# Force. Pressure = ; Area. Force = Mass times Acceleration;

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1 Force Pressure = ; Area Force = Mass times Acceleration; If mass = kg, and acceleration = m/s 2, Force = kg.m/s 2 = Newton (N) If Area = m 2, Pressure = (kg.m/s 2 )/m 2 = N/m 2 = Pascal; (1 Pa = 1 N/m 2 ) Gas Pressure: 1 atm = 760 torr (mmhg) = psi = kpa = x 10 5 Pa Ideal Gas Equation: PV = nrt; R = L.atm/(mol.K) Exercises #1: 1. A person with a mass of 70.0 kg stands squarely on ice in the ice-skating ring. The person is wearing a pair of sneakers with a flat sole and a total surface area of 3.6 x 10-1 m 2. (a) Calculate the pressure exerted on the ice surface by that person? (b) What is this pressure in atmospheres (atm) and in torr? (The acceleration due to gravitational pull is 9.80 m/s 2 ) (Answer: P = 1910 Pa = atm = 14.3 torr) 2. If the same person is wearing a pair of ice-skating shoes in which the total contact area of the shoe blades is 4.5 x 10-3 m 2, what is the pressure exerted by the blades on the ice surface? (b) Express this pressure in atmospheres (atm) and in torr? (Answer: P = 1.52 x 10 5 Pa = 1.50 atm = 1.14 x 10 3 torr) Boyle s Law 3. A 2.50 m 3 of dry air, initially at 1.00 atm, is pumped into a rigid 50.0-L steel tank at constant temperature. What is the final air pressure in the tank? (Answer: 50.0 atm) 4. How many cubic meters of dry air, initially at 1.00 atm, must be pumped into a 50.0-L steel tank at constant temperature so that its final pressure in the tank is 136 atm? (Answer: 6.80 m 3 ) Charles s Law 5. A sample of water vapor has a volume of 25.0 ml at 20 o C and 1.00 atm pressure. What is the volume of the vapor at 100 o C and 1.00 atm? (Answer: 31.8 ml) 6. An aerosol spray can contains residual gas at 1.05 atm and 20 o C. The can is placed in the oven with the temperature set at 325 o F. Assuming that the volume remains constant, calculate the final pressure of the gas at 325 o F? (Answer: 1.56 atm) 1

2 Avogadro s Law 7. If 0.15 mole of a gas sample has a volume of 3.61 L at 20 o C and 1.00 atm, what is the molar volume of the gas under the same temperature and pressure? (Answer: 24.1 L) 8. A 0.15 mole sample of N 2 gas in a 3.4-L flask has a pressure of 1.00 atm at 5.0 o C. What pressure will 0.50 mole of N 2 gas exert at the same temperature? (Assume the volume remains constant) (Answer: 11 atm) Combined Boyle-Charles Law for Ideal Gas 9. The molar volume of ideal gas at STP is L/mol. What is the molar volume of ideal gas at 25 o C if the gas pressure is 605 torr? (Answer: 30.7 L) 10. A sample of helium gas has a volume of 5.60 L at STP. (a) What is the gas volume at 25 o C and 238 torr? (b) What is the gas volume at 25 o C and 4.00 atm? (Answer: (a) 16.2 L; (b) 1.53 L) Dalton s Law of Partial Pressure: The total pressure of a gas mixture is equal to the sum of the partial pressure of individual gas in the mixture; P total = P A + P B + P C + + P i ; 11. A 25.0-L tank contains 295 g N 2, 135 g O 2, and 24.0 He gases. Calculate the partial pressure of each gas and the total gas pressure at 20.0 o C. (Answer: P N2 = 10.1 atm; P O2 = 4.06 atm; P He = 5.77 atm; P total = 19.9 atm) 12. A 5.0-gallon gas tank contains N 2 and H 2 gas, such that the partial pressure of H 2 is three times that of N 2 gas. If the total pressure is 2.4 atm at 25 o C, calculate the mass, in grams, of each N 2 and H 2? (Answer: 13 g of N 2 and 2.8 g of H 2 ) 2

