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EXAMPLE 11.1

Solution Map :. Solution :. SKILLBUILDER 11.1. Converting between Pressure Units. Convert a pressure of 173 in. Hg into pounds per square inch. EXAMPLE 11.1. Converting between Pressure Units.

leonard-townsend
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EXAMPLE 11.1

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  1. Solution Map: Solution: SKILLBUILDER 11.1 Converting between Pressure Units Convert a pressure of 173 in. Hg into pounds per square inch. EXAMPLE 11.1 Converting between Pressure Units A high-performance road bicycle tire is inflated to a total pressure of 125 psi. What is this pressure in millimeters of mercury? You are given a pressure in psi and asked to convert it to mm Hg. Find the required conversion factors in Table 11.1. Given: 125 psi Find: mm Hg Conversion Factors: 1 atm = 14.7 psi 760 mm Hg = 1 atm Begin the solution map with the given units of psi. Use the conversion factors to convert first to atm and then to mm Hg. Follow the solution map to solve the problem.

  2. SKILLBUILDER PLUS Convert a pressure of 23.8 in. Hg into kilopascals. FOR MORE PRACTICE Example 11.13; Problems 27, 28, 29, 30, 33, 34, 35, 36. EXAMPLE 11.1 Converting between Pressure Units Continued

  3. Solution Map: Solution: EXAMPLE 11.2 Boyle’s Law A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume of the cylinder if the applied pressure is decreased to 1.0 atm? You are given an initial pressure, an initial volume, and final pressure. You are asked to find the final volume. This problem requires the use of Boyle's law. Given: P1 = 4.0 atm V1 = 6.0 L V1 = 6.0 L Find: V2 Equation: P1V1 = P2V2 Draw a solution map beginning with the given quantities. Boyle’s law shows the relationship necessary to get to the find quantity. Solve the equation for the quantity you are trying to find (V2)and then substitute the numerical quantities into the equation to compute the answer.

  4. FOR MORE PRACTICE Example 11.14; Problems 37, 38, 39, 40. SKILLBUILDER 11.2 Boyle’s Law A snorkeler takes a syringe filled with 16 mL of air from the surface, where the pressure is 1.0 atm, to an unknown depth. The volume of the air in the syringe at this depth is 7.5 mL. What is the pressure at this depth? If the pressure increases by an additional 1 atm for every 10 m of depth, how deep is the snorkeler? EXAMPLE 11.2 Boyle’s Law Continued

  5. Find: T1 and t1 Equation: Solution Map: EXAMPLE 11.3 Charles’s Law A sample of gas has a volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at t = 0 °C its volume decreases to 2.57 L. What was its initial temperature (in kelvins and in Celsius)? Assume a constant pressure. (To distinguish between the two temperature scales, use t for temperature in °C and T for temperature in K.) You are given an initial volume, a final volume, and a final temperature. You are asked to find the intitial temperature in both kelvins (T1) and degrees Celsius (t1). Given: V1 = 2.80 L V2 = 2.57 t2 = 0 °C This problem requires the use of Charles's law. Draw a solution map beginning with the given quantities. Charles’s law shows the relationship necessary to get to the find quantity.

  6. Solution: EXAMPLE 11.3 Charles’s Law Continued Solve the equation for the quantity you are trying to find (T1). Before you substitute in the numerical values, you must convert the temperature to kelvins. Remember, gas law problems must always be worked using Kelvin temperatures. Once you have converted the temperature to kelvins, substitute into the equation to find Convert the temperature to degrees Celsius to find t1.

  7. FOR MORE PRACTICE Problems 43, 44, 45, 46. SKILLBUILDER 11.3 Charles’s Law A gas in a cylinder with a moveable piston with an initial volume of 88.2 mL is heated from 35°C to 155°C. What is the final volume of the gas in milliliters? EXAMPLE 11.3 Charles’s Law Continued

  8. Equation: Solution Map: EXAMPLE 11.4 The Combined Gas Law A sample of gas has an initial volume of 158 mL at a pressure of 735 mm Hg and a temperature of 34°C. If the gas is compressed to a volume of 108 mL and heated to a temperature of 85°C, what is its final pressure in millimeters of mercury? You are given an initial pressure, temperature, and volume as well as a final temperature and volume. You are asked to find the final pressure. Given: P1 = 735 mm Hg t1 = 34 °C t2 = 85 °C V1 = 158 mL V2 = 108 mL Find:P2 This problem requires the use of the combined gas law. Draw a solution map beginning with the given quantities. The combined gas law shows the relationship necessary to get to the find quantity.

