21. Practice Problem (page 556) What is the volume of 5.65 mol of helium gas at a pressure of 98 kpa and a temperature of 18.0 C?
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1 Section 12.2 The Ideal Gas Law Solutions for Practice Probles Student Edition page Practice Proble (page 556) What is the volue of 5.65 ol of heliu gas at a pressure of 98 kpa and a teperature of 18.0 C? You need to find the volue, V, of heliu gas, He(g). You know the conditions of teperature and pressure: T = 18.0 C P = 98 kpa You know the aount in oles of the heliu gas: n = 5.65 ol Convert the teperature fro the Celsius scale to the Kelvin scale. kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable V. Substitute the given data into the equation and solve for V. Act on Your Strategy Teperature conversion: T 18.0C K Isolation of the variable V: P P V P Chapter 12ExploringtheGasLaws MHR 69
2 Substitution to solve for V: V P kpa 5.65 ol ol 98 kpa L L L K K The volue of the heliu gas is L. Estiate the aount in oles using rounded values: volue 140 L olar volue 6 ol 22 L /ol This estiate of the aount in oles is close to the given aount. The calculated answer sees reasonable and correctly shows two significant digits. 22. Practice Proble (page 556) Propane, C 3 H 8, is a coon gas used to supply energy for barbecue cookers as well as energy requiring appliances in cabins and cottages, and heavy equipent such as the forklift shown in the photograph below. If a tank contains kg of propane, what volue of propane gas could be supplied at 22 C and kpa? Chapter 12ExploringtheGasLaws MHR 70 You need to find the volue, V, of the propane, C 3 H 8 (g). You know the conditions of teperature and pressure: T = 22 C P = kpa You know the ass of the propane gas: = kg
3 Isolation of the variable V: P P V P Substitution to solve for V: V P kpa ol ol kpa L L L K K The volue of the propane gas that could be supplied at 22 C and kpa is L. The correct units have been used and the units of ass and teperature have been converted correctly. The large volue is consistent with the application described in the question and the ass of propane that was used. Two significant digits in the answer are consistent with the data given. 23. Practice Proble (page 556) Find the Celsius teperature of nitrogen gas if a 5.60 g saple occupies L at 3.00 at of pressure. You need to find the Celsius teperature of a saple of nitrogen gas, N 2 (g). You know the ass, volue, and pressure of the saple of nitrogen gas: = 5.60 g V = L P = 3.00 at Convert the volue of the gas fro illilitres to litres. Convert the pressure of the gas fro at to kilopascals Chapter 12ExploringtheGasLaws MHR 72
4 Deterine the olar ass of the saple of N 2 (g). Calculate the aount in oles of N 2 (g) using the relationship n. M kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable T. Substitute the given data into the equation and solve for T. Convert the teperature fro the Kelvin scale to the Celsius scale. Act on Your Strategy Volue conversion: 3 3 V L 1 10 L/ L 2.40 L Pressure conversion: kpa P 3.00 at 1.00 at kpa Molar ass, M, of N 2 (g): M 2( M ) N2 N 2(14.07 g/ol) g/ol Aount in oles, n, of N 2 (g): nn 2 M 5. 6 g g /ol ol Isolation of the variable T: nr nr T nr Chapter 12ExploringtheGasLaws MHR 73
5 Substitution to solve for T: T nr kpa 2.40 L kpa L ol ol K K Teperature conversion: T K C 166 C The teperature of the nitrogen gas is 166 C. The high pressure of 3.00 at would decrease the volue. The teperature is high and would increase the volue. The answer sees reasonable and correctly shows three significant digits. 24. Practice Proble (page 556) What is the pressure of 3.25 ol of hydrogen gas that occupies a volue of 67.5 L at a teperature of 295 K? You need to find the pressure of a saple of hydrogen gas, H 2 (g). You know the aount, volue, and teperature of the saple of hydrogen gas: n = 3.25 ol V = 67.5 L T = 295 K kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable P. Substitute the given data into the equation and solve for P Chapter 12ExploringtheGasLaws MHR 74
