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 2 57.13 g/ol 1 1 Since the ratio of the olar asses is 2:1, the olecular forula of the unknown liquid is C 4 H 9 2 = C 8 H 18. 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. Section 12.2 The Ideal Gas Law Solutions for ractice robles Student Edition page 560 31. ractice roble (page 560) What volue of hydrogen gas will be produced at 93.0 ka and 23 C fro the reaction of 33 g of agnesiu with hydrochloric acid? You need to find the volue of gas that is produced when agnesiu reacts with hydrochloric acid under specific teperature and pressure conditions. You know that the reactants are hydrochloric acid, HCl(aq), and agnesiu, g(s). You known that the products are agnesiu chloride, gcl 2 (aq), and hydrogen gas, H 2 (g). 9780071051071Chapter 12ExploringtheGasLaws HR 88
You know the ass of the agnesiu: = 33 g You know the teperature and pressure: T = 23 C = 93.0 ka lan Your Strategy Write the balanced equation for the cheical reaction. Convert the ass of agnesiu to gras. Deterine the olar ass of agnesiu using the atoic ass fro the periodic table. Calculate the aount in oles of agnesiu using the relationshipn. Use the aount in oles and the ole ratio fro the balanced cheical equation to calculate the aount in oles of H 2 (g) produced. Convert the teperature fro the Celsius scale to the Kelvin scale. ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law:v Rearrange the equation to isolate the variable V. Substitute the given data into the equation and solve for V H 2. Act on Your Strategy Balanced cheical equation: g(s) + 2HCl(aq) gcl 2 (aq) + H 2 (g) ole ratio: 1 ole 2 oles 1 ole 1 ole ass conversion: ass,, of g(s): 33 g 1 10 g/ g g 0.033 g olar ass,, of agnesiu: 24.31 g/ol (fro the periodic table) Aount in oles, n, of g(s): ng 0.033 g 24.31 g /ol 0.0013574 ol 9780071051071Chapter 12ExploringtheGasLaws HR 89
Aount in oles, n, of H 2 (g): 1 ol H n 2 H2 1 ol g 0.0013574 ol g n H2 1 ol H 2 0.0013574 ol g 1 ol g 0.0013574 ol Teperature conversion: T 23C 273.15 296.15 K Isolation of variable V: V V V Substitution to solve for V H 2 : VH 2 ka 0.0013574 ol 8.314 ol 93.0 ka 0.035937 L 0.036 L L K 296.15 K The volue of hydrogen that will be produced is 0.036 L. The sall volue of hydrogen gas produced sees reasonable given the ole ratio in the balanced cheical equation and the sall ass of agnesiu that reacted. The answer correctly shows two significant digits. 9780071051071Chapter 12ExploringtheGasLaws HR 90
The balanced cheical equation indicates that there should be twice as uch HCl(g) produced as either reactant. There is alost an equal aount of each reactant and the volue of HCl(g) is expected to be about 16 L. The answer correctly shows two significant digits. 33. ractice roble (page 560) Deterine the volue of nitrogen gas produced when 120 g of sodiu azide, NaN 3 (s), decoposes at 27 C and 100.5 ka. Sodiu etal is the other product. You need to find the volue of nitrogen that is produced when sodiu azide decoposes. You know that the reactant is sodiu azide, NaN 3 (s). You know that the products are sodiu, Na(s), and nitrogen gas, N 2 (g). You know the ass of the NaN 3 (s): = 120 g You know the teperature and pressure: T = 27 C = 100.5 ka lan Your Strategy Write the balanced equation for the cheical reaction. Deterine the olar ass of NaN 3 (s). Calculate the aount in oles of NaN 3 (s) using the relationship n. Use the aount in oles of NaN 3 (s) and the ole ratio fro the balanced cheical equation to calculate the aount in oles of N 2 (g) produced. Convert the teperature fro the Celsius scale to the Kelvin scale. ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law: V Rearrange the equation to isolate the variable V. Substitute the given data into the equation and solve forv. Act on Your Strategy Balanced cheical equation: 2NaN 3 (s) 2Na(s) + 3N 2 (g) ole ratio: 2 oles 2 oles 3 oles N 2 9780071051071Chapter 12ExploringtheGasLaws HR 95
olar ass,, of NaN 3 (s): 1 3 NaN3 Na N 1(22.99 g/ol) 3(14.01 g/ol) 65.02 g/ol Aount in oles, n, of NaN 3 (s): nnan 3 120 g 65.02 g /ol 1.845585 ol Aount in oles, n, of N 2 (g): 3 ol N n 2 N2 2 ol NaN 1.845585 ol NaN n N2 3 3 3 ol N 1.845585 ol NaN 2 ol NaN 3 2.76837 ol Teperature conversion: T 27C 273.15 300.15 K Isolation of the variable V: V V V 2 3 9780071051071Chapter 12ExploringtheGasLaws HR 96
