2. Gases Chapter 13

3. Some basics Gases have properties that are very different from solids and liquids. Gases have properties that are very different from solids and liquids. They are very sensitive to changes in pressure and temperature and have low density. They are very sensitive to changes in pressure and temperature and have low density. Gases do have mass( although small). Gases do have mass( although small). Think of properties of gases when your ears pop while driving to Tahoe, deep-sea divers or your kid sister’s birthday balloons. Think of properties of gases when your ears pop while driving to Tahoe, deep-sea divers or your kid sister’s birthday balloons.

4. Pressure and Temperature Pressure of gases is usually denoted in atm or mmHg. Pressure of gases is usually denoted in atm or mmHg. 1atm =760 mmHg 1atm =760 mmHg 1atm =760 torr 1atm =760 torr Other units include Pascal and psi. Other units include Pascal and psi. Measured by a barometer Measured by a barometer Temperature of gases is measured in Kelvin Temperature of gases is measured in Kelvin Kelvin = °C +273 Kelvin = °C +273 Other unit for temperature is Fahrenheit. Other unit for temperature is Fahrenheit. Measured by a thermometer Measured by a thermometer

5. Kinetic Molecular Theory Volume of the molecules is negligible (zero) compared to the volume of the container. Volume of the molecules is negligible (zero) compared to the volume of the container. The molecules are colliding with the walls of the container and this causes the pressure of the gas. The molecules do not attract or repel each other. The molecules do not attract or repel each other. The average kinetic energy of the molecules is directly proportional to the Kelvin temperature.

6. Boyle’s Law When pressure of a gas is increased the volume of a gas decreases provided the temperature remains the same. When pressure of a gas is increased the volume of a gas decreases provided the temperature remains the same. PV = k (constant temperature) PV = k (constant temperature) Pressure and volume are inversely proportional Pressure and volume are inversely proportional Or as P goes up, V must go down to keep the above equation correct. Or as P goes up, V must go down to keep the above equation correct. is a relationship that helps us solve problems when conditions are changed for a gas. P 1 V 1 =P 2 V 2 is a relationship that helps us solve problems when conditions are changed for a gas.

7. Sample problem What is the new pressure if 0.500L of oxygen at pressure 0.87atm is changed to 0.750L at constant temperature? What is the new pressure if 0.500L of oxygen at pressure 0.87atm is changed to 0.750L at constant temperature? Solution Solution Since this is at constant temperature, Boyle’s law applies, Since this is at constant temperature, Boyle’s law applies, P 1 V 1 =P 2 V 2 P 1 = 0.87atm, V 1 = 0.500L, P 2 = ?,V 2 = 0.750L P 2 = P 1 V 1 = 0.87atm X 0.500 L = 0.58atm V 2 0.750 L

8. Practice problems The volume of a sample of hydrogen is 250.mL at 3.5 atm pressure. What will be the volume when the pressure is reduced to 0.75atm, assuming that temperature remains constant? The volume of a sample of hydrogen is 250.mL at 3.5 atm pressure. What will be the volume when the pressure is reduced to 0.75atm, assuming that temperature remains constant? 1200mL or 1.2 L The pressure of a 2.34L sample of helium is 785 torr. Calculate the pressure in atm if volume is decreased to 2.04L and temperature kept constant. The pressure of a 2.34L sample of helium is 785 torr. Calculate the pressure in atm if volume is decreased to 2.04L and temperature kept constant. 1.18 atm

9. Charles’s Law According to Charles’s Law, the volume of a gas increases when temperature increases, provided the pressure is kept constant. According to Charles’s Law, the volume of a gas increases when temperature increases, provided the pressure is kept constant. or when temperature increases, volume must Tincrease as well V = k or when temperature increases, volume must Tincrease as well V 1 = V 2 V 1 = V 2 all temperatures have to be in KELVIN scale!!!! T 1 T 2 T 1 T 2 This law can now be used to solve problems This law can now be used to solve problems

10. Sample problem The volume of a gas at 25ºC is 234mL. What will its volume be at 50ºC if pressure is kept constant? The volume of a gas at 25ºC is 234mL. What will its volume be at 50ºC if pressure is kept constant? Solution Solution 25ºC + 273 = 298K = T 1, V 1 = 234mL 25ºC + 273 = 298K = T 1, V 1 = 234mL 50ºC + 273 = 323K = T 2, V 2 = ? 50ºC + 273 = 323K = T 2, V 2 = ? V 1 = V 2, V 2 = V 1 X T 2 V 1 = V 2, V 2 = V 1 X T 2 = 234mL X 323K = 254mL T 1 T 2 T 1 298K T 1 T 2 T 1 298K

