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# The Combined Gas Law

The Combined Gas Law contains six variables  It combines the laws of Boyle, Charles and Gay-Lussac into one formula that can be used to solve for any one of the variables when the others are known.

NOTE** This is used when the MOLES ARE HELD CONSTANT.

Keep in mind that you must use only the Kelvin temperature scale when working with temperature in all gas law formulas!

Regents Practice

 Questions Highlight to reveal the answers below 1. A gas has a volume of 800.0 mL at minus 23.00 °C and 300.0 torr. What would the volume of the gas be at 227.0 °C and 600.0 torr of pressure? 1. V = [ (300 torr) (800 mL) (500 K) ] / [ (250 K) (600 torr) ]; x = 800.0 mL Keep in mind that torr = mmHg. 2. 500.0 liters of a gas are prepared at 700.0 mm Hg and 200.0 °C. The gas is placed into a tank under high pressure. When the tank cools to 20.0 °C, the pressure of the gas is 30.0 atm. What is the volume of the gas? 2. V = [ (700/760) (500) (293) ] / [ (473) (30) ]; x = 9.51 L Note that this problem mixes pressure units. The 700/760 fraction converts mmHg to atm. 3. What is the final volume of a 400.0 mL gas sample that is subjected to a temperature change from 22.0 °C to 30.0 °C and a pressure change from 760.0 mm Hg to 360.0 mm Hg? 3. V = [ (760 mm Hg) (400 mL) (303 K) ] / [ (295 K) (360 mm Hg) ]; x = 867.3 mL 4. What is the volume of gas at 2.00 atm and 200.0 K if its original volume was 300.0 L at 0.250 atm and 400.0 K? 4. V = [ (0.25) (300) (200) ] / [ (400) (2) ] 5. At conditions of 785.0 torr of pressure and 15.0 °C temperature, a gas occupies a volume of 45.5 mL. What will be the volume of the same gas at 745.0 torr and 30.0 °C? 5. V = [ (785) (45.5) (303) ] / [ (288) (745) ] 6. A gas occupies a volume of 34.2 mL at a temperature of 15.0 °C and a pressure of 800.0 torr. What will be the volume of this gas at standard conditions? 6. V = [ (800) (34.2) (273) ] / [ (288) (760) ] 7. The volume of a gas originally at standard temperature and pressure was recorded as 488.8 mL. What volume would the same gas occupy when subjected to a pressure of 100.0 atm and temperature of minus 245.0 °C? 7. V = [ (1) (488.8) (28) ] / [ (273) (100) ] 8. At a pressure of 780.0 mm Hg and 24.2 °C, a certain gas has a volume of 350.0 mL. What will be the volume of this gas at STP? 8. V = [ (780) (350) (273) ] / [ (297.2) (760) ] 9. A gas sample occupies 3.25 liters at 24.5 °C and 1825 mm Hg. Determine the temperature at which the gas will occupy 4250 mL at 1.50 atm. 9. T = [ (1.50 atm) (4.25 L) (297.5 K) ] / [(1825 mm Hg/760 atm mmHg) (3.25 L) ] Note that I cross multiplied. 10. If 10.0 liters of oxygen at STP are heated to 512 °C, what will be the new volume of gas if the pressure is also increased to 1520.0 mm of mercury? 10. V = [ (760) (10) (785) ] / [ (273) (1520) ] 11. What is the volume at STP of 720.0 mL of a gas collected at 20.0 °C and 3.00 atm pressure? 11. P = [ (3.00 atm) (720.0 mL) (273 K) ] / [ (293 K) (1.00 atm) 12. 2.00 liters of hydrogen, originally at 25.0 °C and 750.0 mm of mercury, are heated until a volume of 20.0 liters and a pressure of 3.50 atmospheres is reached. What is the new temperature? 12. T = [ (3.50) (20) (298) ] / [ (750/760) (2.00) ] 13. A gas balloon has a volume of 106.0 liters when the temperature is 45.0 °C and the pressure is 740.0 mm of mercury. What will its volume be at 20.0 °C and 780 .0 mm of mercury pressure? 13. V = [ (740 mmHg) (106 L) (293 K) ] / [ (318 K) (780 mmHg) ] 14. If the absolute temperature of a given quantity of gas is doubled and the pressure tripled, what happens to the volume of the gas? 14. V = [ (1) (10) (2) ] / [ (1) (3) ] 15. 73.0 mL of nitrogen at STP is heated to 80.0 °C and the volume increase to 4.53 L. What is the new pressure? 15. P = [ (1.00 atm) (73.0 mL) (353 K) ] / [ (273 K) (4530 mL) ] 16. 500.0 mL of a gas was collected at 20.0 °C and 720.0 mm Hg. What is its volume at STP? 16. V = [ (720) (500) (273) ] / [ (293) (760) ] 17. A sample of gas occupies 50.0 L at 15.0 °C and 640.0 mm Hg pressure. What is the volume at STP? 17.V = [ (640) (50) (273) ] / [ (288) (760) ]