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# Kinetic molecular theory

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### Kinetic molecular theory

1. 1. Kinetic Molecular Theory  Explains the behavior of gases
2. 2. POSTULATES: Gases are composed of a many particles that behave like hard spherical objects in a state of constant, random motion These particles move in a straight line until they collide with another particle or the walls of the container These particles are much smaller than the distance between particles, therefore the volume of a gas is mostly empty space and the volume of the gas molecule themselves is negligible
3. 3.  There is no force of attraction between gas particles or between the particles and the walls of the container  Collisions between gas particles or collisions with the walls of the container are elastic. That is, none of the energy of the gas particle is lost in a collision. The average kinetic energy of a collection of gas particles is dependent only upon the temperature of the gas  The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else
4. 4. Kinetic Energy  The energy of motion  Directly proportional to the mass of the object and to square of its velocity KE = _1_ mv2 2 where m = mass v = velocity
5. 5. GAS LAWS:  Gases have various properties which we can observe with our senses, including the gas pressure, temperature, mass, and the volume which contains the gas  Scientific observation has determined that these variables are related to one another, and values of these properties determine the state of the gas
6. 6.  Pressure in a closed container changes if 1.temperature changes 2.number of molecules increases or decreases 3.volume changes
7. 7.  Using the Kinetic Molecular Theory to explain the Gas Laws  The Relationship Between P and n  Boyle's Law  Amonton's Law  Charles' Law  Avogadro's Hypothesis  Dalton's Law of Partial Pressures
8. 8. Relationship between P and n  Pressure (P) is the force exerted on the walls of the container during a collision  An increase in the number of particles (n) increases the frequency of collisions with the walls  Therefore, P increases as n increases.
9. 9. Boyle’s Law  By Robert Boyle (1600s) - observed that the product of the pressure and volume are observed to be nearly constant p (V) = C Compressing a gas makes the V smaller but does not alter the average KE of the molecules since temperature is constant Though the speed of the particles remains constant, the frequency of collisions increases because the container is smaller  Therefore, P increases as V decreases.
10. 10. Key Points: •Temperature and moles of gas are constant •Graph is hyperbolic and asymptotic to both axes •Pressure and volume are inversely proportional to each other
11. 11. Equation: P1V1 = P2V2 where P1 is the pressure of a quantity of gas with a volume of V1 P2 is the pressure of the same quantity of gas when it has a volume V2
12. 12. Example: 1. Given a container of air with an initial volume of 28 L and pressure of 40 Pa, calculate the pressure if the volume is changed to 141 L. 2. Sulfur dioxide (SO2) gas is a component of car exhaust and power plant discharge, and it plays a major role in the formation of acid rain. Consider a 3.0 L sample of gaseous SO2at a pressure of 1.0 atm. If the pressure is changed to 1.5 atm at a constant temperature, what will be the new volume of the gas? 3. Find the pressure on 5.25 L of gas that was originally 3.12 L at 1.54 atm
13. 13. CHARLE’S LAW  By Jacques Charles The average KE of a gas particle is proportional to T  Since mass is constant, the average velocity of the particles must increase (KE = 1/2mv2)  At higher velocity, the particles exert greater force which increases P  If the walls are flexible, they will expand to balance the atmospheric pressure outside  Therefore, V is directly proportional to T
14. 14. Key Points: • Pressure and moles of gas are constant • Graph is linear • Volume and temperature are directly proportional to each other
15. 15. Equation: _V1_ = V2_ T1 T2
16. 16. Example: 1. A 5.0 L vessel of gas is held at 25°C. What will be the new volume if the temperature is doubled? 2. What change in volume results if 60.0 mL of gas is cooled from 33.0 °C to 5.00 °C? 3. Given a container of helium gas with an initial volume of 496 L and temperature of 6.4 °C, calculate the volume if the temperature is changed to - 16.9 °C.
17. 17. Gay-Lussac’s Law  By Joseph Louis Gay-Lussac (1778-1850)  Key Points: -- Volume and moles of gas are constant -- Graph is linear (see below) -- Pressure and temperature are directly proportional to each other
18. 18. Equation: _P1_ = P2_ T1 T2
19. 19. Example: 1) 25.0 L of a gas is held in a fixed container at 1.25 atm at 20°C. What will be the pressure of the gas if the is increased to 35°C? 2) If a gas is cooled from 323.0 K to 273.15 K and the volume kept constant what final pressure would result if the pressure was 750.0 mm Hg?
20. 20. AMONTON’S LAW  The pressure of a gas is directly proportional to the Temperature (Kelvin) at a constant V and n
21. 21.  Absolute Zero – The temperature (-273.15 degrees C or 0 Kelvin) at which the volume and pressure of an ideal gas extrapolated to zero. -- Proposed by Joseph Lambert in 1779 Where: TK is measured in Kelvin T0C is measured in Celsius
22. 22. DALTON'S LAW OF PARTIAL PRESSURES Assumptions:  Gases must be unreactive and follow ideal gas behavior  the total pressure of a gas mixture is equal to the sum of the pressures of each individual gas  By John Dalton
23. 23. Example: 1. The pressure of a mixture of nitrogen, carbon dioxide, and oxygen is 150 kPa. What is the partial pressure of oxygen if the partial pressures of the nitrogen and carbon dioxide 100 kPA and 24 kPa, respectively? 2. A container holds three gases: oxygen, carbon dioxide, helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container?
24. 24. AVOGADRO’S HYPOTHESIS  By Amadeo Avogadro  The volume of a gas is directly proportional to the moles of the gas, n at constant P and T  The hypothesis that equal volumes of different gases at the same temperature and pressure contain the same number of particles
25. 25. Avogadro's law can be expressed by the formula: _Vi_ = _Vf_ ni nf Where: Vi = initial volume ni = initial number of moles Vf = final volume nf = final number of moles
26. 26. Example: 1. A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas?