar and the total pressure in the cylinder is 28.2 bar. What is the partial pressure of Helium in this cylinder? 1.9 bar (d) Define mole fraction (X) in words and using an equation. a dimensionless quantity that expresses the ratio of the number of moles of one component to the number of moles of all components present (e) Calculate the mole fraction of each of the gases in (c) XAr = 0.93, XHe = 0.067 A5.7

A mixture containing 0.538 mol He(g), 0.315 mol Ne(g) and 0.103 mol Ar(g) is confined in a 7.00 L vessel at 25°C. (a) Calculate the partial pressure of each of the gases in the mixture. p(He) = 1.90 bar, p(Ne) = 1.11 bar, p(Ar) = 0.365 bar (b) Calculate the total pressure of the mixture. Ptotal = 3.38 bar

A5.8

A sample of natural gas contains 8.24 moles of methane, 0.421 mole of ethane and 0.116 mole of propane. If the total pressure of the gases is 1.37 bar, what are the partial pressures of the gases? PMe = 1.29 bar, PEt = 0. 066 bar, PPr = 0.0181 bar.

*A5.9 What change or changes in the state of a gas bring about each of the following effects? (a) The number of impacts per unit time on a given container wall increases. reduced volume or higher temperature or higher pressure (b) The average energy of impact of molecules with the wall of the container decreases. decrease in temperature (c) The average distance between gas molecules increases. increase in volume or decrease in pressure (d) The average speed of molecules in the gas mixture is increased. increase in temperature *A5.10 Vessel A contains CO(g) at 0°C and 1 bar. Vessel B contains SO2(g) at 20°C and 0.5 bar. The two vessels have the same volume. Hint: Assume 1 L vessel and find pressure for each case. (a) Which vessel contains more molecules? A (b) Which contains more mass? B (c) In which vessel is the average kinetic energy of molecules higher? B (d) In which vessel is the velocity of the molecules higher? A A5.11 (a) What is absolute zero? The lowest theoretical temperature attainable. Absolute zero = 0 K = -273.15°C (b) Describe the experimental process by which the value of absolute zero was first determined. A plot of volume versus temperature for a sample of gas at constant pressure results in a straight line relationship with an intercept on the temperature axis at -273°C. This is the temperature at which the sample of gas would have zero volume and since it is impossible for the sample to have a negative volume, -273°C is absolute zero. (c) Assuming that a sample comprising 2 kg of oxygen gas was cooled to absolute zero, what would be the volume occupied by the oxygen gas? 0 L (d) Consider your answer from (c). Is it possible to cool a sample of matter to absolute zero? No. It is not physically possible to cool the sample to absolute zero. The gas molecules must occupy some volume....