Substitution to solve forv : V N 2 N 2 ka 2.76837 ol 8.314 ol 100.5 ka 68.739511 L 69 L L K 300.15 K The volue of nitrogen gas produced is 69 L. The volue of nitrogen gas produced sees reasonable given the ole ratio in the balanced cheical equation and the ass of sodiu azide that reacted. The answer correctly shows two significant digits. 34. ractice roble (page 560) When calciu carbonate, CaCO 3 (s), is heated, it decoposes to for calciu oxide, CaO(s), and carbon dioxide gas. How any litres of carbon dioxide will be produced at ST if 2.38 kg of calciu carbonate reacts copletely? You need to find the volue of carbon dioxide gas that is produced when calciu carbonate decoposes. You know that the reactant is calciu carbonate, CaCO 3 (s). You know that the products are calciu oxide, CaO(s), and carbon dioxide gas, CO 2 (g). You know the ass of calciu carbonate that reacts: = 2.38 kg You know the teperature and pressure at ST: T = 273.15 K = 101.325 ka lan Your Strategy Write the balanced equation for the cheical reaction. Convert the ass of CaCO 3 (s) to gras. Deterine the olar ass of CaCO 3 (s) using the atoic asses fro the periodic table. Calculate the aount in oles of CaCO 3 (s) using the relationshipn. 9780071051071Chapter 12ExploringtheGasLaws HR 97
Isolation of the variable V: V V V Substitution to solve for V CO 2 : VCO 2 ka L 23.77859 ol 8.314 ol K 101.325 ka 532.94293 L 533 L 273.15 K The volue of carbon dioxide gas that is produced is 533 L. The volue of carbon dioxide gas produced sees reasonable given the ole ratio in the balanced cheical equation and the ass of calciu carbonate that reacted. The answer correctly shows three significant digits. 35. ractice roble (page 560) When iron rusts, it undergoes a reaction with oxygen to for solid iron(iii) oxide. Calculate the volue of oxygen gas at ST that is required to copletely react with 52.0 g of iron. You need to find the volue of oxygen gas that reacts to produce iron(iii) oxide. You know that the reactants are iron, Fe(s), and oxygen gas, O 2 (g). You know that the product is iron(iii) oxide, Fe 2 O 3 (s). You know the ass of the iron, Fe(s): = 52.0 g You know the teperature and pressure at ST: T = 273.15 K = 101.325 ka 9780071051071Chapter 12ExploringtheGasLaws HR 99
9780071051071Chapter 12ExploringtheGasLaws HR 100 lan Your Strategy Write the balanced equation for the cheical reaction. Deterine the olar ass of Fe(s) using the atoic ass in the period table. Calculate the aount in oles of Fe(s) using the relationship n. Use the aount in oles of Fe(s) and the ole ratio fro the balanced cheical equation to calculate the aount in oles of O 2 (g) that reacts. Convert the teperature fro the Celsius scale to the Kelvin scale. ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law:v Rearrange the equation to isolate the variable V. Substitute the given data into the equation and solve for V O 2. Act on Your Strategy Balanced cheical equation: 4Fe(s) + 3O 2 (g) 2Fe 2 O 3 (s) ole ratio: 4 oles 3 oles 2 oles olar ass,, of Fe(s): 55.85 g/ol (fro the periodic table) Aount in oles, n, of Fe(s): nfe 52.0 g 55.85 g /ol 0.93106 ol Aount in oles, n, of O 2 (g): 3 ol O n 2 O2 4 ol Fe 0.93106 ol Fe n O2 3 ol O 2 0.93106 ol Fe 4 ol Fe 0.69829 ol Isolation of the variable V: V V V
Substitution to solve forv : V O 2 ka L 0.69829 ol 8.314 ol K 101.325 ka 15.65069 L 15.6 L O 2 273.15 K 9780071051071Chapter 12ExploringtheGasLaws HR 101 The volue of oxygen that is required is 15.6 L. The volue of oxygen gas sees reasonable given the ole ratio in the balanced cheical equation and the ass of iron that reacted. The answer correctly shows three significant digits. 36. ractice roble (page 560) Oxygen gas and agnesiu react to for 2.43 g of agnesiu oxide, go(s). What volue of oxygen gas at 94.9 ka and 25.0 C would be consued to produce this ass of agnesiu oxide? You need the volue of oxygen consued in a reaction with agnesiu to produce agnesiu oxide. You know that the reactants are agnesiu, g(s), and oxygen gas, O 2 (g). You know that the product is agnesiu oxide, go(s). You know the ass of the go(s): = 2.43 g You know the teperature and pressure: T = 25.0 C = 94.9 ka lan Your Strategy Write the balanced equation for the cheical reaction. Deterine the olar ass of go(s) using the atoic asses fro the period table. Calculate the aount in oles of go(s) using the relationship n. Use the aount in oles of go(s) and the ole ratio fro the balanced cheical equation to calculate the aount in oles of O 2 (g) consued. Convert the teperature fro the Celsius scale to the Kelvin scale.