  9. Solution: EXAMPLE 11.4 The Combined Gas Law Continued Solve the equation for the quantity you are trying to find (P2). Before you substitute in the numerical values, you must convert the temperatures to kelvins. Once you have converted the temperature to kelvins, substitute into the equation to find P2 .

  10. FOR MORE PRACTICE Example 11.15; Problems 55, 56, 57, 58, 59, 60. SKILLBUILDER 11.4 The Combined Gas Law A balloon has a volume of 3.7 L at a pressure of 1.1 atm and a temperature of 30 °C. If the balloon is submerged in water to a depth where the pressure is 4.7 atm and the temperature is 15 °C, what will its volume be (assume that any changes in pressure caused by the skin of the balloon are negligible)? EXAMPLE 11.4 The Combined Gas Law Continued

  11. Given: V1 = 4.8 L n1 = 0.22 mol V2 = 6.4 L Find:n2 Equation: Solution Map: EXAMPLE 11.5 Avogadro’s Law A 4.8-L sample of helium gas contains 0.22 mol of helium. How many additional moles of helium gas must be added to the sample to obtain a volume of 6.4 L? Assume constant temperature and pressure. You are given an initial volume, an initial number of moles, and a final volume. You are (essentially) asked to find the final number of moles. This problem requires the use of Avogadro’s law Draw a solution map beginning with the given quantities. Avogadro’s law shows the relationship necessary to get to the find quantity.

  12. Solution: FOR MORE PRACTICE Problems 49, 50, 51, 52. mol to add = 0.29 – 0.22 = 0.07 mol SKILLBUILDER 11.5 Avogadro’s Law A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.58 mol of a gaseous product. If the cylinder contained 0.11 mol of gas before the reaction and had an initial volume of 2.1 L, what was its volume after the reaction? EXAMPLE 11.5 Avogadro’s Law Continued Solve the equation for the quantity you are trying to find (n2)and substitute the appropriate quantities to compute n2. Since the balloon already contains 0.22 mol, subtract this quantity from the final number of moles to determine how much must be added

  13. Solution Map: Solution: EXAMPLE 11.6 The Ideal Gas Law Calculate the volume occupied by 0.845 mol of nitrogen gas at a pressure of 1.37 atm and a temperature of 315 K. You are given the number of moles, the pressure, and the temperature of a gas sample. You are asked to find the volume. This problem requires the use of the ideal gas law. Given: n= 0.845 mol P = 1.37 atm T = 315 K Find:V Equation: PV = nRT Draw a solution map beginning with the given quantities. The ideal gas law shows the relationship necessary to get to the find quantity. Solve the equation for the quantity you are trying to find (V) and substitute the appropriate quantities to compute V.

  14. FOR MORE PRACTICE Example 11.16; Problems 63, 64, 65, 66. SKILLBUILDER 11.6 The Ideal Gas Law An 8.5-L tire is filled with 0.55 mol of gas at a temperature of 305 K. What is the pressure of the gas in the tire? EXAMPLE 11.6 The Ideal Gas Law Continued

  15. Solution Map: EXAMPLE 11.7 The Ideal Gas Law Requiring Unit Conversion Calculate the number of moles of gas in a basketball inflated to a total pressure of 24.2 psi with a volume of 3.2 L at 25 °C. You are given the pressure, the volume, and the temperature of a gas sample. You are asked to find the number of moles. This problem requires the use of the ideal gas law. Given: P = 24.2 psi V = 3.2 L t = 25 °C Find:n Equation: PV = nRT Draw a solution map beginning with the given quantities. The ideal gas law shows the relationship necessary to get to the find quantity.

  16. Solution: SKILLBUILDER 11.7 The Ideal Gas Law Requiring Unit Conversion How much volume does 0.556 mol of gas occupy when its pressure is 715 mm Hg and its temperature is 58 °C? EXAMPLE 11.7 The Ideal Gas Law Requiring Unit Conversion Continued Solve the equation for the quantity you are trying to find (n). Before substituting into the equation, you must convert P and t into the correct units. (Since 1.6462 is an intermediate answer, mark the least significant digit, but don’t round until the end.) Finally, substitute into the equation to compute n.