11. Practice problems A gas occupies 670mL at 45ºC. At what temperature (in ºC) will it occupy 750mL if pressure is kept unchanged? A gas occupies 670mL at 45ºC. At what temperature (in ºC) will it occupy 750mL if pressure is kept unchanged? 83ºC 83ºC If methane gas occupies 58.0L at 17ºC, what volume will it occupy at 27ºC if pressure is left the same? If methane gas occupies 58.0L at 17ºC, what volume will it occupy at 27ºC if pressure is left the same? 60.L 60.L

12. Avogadro’s Law When the number of moles of gas increases, the volume increases too (duh!!) When the number of moles of gas increases, the volume increases too (duh!!) V = k (at constant temperature and V = k (at constant temperature and n pressure) n pressure) V 1 = V 2 V 1 = V 2 n 1 n 2 n 1 n 2 This above equation can be used to solve problems. This above equation can be used to solve problems.

13. Problems If 6 moles of oxygen occupies 23L how many L will 3.67moles occupy at constant temperature and pressure? If 6 moles of oxygen occupies 23L how many L will 3.67moles occupy at constant temperature and pressure? V 1 = V 2 V 1 = V 2 n 1 n 2 n 1 n 2 V 2 = V 1 X n 2 = 23L X 3.67moles = 14L V 2 = V 1 X n 2 = 23L X 3.67moles = 14L n 1 6 moles n 1 6 moles

14. Ideal Gas An ideal gas is one whose molecules are not attracted to each other and the volume occupied by each molecule is too small to matter. An ideal gas is one whose molecules are not attracted to each other and the volume occupied by each molecule is too small to matter. Most gases behave ideally at high temperatures and low pressures. Most gases behave ideally at high temperatures and low pressures. Gases are not ideal when compressed or cooled down. Gases are not ideal when compressed or cooled down.

15. Ideal Gas Law If we combine all the three gas laws (Boyle’s, Charles’s and Avogadro's) we get the ideal gas law: If we combine all the three gas laws (Boyle’s, Charles’s and Avogadro's) we get the ideal gas law: PV =nRT where R =0.08206 L.atm PV =nRT where R =0.08206 L.atm K.mol K.mol If any three of the properties are known the fourth can be calculated. This equation has some limits, can be used only in low pressures and high temperatures. If the pressure goes up or temperature decreases, corrections need to be applied.

16. Problems What volume is occupied by 0.250mol of CO 2 at 25°C and 371torr? What volume is occupied by 0.250mol of CO 2 at 25°C and 371torr? PV =nRT PV =nRT P = 371/760 = 0.488atm P = 371/760 = 0.488atm T = 298K R =0.08206 L.atm T = 298K R =0.08206 L.atm K.mol K.mol V= nRT =.250mol X 298K X.08206 L.atm V= nRT =.250mol X 298K X.08206 L.atm P 0.488 atm K.mol P 0.488 atm K.mol = = 12.5L

17. Practice A 1.5mol of radon gas has a volume of 21.0L at 33°C. What is the pressure of the gas? A 1.5mol of radon gas has a volume of 21.0L at 33°C. What is the pressure of the gas? 1.8atm What is the mass of oxygen needed to fill a tank of volume 22.7L at temperature 34°C and pressure 1.5 atm? What is the mass of oxygen needed to fill a tank of volume 22.7L at temperature 34°C and pressure 1.5 atm? 43.3g

18. Combined Gas Law We can use the combined gas law if the conditions of pressure, volume or temperature for the same amount of gas are altered. We can use the combined gas law if the conditions of pressure, volume or temperature for the same amount of gas are altered. P 1 V 1 = P 2 V 2 T 1 T 2 Temperature must be in Kelvin !!!!

