Honors Chemistry. Chapter 11: Gas Law Worksheet Answer Key Date / / Period

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1 Honors Chemistry Name Chapter 11: Gas Law Worksheet Answer Key Date / / Period Complete the following calculation by list the given information, rewriting the formula to solve for the unknown, and plugging in the information (number and units), and writing the answer significantly. 1. A sample of moles of gas is placed in a container of volume of 2.50 L. What is the pressure of the gas in torr if the gas is at 25 o C? (Ideal Gas Law) P = nrt = (0.500 moles) ( L atm) (298 K) = P = 4.89 atm = 3720 torr V (mole K) (2.50 L) 2. If 2.00 mol of gas occupies 4.50 L at STP. How much of the same gas will occupy 3.00 L at STP? (Avogadro s Law) n 2 = V 2 n 1 = (3.00 L) (2.00 moles) = 1.33 moles V 1 (4.50 L) 3. Determine the partial pressures of each of the gases in the following mixture: g NH 3, g Ne and g F 2. The gases are at 1.50 atm of pressure. (Dalton s Law of Partial Pressure & Mole Ratios) g NH 3 1 mole NH mole NH mole NH 3 = x 1.50 atm = atm NH g NH moles g Ne 1 mole Ne moles Ne moles Ne = x 1.50 atm = atm Ne g Ne moles g F 2 1 mole F moles F moles F 2 = x 1.50 atm = atm F g F moles moles moles moles = moles 4. If at 1.00 atm of pressure water boils at 100. o C, at what temperature would water boil if the pressure is 600. torr? (This shows why food doesn't cook well at higher elevations) (Gay-Lussac s Law) T 2 = T 1 P 2 = (373 K) (0.789 atm) = 294 K P 1 (1.00 atm) 5. Calculate the volume of 40.6 g of F 2 at STP. (Ideal Gas Law) 40.6 g F 2 1 mole F L F L F g F 2 1 mole F 2 or 40.6 g F 2 1 mole F mole F g F 2 V = nrt = (1.07 moles) ( L atm) (273 K) = 24.0 L F 2 P (mole K) (1.00 atm)) 6. If the winter pressure that most car tire tires should be at to wear evenly is 32.0 psi, what is the pressure in atm? (Pressure Conversion) 32.0 psi 1.00 atm 2.18 atm 14.7 psi

2 7. A gas is placed in a balloon with a volume of 3.0 L at 28 o C and 900. torr. What would be the new volume for the gas if placed under STP? (Combined Gas Law) V 2 = P 1 V 1 T 2 = (900. torr) (3.0 L) (273 K) = 3.2 L T 1 P 2 (301 K) (760. torr) 8. Part of the reason that conventional explosives cause so much damage is that their detonation produces a strong shock wave that can knock things down. While using explosives to knock down a building, the shock wave can be so strong that 12 liters of gas will reach a pressure of 3.8 x 10 4 mm Hg. When the shock wave passes and the gas returns to a pressure of 760 mm Hg, what will the volume of that gas be? (Boyle s Law) V 2 = P 1 V 1 = (3.8 x 10 4 mm) (12 L) = 600 L or 6.0 x 10 2 L P 2 (760 mm) 9. Calculate the volume of 24.0 g of HCl at STP. (Ideal Gas Law) 24.0 g HCl 1 mole HCl 22.4 L HCl 14.7 L HCl g HCl 1 mole HCl or V = nrt = (0.658 moles) ( L atm) (273 K) = 14.7 L HCl P (mole K) (1.00 atm) 10. A hydrogen gas volume thermometer has a volume of cm 3 when immersed in an ice-water bath at 0. C. When immersed in boiling liquid chlorine, the volume of the hydrogen at the same pressure is 87.2 cm 3. Find the temperature of the boiling point of chlorine in C. (Charles Law) T 2 = T 1 V 2 = (273 K) (87.2 cm 3 ) = 238 K = 35 o C V 1 (100.0 cm 3 ) 11. Ammonia (NH 3 ) is placed in 1.50 L flask at 25 o C. If the pressure of the gas is atm, what is the density? (Ideal Gas Law and Density) n = PV = (0.899 atm) (1.50 L) (mole K) = moles NH g NH g NH 3 RT ( L atm) (298 K) 1 mole NH g NH 3 = g/l 1.50 L 12. A mixture of Ar and CO gases is collected over water at 28 o C and an atmospheric pressure of 1.05 atm. If the partial pressure of Ar is 600. torr, what is the partial pressure of CO? (vapor pressure of water at 28 o C is 28.3 mmhg (Dalton s Law of Partial Pressure) P T = P Ar + P CO + P Water P CO = P T (P Ar + P Water ) = 1.05 atm (0.789 atm atm) = 0.22 atm 13. At 1 atm of pressure water boils at 100. o C, if the sample was placed under 2 atm of pressure, what would be the temperature? (This would be like a pressure cooker). (Gay-Lussac s Law) T 2 = T 1 P 2 = (373 K) (2 atm) = 746 K = 700 K (Significantly) P 1 (1 atm)