  17. SKILLBUILDER PLUS Find the pressure in millimeters of mercury of a 0.133-g sample of helium gas at 32 °C and contained in a 648-mL container. FOR MORE PRACTICE Problems 67, 68, 71, 72. EXAMPLE 11.7 The Ideal Gas Law Requiring Unit Conversion Continued

  18. Given: m = 0.311 g V = 0.225 L t = 55 °C P = 886 mm Hg Find:molar mass (g/mol) Equation: Solution Map: EXAMPLE 11.8 Molar Mass Using the Ideal Gas Law and Mass Measurement A sample of gas has a mass of 0.311 g. Its volume is 0.225 L at a temperature of 55 °C and a pressure of 886 mm Hg. Find its molar mass. You are given the mass, the volume, the temperature, and the pressure of a gas sample. You are asked to find the molar mass of the gas. This problem requires the use of the ideal gas law and the definition of molar mass. In the first part of the solution map, use the ideal gas law to find the number of moles of gas from the other given quantities. In the second part, use the number of moles from the first part, as well as the given mass, to find the molar mass.

  19. Solution: EXAMPLE 11.8 Molar Mass Using the Ideal Gas Law and Mass Measurement Continued First, solve the ideal gas law for n. Before substituting into the equation, you must convert the pressure to atm and temperature to K. Now, substitute into the equation to compute n, the number of moles. Finally, use the number of moles just found and the given mass (m) to find the molar mass.

  20. FOR MORE PRACTICE Problems 73, 74, 75, 76. SKILLBUILDER 11.8 Molar Mass Using the Ideal Gas Law and Mass Measurement A sample of gas has a mass of 827 mg. Its volume is 0.270 L at a temperature of 88 °C and a pressure of 975 mm Hg. Find its molar mass. EXAMPLE 11.8 Molar Mass Using the Ideal Gas Law and Mass Measurement Continued

  21. FOR MORE PRACTICE Example 11.17; Problems 77, 78, 79, 80. SKILLBUILDER 11.9 Total Pressure and Partial Pressure A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 745 torr, and the water vapor has a partial pressure of 24 torr. What is the partial pressure of the hydrogen gas? EXAMPLE 11.9 Total Pressure and Partial Pressure A mixture of helium, neon, and argon has a total pressure of 558 mm Hg. If the partial pressure of helium is 341 mm Hg and the partial pressure of neon is 112 mm Hg, what is the partial pressure of argon? You are given the total pressure of a gas mixture and the partial pressures of two (of its three) components. You are asked to find the partial pressure of the third component. This problem requires the use of Dalton’s law of partial pressures. Given: Ptot = 558 mm Hg PHe = 341 mm Hg PNe = 112 mm Hg Find:PAr Equation: Ptot = Pa + Pb + Pc + . . . To solve this problem, simply solve Dalton’s law for the partial pressure of argon and substitute the correct values to compute it. Solution: Ptot = PHe + PNe + PAr PAr = Ptot + PHe + PNe = 558 mm Hg – 341 mm Hg – 112 mm Hg = 105 mm Hg

  22. Given: O2 percent = 2.0% Ptot = 10.0 atm Find: Equation: Partial pressure of component = Fractional composition of component × Total pressure FOR MORE PRACTICE Problems 83, 84, 85, 86. Solution: SKILLBUILDER 11.10 Partial Pressure, Total Pressure, and Percent Composition What must the total pressure be for a diver breathing heliox with an oxygen composition of 5.0% to breathe = 0.21 atm? EXAMPLE 11.10 Partial Pressure, Total Pressure, and Percent Composition Calculate the partial pressure of oxygen that a diver breathes with a heliox mixture containing 2.0% oxygen at a depth of 100 m where the total pressure is 10.0 atm. You are given the percent oxygen in the mixture and the total pressure. You are asked to find the partial pressure of oxygen. You will need the equation that relates partial pressure to total pressure. Calculate the fractional composition of O2 by dividing the percent composition by 100. Calculate the partial pressure of O2 by multiplying the fractional composition by the total pressure.

