FA 13.1

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Show your work, round to the correct significant figures, circle your answers, and label them with units.

(1 atm = 1.013x10⁵ Pa = 101.3 kPa = 14.7 psi = 760 Torr; 1 m³ = 1000 liters; p_absolute = p_gauge + 1 atm; )

Objective F: Ideal Gas Law: PV = nRT, R = 8.31 J/(mol K) (With video solutions)

• Some molar masses:

• H 1.0079

• He 4.003

• N 14.0067

• Br 79.904

• Xe 131.293

1. What is the volume of one mol of an ideal gas at standard temperature and pressure (STP)? (P = 1.000 atm = 1.013x10⁵ Pa, T = 0^oC = 273.15 K) What is the volume in liters? (1 m³ = 1000 liters) (22.4 liters) . Solution

2. George Uss has 0.34 mols of Xenon tetrafluoride in a container with a volume of 0.159 m³ at 78.0 ^oC. What is the pressure? (6.2E3 Pa) Solution

3. Hugh Jass has a volume of 143 liters and 2.56 mols of Xenon gas at a pressure of 67,120 Pa. What must be the temperature in Kelvins? What is the temperature in ^oC (451 K, 178 ^oC) Solution

4. Anita Breke fills a large helium balloon with 2.18 grams of Helium gas. How many mols of He is this? What is the pressure in the balloon if the gas occupies a volume of 12.05 liters (1000 liters = 1 m³) at a temperature of 18.0 ^oC? (Beware the ides of Celsius!) What is that pressure in atmospheres? What is the gauge pressure in Pa and Atmospheres? (0.545 mols,1.09 x 10⁵ Pa, 1.08 atm, 8 x10³ Pa, .08 atm) Solution

5. A reaction vessel operates at 3.14 atmospheres. What is that pressure in Pa? If the vessel has a volume of 0.113 m³, is at a temperature of 145 ^oC, and contains pure Nitrogen gas, how many mols of nitrogen gas does it contain? How many grams of Nitrogen does it contain? (None Of Fred’s Clients Bring Iron Hats – Nitrogen is a diatomic gas) (3.18x10⁵ Pa, 10.3 mols, 290. g) Solution

6. A container has a volume of 216 liters. (1000 liters = 1 m³) If it can sustain a pressure of 13.5 atmospheres before bursting, and contains 89.1 grams of Hydrogen gas, a) what is its bursting pressure in Pa? b) how many mols of Hydrogen does it contain? and c) what is its maximum operating temperature in K and ^oC? (1.37x10⁶ Pa, 44.2 mols, 804 K, 531 ^oC) Solution

7. A 2.00 liter bottle contains 18.15 grams of Bromine gas and is at a gauge pressure of 0.153 atm. What is its temperature in Celsius? (-26 ^oC) Solution

8. George has 205 grams of Hydrogen gas at 1275 Torr Gauge pressure and 127.0 ^oC. What must be the volume of the container? (1.25 m³) Solution

9. Jeanne has 1,529 grams of Xenon gas in 127 liters at a temperature of –16.0 ^oC. What must be the gauge pressure in psi? (13.7 psi gauge) Solution

Objective G: Combined Gas Law:

10. An aerosol can is at an absolute pressure of 603 Boogalas when it is at 312 K. If I put it in liquid nitrogen and lower its temperature to 77.0 K, what is the new pressure in Boogalas? (1000 milli Boogalas = 1 Boogala) (Assume it does not leak, and the volume remains constant) (149 Boogalas) Solution

11. Air trapped in an airtight cylinder when the piston is 34.1 inches high is at 57.0 Jukkulas. How high must the piston be if the pressure is later at a pressure of 115 Jukkulas? Assume temperature remains constant. (16.9 inches) Solution

12. A Tupperware container is at 1.00 atm at 21.0 ^oC. (Convert to K) It is heated in a microwave to 99.5 ^oC with the lid on. Assuming no gas escapes, what is the pressure inside in atm? (1.27 atm) Solution

13. A quantity of ideal gas is compressed at constant temperature from 34.5 liters to 12.4 liters. What was the initial pressure if the final pressure was 2.45x10⁵ Pa? (8.81x10⁴ Pa) Solution

14. A balloon has a volume of 1.25 liters at 20.5 ^oC. At what temperature does it have a volume of 1.02 liters, assuming the pressure and mols remain constant? (-33.5 ^oC) Solution

15. One mol of an ideal gas occupies 22.4 liters at STP. (P = 1.000 atm T = 0.00^oC) What volume does it occupy at 97.0 ^oC and 1.29 atm? (23.5 liters) Solution

16. My car tire has a gauge pressure of 32.0 PSI when the temperature is 23.0 ^oC, what is the temperature in Celsius if the gauge pressure is later 48.0 PSI? (Assume that the tire does not leak, and that the volume remains constant) (124 ^oC) Solution

17. A container with a volume of 3.7 bushels is at a gauge pressure of 274 kPa and 57.0 ^oC. If it does not leak, and later the gauge pressure is 117 kPa at 145 ^oC, what is the new volume of the container? (8.06 bushels) Solution

18. An airtight container has a sliding wall, so its volume can change. When the volume is 13.7 cc, the gauge pressure is 0.150 ATM and the temperature is 25.0 ^oF. What must be the new gauge pressure if the container has a volume of 42.1 cc at 450. ^oF? (Absolute zero is -459.67 ^oF) (-0.298 atm) Solution

19. A steel nitrogen tank has a mass of 5.36 kg. When it is at 68.0 ^oF, and 742 psi gauge, it has a mass of 9.83 kg because of the added nitrogen gas. If the gauge pressure is 347 psi, and the mass of the tank is 7.15 kg because some nitrogen was released, what must be the temperature? (170. ^oF) Solution

More Practice Problems: (Solved on the old website: Ideal Gas Law)