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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.

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**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 kPa/14.7 psi = 241 kPa. Multiply across the top and divide by the value on the bottom.

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**Practice Problems Section 11.1**

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 7.35 psi to mm Hg (7.35 psi) x (760 mm Hg/14.7 psi) = 380 mm Hg mm Hg to kPa (1140 mm Hg) x (101.3 kPa/760 mm Hg) = 152 kPa

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**Practice Problems Section 11.1**

psi to kPa (19.0 psi) x (101.3 kPa/14.7 psi) = 131 kPa kPa to psi (202 kPa) x (14.7 psi/101.3 kPa) = 29.3 kPa

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**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 mm Hg, what volume would be produced at 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!

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**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.

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**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.

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**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 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.

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**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 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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**Practice Problems Section 11.2**

23. A chunk of subliming CO2 (dry ice) generates a 0.80-L 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.

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