  23. How many liters of oxygen gas form when 294 g of KClO3 completely react in the following reaction (which is used in the ignition of fireworks)? Assume that the oxygen gas is collected at P = 755 mm Hg and T = 305 K. Solution Map: EXAMPLE 11.11 Gases in Chemical Reactions You are given the mass of a reactant in a chemical reaction. You are asked to find the volume of a gaseous product at a given pressure and temperature. You will need the molar mass of KClO3 and the stoichiometric relationship between KClO3 and O2 (from the balanced chemical equation). You will also need the ideal gas law. Given: 294 g KClO3 P = 755 mm Hg (of oxygen gas) T = 305 K Find:Volume of O2 in liters Equations and Conversion Factors: 1 mol KClO3 = 122.6 g 2 mol KClO3 = 3 mol O2 PV = nRT The solution map has two parts. In the first part, convert from g KClO3 to mol KClO3 and then to mol O2 In the second part, use mol O2 as n in the ideal gas law to find the volume of O2 .

  24. Solution: FOR MORE PRACTICE Problems 93, 94, 95, 96, 97, 98. SKILLBUILDER 11.11 Gases in Chemical Reactions In the following reaction, 4.58 L of O2 were formed at 745 mm Hg and 308 K. How many grams of Ag2O must have decomposed? EXAMPLE 11.11 Gases in Chemical Reactions Continued Begin by converting mass KClO3 to mol KClO3 and then to mol O2. Then solve the ideal gas equation for V. Before substituting the values into this equation, you must convert the pressure to atm. Finally, substitute the given quantities along with the number of moles just calculated to compute the volume.

  25. How many grams of water form when 1.24 L of H2 gas at STP completely reacts with O2? Solution Map: EXAMPLE 11.12 Using Molar Volume in Calculations You are given the volume of a reactant at STP and asked to find the mass of the product formed. You will need the molar volume at STP, the stoichiometric relationship between H2 and H2O (from the balanced chemical equation), and the molar mass of H2O. Given: 1.24 L H2 Find:g H2O Conversion Factors: 1 mol = 22.4 L (at STP) 2 mol H2 = 2 mol H2O 18.02 g H2O = 1 mol H2O The solution map has two parts. In the first part, convert from g KClO3 to mol KClO3 and then to mol O2 In the second part, use mol O2 as n in the ideal gas law to find the volume of O2 .

  26. Solution: FOR MORE PRACTICE Problems 99, 100, 101, 102. SKILLBUILDER 11.12 Using Molar Volume in Calculations How many liters of oxygen (at STP) are required to form 10.5 g of H2O? EXAMPLE 11.12 Using Molar Volume in Calculations Continued Begin with the volume of H2 and follow the solution map to arrive at mass H2O in grams.

  27. Given: 18.4 in. Hg Find: torr Conversion Factors: 1 atm = 29.92 in. Hg 760 torr = 1 atm Solution Map: Solution: EXAMPLE 11.13 Pressure Unit Conversion Convert 18.4 in. Hg to torr.

  28. Given: P1 = 3.2 atm V1 = 5.7 L P2 = 4.7 atm Find: V2 Equation: P1V1 = P2V2 Solution Map: Solution: EXAMPLE 11.14 Simple Gas Laws A gas has a volume of 5.7 L at a pressure of 3.2 atm. What is its volume at 4.7 atm? (Assume constant temperature.)

  29. Given: P1 = 855 mm Hg V1 = 2.4 L T1 = 298 K V2 = 4.1 L T2 = 387 K Find: P2 Equation: Solution Map: EXAMPLE 11.15 The Combined Gas Law A sample of gas has an initial volume of 2.4 L at a pressure of 855 mm Hg and a temperature of 298 K. If the gas is heated to a temperature of 387 K and expanded to a volume of 4.1 L, what is its final pressure in millimeters of mercury?

  30. Solution: EXAMPLE 11.15 The Combined Gas Law Continued

  31. Given: n = 1.2 mol V = 28.2 L T = 334 K Find: P Equation: PV = nRT Solution Map: Solution: EXAMPLE 11.16 The Ideal Gas Law Calculate the pressure exerted by 1.2 mol of gas in a volume of 28.2 L and at a temperature of 334 K.

  32. A mixture of three gases has the following partial pressures. What is the total pressure of the mixture? Given: Find: Ptot Equation: Ptot = Pa + Pb + Pc + . . . Solution: = 289 mm Hg + 342 mm Hg + 122 mm H = 289 mm Hg + 342 mm Hg + 122 mm Hg EXAMPLE 11.17 Total Pressure and Partial Pressure

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