3 Molar Mass and Density of Gaseous Compounds PM Gas Density, d = ; RT (P = pressure in atm; M = molar mass in g/mol; R = L.atm/(mol.K) Mass Density = Volume ; Mass of gas = mole x Molar mass = nm (M = molar mass) Density (d) = nm ; but mole (n) = PV/RT; Then, d = (PV/RT)M = PM/RT V V PM So, gas density can be expressed by the formula, d = ; and M = RT P Gas density increases as the pressure and/or molar mass increase, but decreases as the temperature increases. The molar mass of a gaseous substance can be calculated from its density measured at a given temperature and pressure. drt Exercises #2: 1. The ideal gas constant is R = L.atm/(mol.K). What are the values of R in units: (a) L.torr/(mol.K) ; (b) ml.torr/mol.k, and (c) ml.atm/mol.k, respectively? (Answer: (a) L.torr/(mol.K); (b) x 10 4 ml.torr/mol.k; (c) ml.atm/mol.k) 2. Assume that the molar mass of dry air is 29.0 g/mol. (a) What is the density of air at STP? (b) What is the density of air at 25 o C and 605 torr? (Answer: (a) 1.29 g/l; (b) g/l) 3. (a) What is the density of sulfur hexafluoride (SF 6 ) gas at STP? (b) What is the density of the gas at 25 o C and 1.00 atm? (Answer: density of SF 6 = 6.52 g/l at STP and 5.97 g/l at 25 o C) 4. A gaseous CFC compound has a density of g/l at 1.00 atm and 22.0 o C. (a) Calculate the molar mass of the compound. (b) If the compound is composed of 18.06% C, 28.59% F, and 53.35% Cl, by mass, determine the molecular formula of the compound. (CFC = chlorofluorocarbon) (Answer: (a) molar mass = 133 g/mol; (b) molecular formula = C 2 Cl 2 F 2 ) 5. (a) How many grams of methane gas (CH 4 ) will occupy a volume of 12.0 gallons at STP? (b) How many grams will occupy 12.0 gallons at 25 o C and 4.0 atm? (R = L.atm / mol.k ) (Answer: (a) 32.5 g; (b) 119 g) 6. A 50.0-L tank contains 6.80 kg of propane gas (C 3 H 8 ; molar mass = g/mol). What is the gas pressure (in atm) at 20.0 o C? (R = L.atm / mol.k ) (Answer: 74.2 atm) 3