6 Act on Your Strategy Isolation of the variable P: V V P V Substitution to solve for P: P V kpa 3.25 ol ol 67.5 L kpa 118 kpa L K 295 K Chapter 12ExploringtheGasLaws MHR 75 The pressure of the hydrogen gas is 118 kpa. The ideal gas equation has been rearranged correctly and the variables have been substituted into the equation using the correct units. The answer sees reasonable and correctly shows three significant digits. 25. Practice Proble (page 556) A weather balloon filled with heliu gas has a volue of 960 L at 101 kpa and 25 C. What ass of heliu was required to fill the balloon? You need to find the ass of a saple of heliu gas, He(g). You know the volue, pressure, and teperature of the saple of heliu gas: V = 960 L P = 101 kpa T = 25 C Convert the teperature fro the Celsius scale to the Kelvin scale. kpa L Use the universal gas constant: R ol K
7 Use the ideal gas law: Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n. Deterine the olar ass of the He(g) using the atoic ass fro the periodic table. Calculate the ass of the He(g) using the relationship n M. Act on Your Strategy Teperature conversion: T 25C K Isolation of the variable n: n Substitution to solve for n: n 101 kpa 960 L kpa L K ol K ol Molar ass, M, of He(g): 4.00 g/ol (fro the periodic table) Mass,, of He(g): n M He ol g 160 g 4.00 g/ ol The ass of the heliu gas required to fill the balloon is 160 g Chapter 12ExploringtheGasLaws MHR 76
8 The ideal gas equation has been correctly rearranged to solve for the aount of oles. The variables are substituted correctly into the equation and the units are correct. The answer sees reasonable and correctly shows two significant digits. 26. Practice Proble (page 556) Find the olar ass of 6.24 g of an unknown gas that occupies 2.5 L at 18.3 C and kpa. You need to find the olar ass of a saple of gas. You know the volue, pressure, teperature, and ass of the saple of the gas: V = 2.5 L P = kpa T = 18.3 C = 6.24 g Convert the teperature fro the Celsius scale to the Kelvin scale. kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n. Calculate the olar ass of the gas using the relationship M. n Chapter 12ExploringtheGasLaws MHR 77 Act on Your Strategy Teperature conversion: T 18.3C K Isolation of the variable n: n
9 Substitution to solve for n: n kpa 2.5 L kpa L K ol K ol Molar ass, M, of the gas: M n 6.24 g ol g/ol g/ol The olar ass of the gas is g/ol. The ideal gas equation has been correctly rearranged to solve for the aount of oles. The variables are substituted into the equation correctly and the units are correct. The answer sees reasonable and correctly shows two significant digits. 27. Practice Proble (page 556) A scientist isolates g of a gas. The saple occupies a volue of L at 78.0 C and 103 kpa. Calculate the olar ass of the gas. Is the gas ost likely to be broine, krypton, neon, or fluorine? You need to find the olar ass of a saple of gas and deterine its possible identity. You know the volue, pressure, teperature, and ass of the saple of gas: V = L P = 103 kpa T = 78.0 C = g Chapter 12ExploringtheGasLaws MHR 78
10 Convert the teperature fro the Celsius scale to the Kelvin scale. Convert the volue to litres. kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n. Calculate the olar ass of the gas using the relationship M. n Act on Your Strategy Teperature conversion: T 78.0C K Volue conversion: 2 V L L L/ L Isolation of the variable n: n Substitution to solve for n: n 103 kpa L kpa L K ol K ol Chapter 12ExploringtheGasLaws MHR 79
11 Molar ass, M, of the gas: M n g ol g/ol 83.8 g/ol The olar ass of the gas is 83.8 g/ol. The gas is likely krypton. The ideal gas equation has been correctly rearranged to solve for the aount of oles. The variables are substituted correctly into the equation and the units are correct. The answer sees reasonable and correctly shows three significant digits. 28. Practice Proble (page 556) What is the density of carbon dioxide gas, in gras per litre, at SATP? You need to find the density of carbon dioxide gas, CO 2 (g), at SATP. You know the volue, pressure, and teperature of the carbon dioxide gas: V = L P = kpa T = K You know that density is the ass per unit volue. Calculate the olar ass of the CO 2 (g) using the atoic asses fro the periodic table. kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n. Calculate the ass of the CO 2 (g) using the relationship n M. Calculate the density of the CO 2 (g) using the relationship D. V Chapter 12ExploringtheGasLaws MHR 80