Substitution to solve for V O 2 : VO 2 ka 0.0301414 ol 8.314 ol 94.9 ka 0.7873029 L 0.787 L L K 298.15 K 9780071051071Chapter 12ExploringtheGasLaws HR 103 The volue of oxygen gas that would be consued is 0.787 L. The volue of oxygen gas sees reasonable given the ole ratio in the balanced cheical equation and the ass of agnesiu oxide produced. The answer correctly shows three significant digits. 37. ractice roble (page 560) In the seiconductor industry, hexafluoroethane, C 2 F 6 (g), is used to reove silicon dioxide, SiO 2 (s), according to the following cheical equation: 2SiO 2 (s) + 2C 2 F 6 (g) + O 2 (g) 2SiF 4 (g) + 2COF 2 (g) + 2CO 2 (g) What ass of silicon dioxide reacts with 1.270 L of hexafluoroethane at 0.200 ka and 400.0 C? You need to find the ass of silicon dioxide that reacts with a specific volue of hexafluoroethane. You know the balanced cheical equation: 2SiO 2 (s) + 2C 2 F 6 (g) + O 2 (g) 2SiF 4 (g) + 2COF 2 (g) + 2CO 2 (g) You know the volue of hexafluoroethane that reacts: V = 1.270 L You know the teperature and pressure: T = 400.0 C = 0.200 ka lan Your Strategy Write the balanced equation for the cheical reaction. Convert the teperature fro the Celsius scale to the Kelvin scale. ka L Use the universal gas constant: R 8.314 ol K
9780071051071Chapter 12ExploringtheGasLaws HR 104 Use the ideal gas law: V Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve for n. Use the aount in oles of C 2 F 6 (g) and ole ratio fro the balanced cheical equation to calculate the aount in oles of SiO 2 (s) that react. Deterine the olar ass of SiO 2 (s) using the atoic asses fro the periodic table. Calculate the ass of SiO 2 (s) using the relationship n. Act on Your Strategy Balanced cheical equation: 2SiO 2 (s) + 2C 2 F 6 (g) + O 2 (g) 2SiF 4 (g) + 2COF 2 (g) + 2CO 2 (g) ole ratio: 2 oles 2 oles 1 ole 2 oles 2 oles 2 oles Teperature conversion: T = 400.0 C + 273.15 = 673.15 K Isolation of the variable n: V V RT RT V n RT Substitution to solve forn : n C2F6 C2F6 V RT 0.200 ka 1.270 L ka L 8.314 673.15 K ol K 5 4.53849 10 ol Aount in oles, n, of SiO 2 (s): 2 ol SiO n 2 SiO2 5 2 ol C F 4.53849 10 ol C F n 2 6 2 6 SiO2 2 ol SiO 4.53849 10 ol C F 2 ol C2F6 5 4.53849 10 ol 5 2 2 6 C2F6
olar ass,, of SiO 2 (s): 1 2 SiO2 Si O 1(28.09 g/ol) + 1(16.00 g/ol) 60.09 g/ol ass,, of SiO 2 (s): n SiO 2 5 4.53849 10 ol 60.09 g/ ol 2.72717 10 g 2.73 10 g The ass of silicon dioxide that reacts is 2.73 10 g. The sall ass of silicon dioxide sees reasonable given the ole ratio in the balanced cheical equation, the conditions of the reaction, and the volue of hexafluoroethane that reacted. The answer correctly shows three significant digits. 38. ractice roble (page 560) What ass of oxygen gas reacts with hydrogen gas to produce 0.62 L of water vapour at 100.0 C and 101.3 ka? You need to find the ass of oxygen gas that reacts with hydrogen to produce a specific volue of water vapour, H 2 O(g). You know the volue of the water vapour: V = 0.62 L You know the teperature and pressure: T = 100.0 C = 101.3 ka lan Your Strategy Convert the teperature fro the Celsius scale to the Kelvin scale. ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law:v Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve forn H2O. 9780071051071Chapter 12ExploringtheGasLaws HR 105
ass,, of O 2 (g): n O 2 2 1.01222 10 ol 32.00 g/ ol 0.32391 g 0.32 g The ass of oxygen that reacts is 0.32 g. The sall ass of oxygen sees reasonable, given the ole ratio in the balanced cheical equation and the sall volue of water vapour that was produced. The answer correctly shows two significant digits. 