4 Exercises #3: Stoichiometry Involving Gaseous Reactants or Products. 1. Zinc metal reacts with dilute hydrochloric acid to produce hydrogen gas according to the following equation: Zn(s) + H 2 SO 4 (aq) ZnSO 4 (aq) + H 2 (g); (a) How many milliliters (ml) of hydrogen gas, measured at STP, are produced if 1.00 g of zinc is completely reacted with excess H 2 SO 4? (b) How many ml of H 2 are produced if the gas is measured at 20.0 o C and torr? (Answer: (a) 343 ml at STP; (b) 383 ml at 20 o C and torr) 2. Hydrogen gas produced by the reaction of magnesium and with hydrochloric acid is collected over water at 25 o C. (a) Write a balanced equation for the reaction. (b) If 88.5 ml of H 2 were collected and the total pressure of H 2 and water vapor was torr, and the water vapor pressure at 25 o C is 23.8 torr, calculate the amount (in mol) of H 2 gas collected and the mass of magnesium reacted. (Answer: (b) mole of H 2 = 3.52 x 10-3 mol; mass of Mg = g) 3. Sodium azide (NaN 3 ) decomposes when ignited according to the following equation: 2NaN 3 (s) 2 Na(s) + 3N 2 (g) How many grams of sodium azide should decompose to produce enough nitrogen gas to fill a 45.0-L airbag at 30 o C and 805 torr? (Answer: 83.1 g of NaN 3 ) 4. Potassium chlorate, KClO 3, decomposes when heated to produce O 2 gas according to the following equation: 2KClO 3 (s) 2KCl(s) + 3 O 2 (g) A 1.20-g mixture of potassium chlorate and potassium chloride (KCl) is placed in a test-tube fitted with stopper that has rubber tubing that would allow O 2 gas produced by KClO 3 to flow into a graduated gas jar. (a) If 240. ml of O 2 was collected at 24 o C and atm, how many moles of O 2 were produced? (b) How many percent (by mass) of the mixture is KClO 3? (R = L.atm / mol.k ) (Answer: (a) 9.57 x 10 3 mol of O 2 ; (b) % of KClO 3 = 65.2%) 5. A reactor with an internal capacity of 42.0 gallons is charged with N 2 and H 2 gases which pressures are 75.0 atm and 145 atm, respectively, at 200. o C. The two gases are allowed to react according to the following equation until the limiting reactant is completely consumed. N 2 (g) + 3H 2 (g) 2NH 3 (g) How many grams of NH 3 are produced if the yield is: (a) 100%; (b) 67.0% (Answer: (a) 6.74 x 10 3 g of NH 3 ; (b) 4.52 x 10 3 g of NH 3 ) 4

5 Kinetic Molecular Theory, Root-Mean-Square Speed, and Rate of Gas Diffusion The root-mean-square speed of gas molecules at temperature T is given by the following expression: u rms = (3RT/M) (where, R = J/(mol.K) and the molar mass M is in kg/mol. (J = kg.m 2 /s 2 ). ) Exercises #4: 1. A 5.0-L flask contains a mixture of nitrogen and hydrogen gas, such that the molar quantity of H 2 is twice that of N 2 and the temperature of the gases is 22.0 o C. Assume no reaction has taken place, which gas (N 2 or H 2 ) has: (i) the greater partial pressure; (ii) the greater root-mean-square speed (u rms ); (iii) the higher rate of diffusion; (iv) the higher average molecular kinetic energy, and (v) the higher frequency of collisions with the container walls? 2. (a) At a given temperature, which gas has the higher average molecular kinetic energy? Which gas molecule, H 2 or O 2, has the greater molecular velocity? (b) Calculate the root-mean-square speed of H 2 and O 2 molecules, respectively, at STP. (c) Which gas will effuse at a higher rate? (Answer: (b) u rms (H 2 ) = 1840 m/s; u rms (O 2 ) = 460 m/s) 3. The effusion rate of a gaseous compound at a certain temperature and pressure is 25.0 ml/min. Under the same conditions, the diffusion rate of N 2 is 57.1 ml/min. (a) Calculate the molar mass of the unknown compound. (b) If the compound is composed of 21.95% S and 78.05% F, by mass, what is the empirical formula of the compound? (Answer: (a) 146 g/mol; (b) SF 6 ) Exercises #5: Real Gases 1. Explain why real gases deviate from ideal behavior? 2. Which gas has a larger deviation from ideal behavior under identical conditions, N 2 or Cl 2? Explain your reasoning. 3. Under which conditions N 2 gas deviate greatly from ideal behavior: (a) higher temperature or low temperature? (b) higher pressure or low pressure? Give an explanation for each response. 4. If mole of ideal gas were confined to L at 0.0 o C, it would exert a pressure of atm (760.0 torr). Use the van der Waals equation and constants for N 2 and Cl 2 to estimate the pressure exerted by mole of each gas in L at 0.0 o C. (N 2 : a = 1.39 L 2 -atm/mol 2, b = L/mol; Cl 2 : a = 6.49 L 2 -atm/mol 2, b = L/mol) (Answer: P N2 = atm; P Cl2 = atm) 5

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