19. Sample problem A sample of neon gas has a volume of 27.5mL at 22.0°C and 740. torr pressure. What will its volume be at temperature 15.0°C and pressure 755 torr? A sample of neon gas has a volume of 27.5mL at 22.0°C and 740. torr pressure. What will its volume be at temperature 15.0°C and pressure 755 torr? P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2 740.torr X 27.5mL = 755torr X V 2 740.torr X 27.5mL = 755torr X V 2 295K 288K 295K 288K V 2 =26.3mL V 2 =26.3mL

20. Dalton’s Law of partial pressures According to Dalton’s law the pressure of a mixture of gases is related to the number of moles of the gas in the mixture. According to Dalton’s law the pressure of a mixture of gases is related to the number of moles of the gas in the mixture. P total = p 1 +p 2 + p 3 +….. P total = p 1 +p 2 + p 3 +….. n total = n 1 + n 2 + n 3 + ….. n total = n 1 + n 2 + n 3 + ….. P total V =n total RT P total V =n total RT

21. Problem A 6.00L tank contains 32.0g of oxygen gas and 18.02g of water vapor. At 20°C what is the total pressure of the tank? A 6.00L tank contains 32.0g of oxygen gas and 18.02g of water vapor. At 20°C what is the total pressure of the tank? 32.0g = 1.00mol O 2 ; 18.02g = 1.00mol H 2 O 32.0g = 1.00mol O 2 ; 18.02g = 1.00mol H 2 O n total = 1.00 + 1.00 = 2.00mol n total = 1.00 + 1.00 = 2.00mol P total = n total RT = 2.00* 0.0821* 293K = P total = n total RT = 2.00* 0.0821* 293K = 8.01atm V 6.00L

22. Practice If a 23.0L tank contains 3.00mol of H 2, 2.00mol of He and 1.00mol of Ne gases, calculate the total pressure of the tank at 40°C? Calculate the partial pressure of each gas as well. If a 23.0L tank contains 3.00mol of H 2, 2.00mol of He and 1.00mol of Ne gases, calculate the total pressure of the tank at 40°C? Calculate the partial pressure of each gas as well. P total = 6.7atm p H2 = 3.35atm p He = 2.23atm p Ne = 1.12atm

23. Gas Stoichiometry First write a balanced chemical equation. First write a balanced chemical equation. Calculate moles of given Calculate moles of given Calculate moles of asked Calculate moles of asked Calculate volume of gas produced Calculate volume of gas produced MOLES OF GIVEN MOLES OF ASKED n Grams of Given V=nRT P Mole ratio

24. Sample problem Calculate the volume of NH produced when 43g of N reacts with excess H at 29°C and 0.997atm pressure. Calculate the volume of NH 3 produced when 43g of N 2 reacts with excess H 2 at 29°C and 0.997atm pressure. NHNH N 2 + 3H 2 2NH 3 NH 43g X 1molN 2 X 2mol NH 3 = 3.07mol NH 3 28.02g 1molN 2 V = nRT = 3.07mol* 0.0821* 302K = 76. L P 0.997atm

25. Practice problem Calculate the volume of oxygen produced from the decomposition of 6.00g of KClO 3 to KCl and O 2 at 30.0°C and 100.kPa pressure. Calculate the volume of oxygen produced from the decomposition of 6.00g of KClO 3 to KCl and O 2 at 30.0°C and 100.kPa pressure. 1.85L

26. Graham’s Law of Diffusion According to Graham’s law, the rates of diffusion of two gases is inversely proportional to the square root of their molar masses. In other words, lighter gases travel faster under similar conditions of temperature. Rate A = √molar mass B Rate B √ molar mass A

27. Practice Find the molar mass of a gas that diffuses 0.31 times as fast as oxygen gas. Find the molar mass of a gas that diffuses 0.31 times as fast as oxygen gas. If oxygen travels at a rate of 1, then the other gas travels at 0.31, If oxygen travels at a rate of 1, then the other gas travels at 0.31, Rate O 2 = √molar mass gas Rate O 2 = √molar mass gas Rate gas √molar mass O 2 Rate gas √molar mass O 2 1 = √molar mass gas 1 = √molar mass gas 0.31 √32.0g/mol molar mass gas = 330 g/mol

28. Suppose a gas diffuses 1.41 times faster than sulfur dioxide. What is the molar mass of this gas? Suppose a gas diffuses 1.41 times faster than sulfur dioxide. What is the molar mass of this gas? Rate gas =√64.0g/mol Rate gas =√64.0g/mol Rate SO 2 √molar mass gas Rate SO 2 √molar mass gas 1.41 = √64.0g/mol 1.41 = √64.0g/mol √ molar mass gas √ molar mass gas molar mass gas = 32.2g/mol molar mass gas = 32.2g/mol