39. ractice roble (page 560) One ethod of producing aonia gas involves the reaction of aoniu chloride, NH 4 Cl(aq), with sodiu hydroxide, NaOH(aq); water and aqueous sodiu chloride are also products of the reaction. During an experient, 98 L of aonia gas was collected using water displaceent. If the gas was collected at 20.0 C and 780 Hg, deterine the aount of sodiu hydroxide that ust have reacted. You need to find the aount, in gras, of NaOH(s) that reacts to produce a specific volue of aonia, NH 3 (g), collected over water. You know that the reactants are aoniu chloride, NH 4 Cl(aq), and sodiu hydroxide, NaOH(aq). You know that the products are water, H 2 O(); sodiu chloride, NaCl(aq); and aonia, NH 3 (g). You know the volue of the aonia gas: V = 98 L You know the teperature and the total pressure: T = 20.0 C total = 780 Hg artial pressure of water vapour at 20.0 C: H2O = 2.33 ka lan Your Strategy Write the balanced equation for the cheical reaction. Convert the teperature fro the Celsius scale to the Kelvin scale. Convert the total pressure fro Hg to kilopascals. 9780071051071Chapter 12ExploringtheGasLaws HR 107
Use Dalton s law of partial pressures to deterine the partial pressure of the dry aonia gas: total = gas + water vapour Convert the volue of aonia gas to litres. ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law:v Rearrange the equation to isolate the variable n. Substitute the given data into the equation and solve forn. Use the aount in oles of NH 3 (g) and the ole ratio fro the balanced cheical equation to calculate the aount in oles of NaOH(s) that reacts. Deterine the olar ass of NaOH(s) using the atoic asses fro the periodic table. Calculate the ass of NaOH(s) using the relationship n. Act on Your Strategy Balanced cheical equation: NH 4 Cl(aq) + NaOH(aq) NaCl(aq) + H 2 O() + NH 3 (g) ole ratio: 1 ole 1 ole 1 ole 1 ole 1 ole Teperature conversion: T 20.0C 273.15 293.15 K NH 3 ressure conversion: total 780 Hg 103.99144 ka 101.325 ka 760 Hg artial pressure of the dry aonia gas: total NH3 water vapour NH3 total water vapour 103.99144 ka 2.33 ka 101.66 ka Volue conversion: V 98 L 1 10 L/ L 0.098 L 9780071051071Chapter 12ExploringtheGasLaws HR 108
Isolation of the variable n: V V RT RT V n RT Substitution to solve for n NH 3 : V nnh 3 RT 101.66 ka 0.098 L ka L 8.314 293.15 K ol K 4.08767 10 ol Aount in oles, n, of NaOH(s): 1 ol NaOH nnaoh 1 ol NH 4.08767 10 ol NH n 3 3 NaOH 1 ol NaOH 4.08767 10 ol NH3 4.08767 10 ol olar ass,, of NaOH(s): 1 1 1 NaOH Na O H 1 ol NH 3 1 22.99 g/ol + 1 16.00 g/ol + 1 1.01 g/ol 40.00 g/ol ass,, of NaOH(s): n NaOH 4.08767 10 ol 40.00 g/ ol 0.16350 g 0.16 g The ass of sodiu hydroxide that reacts is 0.16 g. 9780071051071Chapter 12ExploringtheGasLaws HR 109
The sall ass of sodiu hydroxide sees reasonable given the ole ratio in the balanced cheical equation and the volue of aonia that reacted. The answer correctly shows two significant digits. 40. ractice roble (page 560) A student reacts 0.15 g of agnesiu etal with excess dilute hydrochloric acid to produce hydrogen gas, which she collects over water. What volue of dry hydrogen gas does she collect over water at 28 C and 101.8 ka? You need to find the volue of hydrogen gas, H 2 (g), that is collected over water. You know that the reactants are agnesiu, g(s), and hydrochloric acid, HCl(aq). You know that the products are agnesiu chloride, gcl 2 (aq), and hydrogen gas, H 2 (g). You know the ass of the g(s): = 0.15 g You know the teperature and the total pressure T = 28 C total = 101.8 ka artial pressure of water vapour at 28 C: H2O = 3.78 ka lan Your Strategy Write the balanced equation for the cheical reaction. Find the olar ass of g(s) fro the atoic ass in the periodic table. Calculate the aount in oles of g(s) using the relationshipn. Use the aount in oles of g(s) and the ole ratio fro the balanced cheical equation to calculate the aount in oles of H 2 (g) that is produced. Convert the teperature fro the Celsius scale to the Kelvin scale. Use Dalton s law of partial pressures to deterine the partial pressure of the dry hydrogen gas: total = gas + water vapour ka L Use the universal gas constant: R 8.314 ol K Use the ideal gas law: V Rearrange the equation to isolate the variable V. Substitute the given data into the equation and solve for V H 2. 9780071051071Chapter 12ExploringtheGasLaws HR 110