3 14. On hot days, you may have noticed that potato chip bags seem to inflate, even though they have not been opened. If I have a 250. ml bag at a temperature of 19 o C, and I leave it in my car which has a temperature of 60. o C, what will the new volume of the bag be? (Charles Law) V 2 = V 1 T 2 = (250. ml) (333 K) = 285 ml T 1 (292 K) 15. What is the volume of mol of gas at 72 o C and 2.00 atm? (Ideal Gas Law) v = nrt = (0.750 moles) ( L atm) (345 K) = 10.6 L P (mole K) (2.00 atm) 16. In a certain experiment a sample of helium in a vacuum system was compressed at 25 C from a volume of ml to a volume of ml where its pressure was found to be 30.0 mm Hg. What was the original pressure of the helium? (Boyle s Law) P 1 = P 2 V 2 = (30.0 mm) (0.240 ml) = mm V 1 (200.0 ml) 17. Some students believe that teachers are full of hot air. If I inhale 2.20 liters of gas at a temperature of 18 o C and it heats to a temperature of 38 o C in my lungs, what is the new volume of the gas? (Charles Law) V 2 = V 1 T 2 = (2.20 L) (311 K) = 2.35 L T 1 (291 K) L of a certain gas are prepared at kpa and -108 C. The gas is then forced into an 855 ml cylinder in which it warms to room temperature, 22 C. Find the pressure of this gas in kilopascals. (Combined Gas Law) P 2 = P 1 V 1 T 2 = (100.0 kpa) (12.8 L) (295 K) = 2680 kpa T 1 V 2 (165 K) (0.855 L) 19. Air from the prairies of North Dakota in winter contains essentially only nitrogen, oxygen, and argon. A sample of air collected at Bismarck at -22 C and kpa had 78.0 % N 2, 21.0 % O 2, and 1.00 % Ar. Find the partial pressures of each of these gases. (Dalton s Law of Partial Pressure) kpa x = 77.1 kpa N kpa x = 20.8 kpa O kpa x = kpa Ar 20. A lighter-than-air balloon is designed to rise to a height of 6 miles at which point it will be fully inflated. At that altitude the atmospheric pressure is 210 mm Hg and the temperature is -40. C. If the full volume of the balloon is 100,000.0 L, how many kilograms of helium will be needed to inflate the balloon? (Ideal Gas Law) n = PV = (0.28 atm) (100,000.0 L) (mole K) = 1464 moles = 1500 moles (significantly) RT ( L atm) (233 K) 1500 moles He 4.00 g He 1 kg 6.0 kg He 1 mole He 1000 g

4 21. What would be the partial pressure of N 2 in a container at 50. C in which there is 0.20 mole N 2 and 0.10 mole CO 2 at a total pressure of kpa? (Dalton s Law of Partial Pressure) 0.20 mole N 2 = 0.67 x kpa = 68 kpa 0.30 moles 0.10 mole CO 2 = 0.33 x kpa = 33 kpa 0.30 moles 22. If 23.2 g of a given gas occupies a volume of 93.2 L at a particular temperature and pressure, what mass of the gas occupies a volume of 10.4 L under the same conditions? (Avogadro s Law) n 2 = n 1 V 2 = (23.2 g) (10.4 L) = 2.59 g V 1 (93.2 L) 23. What volume of Ne at one atm and 25 C would have to be added to a sign having a volume of 250. ml to create a pressure of one mm Hg at that temperature? (Boyle s Law) V 1 = P 2 V 2 = ( atm) (250. ml) = ml P 1 (1.00 atm) 24. Find the volume of a gas at mm Hg and 40.0 C if its volume at mm Hg and 15 C is 6.84 L. (Combined Gas Law) V 2 = P 1 V 1 T 2 = (720.0 mm) (6.84 L) (313 K) = 6.69 L T 1 P 2 (288 K) (800.0 mm) 25. What is the mass of 18.9 L of NH 3 at 31 C and kpa? (Ideal Gas Law) n = PV = ( atm) (18.9 L) (mole K) = mole NH g NH g NH 3 RT ( L atm) (304 K) 1 mole NH moles of O 2 in a 1.85 L cylinder exert a pressure of 3.68 atm. What is the temperature in the cylinder (in C)? (Ideal Gas Law) T = PV = (3.68 atm) (1.85 L) (mole K) = 297 K = 24 o C nr (0.279 moles) ( L atm) 27. A quantity of potassium chlorate is selected to yield, through heating, 75.0 ml of O 2 when measured at STP. If the actual volume is 92.5 ml and the actual pressure is atm, what is the resulting temperature of oxygen in degrees Celsius? (Combined Gas Law) T 2 = P 2 V 2 T 1 = (0.894 atm) (92.5 ml) (273 K) = 301 K = 28 o C P 1 V 1 (1.00 atm) (75.0 ml)

