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Practice Problems Section 11.1 • You can convert pressure measurements to other equivalent units. • The method used to convert units of measurement to other units is called dimensional analysis. • This method simply converts units by multiplying a given value with one set of units by a fraction that equals 1. Practice Problems Section 11.1 Example: • The reading of a tire-pressure gauge is 35.0 psi. What is the equivalent pressure in kilopascals? • Multiply 35.0 psi by a fraction that has the units you want to go to over the units you are trying to leave. • The fraction should have a value of 1. • 35.0 psi x 101.3 kPa/14.7 psi = 241 kPa. • Multiply across the top and divide by the value on the bottom. Practice Problems Section 11.1 1. 59.8 in Hg to psi (1.00 in = 25.4 mm) (59.8 in Hg) x (25.4 mm/1.00 in) x (14.7 psi/ 760 mm Hg) = 29.4 psi 2. 7.35 psi to mm Hg (7.35 psi) x (760 mm Hg/14.7 psi) = 380 mm Hg 3. 1140 mm Hg to kPa (1140 mm Hg) x (101.3 kPa/760 mm Hg) = 152 kPa Practice Problems Section 11.1 4. 19.0 psi to kPa (19.0 psi) x (101.3 kPa/14.7 psi) = 131 kPa 5. 202 kPa to psi (202 kPa) x (14.7 psi/101.3 kPa) = 29.3 kPa Practice Problems Section 11.2 11. Bacteria produce methane gas in sewage treatment plants. This gas is often captured or burned. If a bacterial culture produces 60.0 mL of methane gas at 700.0 mm Hg, what volume would be produced at 760.0 mm Hg? • The pressure is increasing, so volume will decrease. • If you want the volume to decrease, multiply the volume by the smaller pressure over the larger pressure. • (60.0 mL) x (700.0 mmHg/760.0 mm Hg) = 55.3 mL • Keep 3 significant figures and don’t forget the units! Practice Problems Section 11.2 12. At one sewage treatment plant, bacteria cultures produce 1000 L of methane gas per day at 1.0 atm pressure. What volume tank would be needed to store one day’s production at 5.0 atm? • Pressure is increasing, so volume will decrease. • Multiply the volume by the smaller pressure over the larger pressure. • (1000 L) x (1.0 atm/5.0 atm) = 200 L • Keep 2 significant figures and don’t forget the units! • Zeros are decimal place holders in this case. You can also write it as: 2.0 x 102 L. Practice Problems Section 11.2 13. Hospitals buy 400-L cylinders of oxygen gas compressed at 150 atm. They administer oxygen to patients at 3.0 atm in a hyperbaric oxygen chamber. What volume of oxygen can a cylinder apply at this pressure? • Pressure is decreasing, so volume will increase. • Multiply the volume by the larger pressure over the smaller pressure. • (400 L) x (150 atm/3.0 atm) = 20,000 L • Keep 2 significant figures and don’t forget units. • Zeros are decimal place holders in this case. You can also write it as: 2.0 x 104 L. Practice Problems Section 11.2 15. The volume of a scuba tank is 10.0 L. It contains a mixture of nitrogen and oxygen at 290.0 atm. What volume of this mixture could the tank supply to a diver at 2.40 atm? • Pressure is decreasing, so volume will increase. • Multiply the volume by the larger pressure over the smaller pressure. • (10.0 L) x (290.0 atm/2.40 atm) = 1208 L but you can’t keep all those numbers as significant figures, only 3 of them. • The best answer is 1210 L or 1.21 x 103 L. Practice Problems Section 11.2 16. A 1.00 L balloon is filled with helium at 1.20 atm. If the balloon is squeezed into a 0.500 L beaker and doesn’t burst, what is the pressure of the helium? • Volume is decreasing, so pressure will increase. • Multiply the pressure by the larger volume over the smaller volume. • (1.20 atm) x (1.00 L/0.500 L) = 2.40 atm • You should have 3 significant figures, so you can add a zero to the end of your answer. • Don’t forget units. Practice Problems Section 11.2 17. A balloon is filled with 3.0 L of helium at 310 K and 1 atm. The balloon is placed in an oven where the temperature reaches 340 K. What is the new volume of the balloon? • The pressure measurement is extra information. • Temperature is increasing, so volume will increase. • Multiply the volume by the larger temperature over the smaller temperature. • (3.0 L) x (340 K/310 K) = 3.3 L • You should have 2 significant figures. • Don’t forget units. Practice Problems Section 11.2 18. A 4.0 L sample of methane gas is collected at 30.0°C. Predict the volume of the sample at 0°C. • All temperatures must be in Kelvins! Add 273. • Temperature is decreasing, so volume will decrease. • Multiply the volume by the smaller temperature over the larger temperature. • (4.0 L) x (273 K/303 K) = 3.6 L or 4 L • You should have 1 significant figure. • Don’t forget units. Practice Problems Section 11.2 19. A 25 L sample of nitrogen is heated from 110°C to 260°C. What volume will the sample occupy at the higher temperature? • All temperatures must be in Kelvins. Add 273. • Temperature is increasing, so volume will increase. • Multiply the volume by the larger temperature over the smaller temperature. • (25 L) x (533 K/383 K) = 35 L • You should have 2 significant figures. • Don’t forget units. Practice Problems Section 11.2 20. The volume of a 16 g sample of oxygen is 11.2 L at 273 K and 1.00 atm. Predict the volume of the sample at 409 K. • The mass and pressure measurements are extra information. • Temperature is increasing, so volume will increase. • Multiply the volume by the larger temperature over the smaller temperature. • (11.2 L) x (409 K/273 K) = 16.8 L • You should have 3 significant figures. • Don’t forget units. Practice Problems Section 11.2 21. The volume of a sample of argon is 8.5 mL at 15°C and 101 kPa. What will its volume be at 0.00°C and 101 kPa? • The pressure measurement is extra information. • Temperatures must be in Kelvins. Add 273. • Temperature is decreasing, so volume will decrease. • Multiply the volume by the smaller temperature over the larger temperature. • (8.5 mL) x (273 K/288 K) = 8.1 mL • You should have 2 significant figures. • Don’t forget units. Practice Problems Section 11.2 22. A 2.7 L sample of nitrogen is collected at 121 kPa and 288K. If the pressure increases to 202 kPa and the temperature rises to 303 K, what volume will the nitrogen occupy? • Pressure is increasing, so volume will decrease. • Temperature is increasing, so volume will increase. • Multiply the volume by the smaller pressure over the larger pressure, and the larger temperature over the smaller temperature. • (2.7 L) x (121 kPa/202 kPa) x (303 K/288 K) = 1.7 L • You should have 2 significant figures. • Don’t forget units. Practice Problems Section 11.2 23. A chunk of subliming CO2 (dry ice) generates a 0.80L sample of gaseous CO2 at 22°C and 720 mm Hg. What volume will the CO2 have at STP? • STP = 273 K and 760 mm Hg • Pressure is increasing, so volume will decrease. • Temperature is decreasing, so volume will decrease. • Multiply the volume by the smaller pressure over the larger pressure, and the smaller temperature over the larger temperature in Kelvins. • (0.80 L) x (720 mmHg/760 mmHg) x (273 K/295 K) = 0.70 L (You should have 2 significant figures.) • Don’t forget units.