12 The ideal gas equation has been correctly rearranged to solve for the aount of oles. The variables are substituted into the equation correctly and the units are correct. The answer sees reasonable and correctly shows four significant digits. 29. Practice Proble (page 556) A hydrocarbon gas used for fuel contains the eleents carbon and hydrogen in percentages of percent and percent. Soe of the gas, 1.77 g, was trapped in a 750 L round-botto flask. The gas was collected at a teperature of 22.1 C and a pressure of 99.7 kpa. a. Deterine the epirical forula for this gas. b. Calculate the olar ass of the gas. c. Deterine the olecular forula for this gas. You need to find a. the epirical forula for the gas. b. the olar ass of the gas. c. the olecular forula for the gas. You know the teperature, pressure, volue, and ass of the gas: T = 22.1 C P = 99.7 kpa V = 750 L = 1.77 g You know that the percentage coposition of the gas is 82.66% carbon and 17.34% hydrogen. a. epirical forula for the gas Find the epirical forula using the olar asses of carbon and hydrogen and the percentage copositions. b. olar ass of the gas Convert the teperature fro the Celsius scale to the Kelvin scale. Convert the volue to litres. kpa L Use the universal gas constant: R ol K Use the ideal gas law: Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n Chapter 12ExploringtheGasLaws MHR 82
13 Calculate the olar ass of the gas using the relationship M. n c. olecular forula for the gas Copare the olar ass of the unknown gas with the olar ass of the epirical forula. Multiply the epirical forula by the ratio of the two olar asses to obtain the olecular forula. Act on Your Strategy a. epirical forula for the gas For a 100 g saple: Mass of 82.66% carbon: g = g Mass of 17.34% hydrogen: g = g Aount in oles of each eleent using the relationship For carbon (M = g/ol): nc M g g /ol ol n : M For hydrogen (M = 1.01 g/ol): nh M g 1.01 g /ol ol The siplest ole ratio between the two eleents provides the epirical forula ol of C : ol of H 1 ol of C : ol H 2 ol of C : 5 ol H The ole ratio between the carbon and the hydrogen is 2:5. The epirical forula for the gas is C 2 H Chapter 12ExploringtheGasLaws MHR 83
14 b. olar ass of the gas Teperature conversion: T 22.1C K Volue conversion: 3 V 750 L 1 10 L/ L L 0.75 L Isolation of the variable n: n Substitution to solve for n: n 99.7 kpa 0.75 L kpa L K ol K ol Molar ass, M, of the gas: M n 1.77 g ol g/ol 58 g/ol The olar ass of the unknown gas is 58 g/ol Chapter 12ExploringtheGasLaws MHR 84
15 c. olecular forula for the gas Molar ass of the unknown gas: M = 58 g/ol Molar ass, M, of the epirical forula C 2 H 5 : M 2M 5M C2H5 C H 2(12.01 g/ol) 5(1.01 g/ol) g/ol Ratio of olar asses: 58 g/ol g/ol 1 Since the ratio of the olar asses is 2:1, the olecular forula is C 2 H 5 2 = C 4 H 10. The olecular forula for the unknown gas is C 4 H 10. The siple integer ratio of the two olar asses akes the olecular forula a reasonable answer. The variables are substituted correctly into the ideal gas law equation and the units are correct. The olar ass is correctly expressed to two significant digits. 30. Practice Proble (page 556) A 10.0 g saple of an unknown liquid is vaporized at C and 5.0 at. The volue of the vapour is found to be L. The liquid is deterined to be ade up of 84.2% carbon and 15.8% hydrogen. What is the olecular forula for the liquid? You need to find the olecular forula for an unknown liquid. You know the teperature, pressure, volue, and ass of the vaporized liquid: T = C P = 5.0 at V = L = 10.0 g You also know that the percentage coposition of the liquid is 84.2% carbon and 15.8% hydrogen Chapter 12ExploringtheGasLaws MHR 85
Molar mass, M, of the empirical formula C 4 H 9 : M 4M 9M g/mol g/mol g/mol
olar ass,, of the unknown gas: n 10.00 g 0.088037 ol 113.16057 g/ ol olar ass,, of the epirical forula C 4 H 9 : 4 9 C4H9 C H 4 12.01 g/ol 9 1.01 g/ol 57.13 g/ol Ratio of olar asses: 113.16057 g/ol 1.9807
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