5 28. A mixture of hydrocarbons contains three moles of methane, four moles of ethane, and five moles of propane. The container has a volume of 124 liters and the temperature is 22 C. Find the partial pressures of the three gases, in kpa. (Ideal Gas Law and Dalton s Law of Partial Pressure) P = nrt = (12.0 moles) ( L atm) (295 K) = 2.34 atm = 237 kpa V (mole K) (124 L) 3 = x 237 kpa = 59.3 kpa methane 12 4 = x 237 kpa = 79.0 kpa ethane 12 5 = x 237 kpa = 98.8 kpa propane The highest pressure ever produced in a laboratory setting was about 2.00 x 10 6 atm. If we have a 1.00 x 10-5 liter sample of a gas at that pressure, then release the pressure until it is equal to atm, what would the new volume of that gas be? (Boyle s Law) V 2 = P 1 V 1 = (2.00 x 10 6 atm) (1.00 x 10-5 L) = 72.7 L P 2 (0.275 atm) 30. How many moles of gas would occupy a volume of 14 L at a pressure of 700. torr and a temperature of 30. o C? (Ideal Gas Law) n = PV = (0.921 atm) (14 L) (mole K) = 0.52 moles RT ( L atm) (303 K) 31. Submarines need to be extremely strong to withstand the extremely high pressure of water pushing down on them. An experimental research submarine with a volume of 15,000 liters has an internal pressure of 1.2 atm. If the pressure of the ocean breaks the submarine forming a bubble with a pressure of 250. atm pushing on it, how big will that bubble be? (Boyle s Law) V 2 = P 1 V 1 = (1.2 atm) (15,000 L) = 72 L P 2 (250. atm) 32. If 3.25 mol of argon gas occupies a volume of 100. L at a particular temperature and pressure, what volume does mol of argon occupy under the same conditions? (Avogadro s Law) V 2 = V 1 n 2 = (100. L) (14.15 mole) = 435 L n 1 (3.25 mole) 33. A sample of gas is placed in a container at 25 o C and 2.00 atm of pressure. If the temperature is raised to 50. o C, what is the new pressure? (Gay-Lussac s Law) P 2 = P 1 T 2 = (2.00 atm) (323 K) = 2.17 atm T 1 (298 K)

6 grams of XeF 4 is introduced into an evacuated 3.00 liter container at 80. C. Find the pressure in atmospheres in the container. (Ideal Gas Law) 2.50 g XeF 4 1 mole XeF mole XeF g XeF 4 P = nrt = ( mole) ( L atm) (353 K) = atm V (3.00 L) 35. For a mole of ideal gas, sketch graphs of a. P vs. V at constant T. a hyperbola b. P vs. T at constant V. b&c - straight lines c. V vs. T at constant P.

7 36. How are temperature and pressure related (directly or inversely)? How would doubling the pressure effect the temperature, at constant volume? It would increase the temperature. Since it was not specified what unit of temperature, It can not be stated that the temperature would be double. 37. How are volume and temperature related (directly or inversely)? How would reducing the Kelvin temperature by one half effect the volume, at constant pressure? Since the temperature is in Kelvin, the volume would reduce to one half of the original amount. 38. How are volume and pressure related (directly or inversely)? How would tripling the pressure effect the volume, at constant temperature? It would reduce the volume to one third of the original amount. 39. How are volume and moles related (directly or inversely)? What is the volume of any gas at STP? The volume of any gas at STP is equal to 22.4 L for one mole of the gas. 40. If a gas is collected over water, what must be done to determine the pressure of the gas? The water vapor pressure, at the specific temperature, must be subtracted from the total pressure to determine the pressure of the gas.

8 Gas Law Worksheet Answer Key atm = 3720 torr moles atm NH 3, atm Ne, atm F K L F atm L x 10 2 L L HCl K = 35 o C g/l atm K = 700 K (Significantly) ml L mm L kpa kpa N 2, 20.8 kpa O 2, kpa Ar kg He kpa N 2, 33 kpa CO g ml L g NH K = 24 o C K = 28 o C kpa methane, 79.0 kpa ethane, 98.8 kpa propane L moles L L atm atm