Combined-Avogadros-and-Ideal-Gas-Laws [Autosaved].pptx
- 2. 2 No one is credited for the Combined Gas Law. Putting together Boyle’s, Charles’ and Gay- Lussac’s together will result to this statement: The pressure and volume of a gas are inversely proportional to each other but are both directly proportional to the temperature of the gas.
- 3. 3 Translating it to mathematical equation will give us the following: T= VP/k or V= kT/P or P= kT/ V or k= PV/T The constant k in the equation above is known as the universal gas constant. It is the result of the combination of the proportionality constants in the three gas laws. Note that the formula is equal to a constant, thus, it is possible to compute for the change in volume, temperature or pressure using the following proportion: P1V1/T1 = P2V2/T2
- 4. 4 If P2 is unknown then P2 = P1V1T2/ V2T1 If V2 is unknown then V2 = P1V1T2/ P2T1 If T2 is the unknown then T2 = P2V2T1/P1V1 Let’s use the Combined Gas law in determining change in the final volume, temperature or pressure of gases
- 5. 5 Sample problem: The oxygen tank manufacturer used to produce 5.00 L oxygen tank at 2000. psi and 25 oC. Statistics suggests that the 3.00 L oxygen tank at 1500. psi is more marketable. What temperature requirement is needed to produce a 3.00 L oxygen tank at 1500. psi?
- 6. 6 The given values: V1= 5.00 L T1= 25oC = 298K P1 = 2000. psi V2= 3.00 L P2= 1500. psi T2= ?
- 7. 7 Solving for T2 T2= P2V2T1/P1V1 T2= (298K)(1500.psi)(3.00L) (2000.psi)95.00L) T2= 134 K
- 8. 8 Try it! The volume of a gas at 27 oC and 700.0 mmHg is 600.0 mL. What is the volume of the gas at -20.0 oC and 500.0 mmHg?
- 9. 9 Avogadro’s Law Do you still remember the mole concept? Can you still recall what a mole is? The number of moles quantifies the amount of a substance.
- 10. 10 What could be the possible relationship of the amount of gas in a mole to its volume? In 1811, Amedeo Avogadro wrote in a paper that, “ Equal volumes of all gases , kept at the same temperature and pressure, contain the same number of molecules.
- 11. 11 Using the proportionality symbol, we can express the proportionality between the volume and the number of moles of a gas as: V ∞ n at constant T and P Mathematically, it can be expressed as: V/n = k
- 12. 12 Where V= volume of the gas n= amount of gas in moles k=proportionalityconstant This can also be expressed as V1/n1= V2/n2 or V1n2= V2n1
- 13. 13 Sample Problems: 1. A balloon containing 2.00 moles of He has a volume of 880. mL. What is the new volume after 4.00 moles of He are added to the balloon at the same temperature and pressure?
- 14. 14 Sample Problems: 2. How many oxygen molecules are in 3.36 L of Oxygen gas at STP?
- 15. 15 Sample Problems: 2. How many oxygen molecules are in 3.36 L of Oxygen gas at STP?
- 16. 16 Ideal Gas Law Let’s recall the three gas laws: Boyle’s Law Charles’Law Avogadro’s Law Combining the three laws, you will get:
- 17. 17 V ∞ nT/ P Using the sign of equality will result to this equation: V= RnT/P or PV= nRT Where: V= volume in liters P= pressure in atmosphere n= mole T= temperature in Kelvin R=universal gas constant = 0.0821 L .atm/ mol.k
- 18. 18 Sample Problem: 1. What is the volume of the container that can hold 0.50 mole of gas at 25.0 oC and 1.25 atm? Try this: A 2.0g sample of dry ice (solid Carbon dioxide) is placed in an evacuated 3.5L vessel at 30oC. Compute for the pressure inside the vessel after all the dry ice has been converted to carbon dioxide gas. (2 significant figures)
- 19. 19 PERFORMANCE TASK #1 Solve the following problems 1. A chemist collected 56.1cm3 of gas in an open manometer. The next day, the chemist noted that the volume had changed to 57.9 cm3 and the barometer reading was 99.4 kPa. The temp. had not changed. What had been the barometer reading on the previous day when the gas was collected? 2. A 1.00 L balloon is filled with He 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?
- 20. 20 3. A balloon has a volume of 2500.0 mL on a day when the temperature is 30.0 OC. If the temperature at night falls to 10.0 OC, what will be the volume of the balloon if the pressure remains constant? 4. An 800.0 mL sample of nitrogen is warmed from 77OF to 86OF. What is its new volume if the pressure remains constant?
- 21. 21 5. A sample of helium gas has a pressure of 1.20 atm. At 22.0oC. At what Celsius temperature will the helium reach a pressure of 2.00 atm., assuming constant volume? 6. A gas balloon has a volume of 96.0 L when the temperature is 35oC and the pressure is 0.974 atm. What will be its volume at 21oC and 1.08 atmospheres? (3 significant figures)
- 22. 22 7. A sample of 0.500 moles NH3 gas had a volume of 235 mL. The temperature and pressure were held constant, and some NH3 was removed from the sample; its new volume was 175 mL. How many grams of NH3 were removed? (3 significant figures) 8. How many Ammonia (NH3) molecules are in 2.00 kg of NH3 gas at STP? (3 significant figures)
- 23. 23 9. The density of an unknown gas is 1.429 g/L at STP. Calculate its molecular mass.(2 Significant Figure) 10. Calculate the density of air at 22.0oC and 745 mmHg if its molecular mass is 29.0 g/mole. (2 Significant Figure)
- 24. 24 Rubrics: Given- 1 pt. Find- 1 pt. Formula – 1 pt. Solution- 1 pt. Final answer- 1 pt.
- 25. THANKS! ANY QUESTIONS? You can find me at: ⬥ aurelia.garcia001 ⬥ @deped.gov.ph 25