NJC 2023 Gases Tutorial Suggested Answers

National Junior College SH1 H2 Chemistry 1 The Gaseous State Discussion Questions 1 Which option has the largest volume at 25 °C and 101 kPa? A 9 g of CH4 B 12 g of H2O C 15 g of C2H6 D 20 g of CO2 At 25 °C, H2O is in liquid state and occupy smaller volume than gas Amount of CH4 = 0.563 mol Amount of C2H6 = 0.5 mol Amount of CO2 = 0.455 mol From the Ideal Gas Equation: pV = nRT, we have V ∝ n. Hence CH4 would have the largest volume 2 2.5 dm3 of methane, CH4, at a pressure of 1.50 atm and 4.5 dm 3 of ethane, C 2H6, at a pressure of 1.00 atm were introduced into a 3.0 dm3 vessel at constant temperature. What is the final pressure of the gas mixture? A 0.825 atm B 2.50 atm C 2.75 atm D 3.57 atm For methane: p1 V1 = p2 V2 (1.50)(2.5) = (pmethane)(3.0) pmethane =1.25 atm For ethane: p1 V1 = p2 V2 (1.0)(4.5) = (pethane)(3.0) pethane =1.5 atm ptotal = pmethane + pethane = 1.25 + 1.5 = 2.75 atm 3 Which graph is not a correct description of the behaviour of a fixed mass of an ideal gas? (Note: T is measured in Kelvin scale.) A B C D From the Ideal Gas Equation: pV = nRT, we have pV ∝ T (when n is constant). With increasing T, the value of pV should increase proportionally. Hence graph B and D are correct. So the value of pV remains constant with constant T, hence a horizontal line for graph A is correct. This also means a horizontal line for graph C should be expected instead. pV 1/p 0 constant T pV T 0 constant V pV V 0 constant T pV T 0 constant p

National Junior College SH1 H2 Chemistry 2 4 A vessel contained a gas mixture of nitrogen and oxygen at 30 C and a pressure of 200 kPa. After all the oxygen has reacted with zinc, the total pressure in the vessel was 150 kPa at 30 C. 2 Zn (s) + O2 (g) → 2 ZnO (s) What was the molar ratio of nitrogen to oxygen in the mixture initially? A 1 : 3 B 2 : 3 C 3 : 1 D 3 : 2 After the reaction has occurred, only N2 is left in the vessel. So pnitrogen = 150 kPa ptotal = pnitrogen + poxygen = 200 kPa So poxygen = 50 kPa Since p ∝  at constant temperature , nnitrogen noxygen = pnitrogen poxygen = 150 50 = 3 1 5 A container contains 1 dm3 of gas X and 1 dm3 of gas Y at s.t.p. Both X and Y behave as ideal gases and the relative molecular mass of X is 4 times that of Y. Which statement is true? A The amount of gas X is 4 times that of Y. B The partial pressure of each gas is 50 kPa. C The total pressure of the system will decrease when 1 mole of Ne is pumped into the container. D The volume of the container doubles when the temperature of the system increases from 20 C to 40 C under constant pressure. Statement A is false. At s.t.p, amount of gas ∝ volume of gas, both gases have the same amount of gas particles. Statement C is false. An increase in the amount of gases at constant volume, should result in an increase in total pressure. Statement D is false. Under constant pressure, V2 T2 = V1 T1 V2 40 + 273 = V1 20 + 273 V2= 313 293 V1 Statement B is true. With same gas volume for A and B at s.t.p, there is equal amount of gas A and B. Since ptotal = pA + pB = 1 bar (105 Pa) @ s.t.p and p ∝  , pA = pB = ½ (100 kPa) = 50 kPa

National Junior College SH1 H2 Chemistry 3 6 When magnesium powder reacts with dilute hydrochloric acid, hydrogen gas is evolved. How would the volume of the hydrogen gas be affected by temperature and pressure? A It increases with increase in temperature and is independent of pressure. B It decreases with increase in temperature and is independent of pressure. C It increases with increase in both temperature and pressure. D It increases with increase in temperature and decreases with increase in pressure. From the Ideal Gas Equation: pV = RT, we have V∝ 1 p and V∝T (for a given amount of gas) 7 Which expression gives the pressure exerted by 1.6 × 10−3 mol of N 2 in a container of volume 3.0 dm3 at 273 C? A 1.6 × 10–3 × 8.31 × 273 3.0 × 10–6 Pa B 1.6 × 10–3 × 8.31 × (273 + 273) 3.0 × 10–6 Pa C 1.6 × 10–3 × 8.31 × 273 3.0 × 10–3 Pa D 1.6 × 10–3 × 8.31 × (273 + 273) 3.0 × 10–3 Pa From the Ideal Gas Equation: pV = RT, We have p = ηRT V and the units of V and T must be converted to SI units. 8 Flask A contains 1 dm 3 of helium at 2 kPa pressure and flask B contains 2 dm 3 of neon at 1 kPa pressure. If the flasks are connected at constant temperature, what is the final pressure (in kPa)? A 1 1 3 B 1 1 2 C 1 2 3 D 2 For He: p1 V1 = p2 V2 (2)(1) = (pHe)(3) pHe =2/3 kPa For Ne: p1 V1 = p2 V2 (1)(2) = (pNe)(3) pNe =2/3 kPa ptotal = pHe + pNe = 2/3 + 2/3 = 1 1/3 kPa

National Junior College SH1 H2 Chemistry 4 9 Which set of changes will have the greatest effect on the density of a fixed mass of an ideal gas? Pressure Temperature / K A double halve B double double C halve halve D halve constant From the Ideal Gas Equation: pV = RT, We have  = pM RT, thus when pressure is doubled and temperature is halved, the density of the gas will quadruple. 10 Which statements are correct? 1 The density of an ideal gas at constant pressure is inversely proportional to the temperature. 2 One of the assumptions of the kinetic theory of gases is that gaseous particles are separated by distances which are large compared with their dimensions. 3 Real gases behave most nearly as an ideal gas at high pressures and low temperatures. A 1, 2 and 3 are correct B 1 and 2 only are correct C 2 and 3 only are correct D 1 only is correct From the Ideal Gas Equation, we have  = pM RT. So statement 1 is true. An ideal gas has gaseous particles with negligible volumes compared to the volume of container. Thus the gas particles are far apart. So statement 2 is true. Real gases behave least as an ideal gas at high pressures and low temperatures. At high pressure , the gas particles are very close together that there are significant intermolecular forces of attractions & significant volume occupied by the gas particles. At low temperature, the gas particles have low KE to overcome intermolecular forces of attractions between them. Hence Statement 3 is wrong.

National Junior College SH1 H2 Chemistry 5 11 Which graphs show the ideal behavior of a gas? 1 2 3 A 1, 2 and 3 are correct B 1 and 2 only are correct C 2 and 3 only are correct D 1 only is correct From the Ideal Gas Equation: pV = RT, (for a given amount of gas) Graph 1 and 2 show the correct pressure – volume relationship, p ∝ 1 V. At a particular volume, p ∝ T. This is correctly shown in both graphs 1 and 2. Graph 3 shows the correct volume – temperature relationship, V ∝ T. At a particular temperature, Vol ∝ 1 p . This is incorrectly shown, gradient should be smaller at P1 12 Two moles of oxygen and one mole of argon are contained in a cylinder with a volume of 10.0 dm3 at 298 K. Calculate the total pressure and partial pressure of oxygen. ptotal (10.0 × 10−3) = (2+1)(8.31)(298) ptotal = 742 kPa pO2 = ( 2 3)(742) = 495 kPa 1