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Gas Laws and Kinetic Theory

Gas Laws and Kinetic Theory. Why do we need Gas Laws?. Although the expansion/contraction of solids (and liquids) are easily describe by the equations of thermal expansion, gasses are not.

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Gas Laws and Kinetic Theory

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  1. Gas Laws and Kinetic Theory

  2. Why do we need Gas Laws? • Although the expansion/contraction of solids (and liquids) are easily describe by the equations of thermal expansion, gasses are not. • Unlike solids and liquids that have fixed volume (if not shape), however, the volume of a gas conforms to the volume of the container. • The volume of gas is also highly dependent on external pressure, while this is not true for solids or liquids. • Gas will try to expand when heated, if it can not the pressure of the gas will increase in a effort to increase it’s volume.

  3. The Ideal Gas Law • The ideal Gas law is a combination of three different gas laws • Boyle’ Law • Charles's Law • Gay-Lussac’s Law • Charles's Law is where we developed the Kelvin unit for Temperature. • When working with gas laws the only unit for temperature you want to use is KELVIN.

  4. Where do Kelvin’s come from? • Charles’s law says that if a gas’s pressure is allowed to remain constant then… Volume a Temperature Volume (m3) Temp (OC)

  5. –273.15 OC But the smallest volume anything can have is 0 m3. This happens a a specific temperate of –273.15 OC. Volume (m3) Temp (OC) We can now extrapolate the line and see that a gas a a theoretical maximum that is undefined at an undefined temperature.

  6. And so for convenience we developed the unit of temperature known as a Kelvin. Which is simple a shifting of the Celsius scale so that a gas will a zero volume at a temperature of zero Kelvin. Volume (m3) K = OC + 273.15 0 K Temp (K)

  7. Getting the Ideal Gas Law Boyle’ Law [ P a 1/V at constant T] Charles's Law [ V a T at constant P] Gay-Lussac’s Law [P a T at constant V] Using Boyle’s Law: we can say that : PV a 1 (if T is constant) so that means (if T is constant) : PV = constant Although T is A CONSTANT it does not mean that is THE CONSTANT PV equals. But, PV will be proportional to it!! PV a T P1V1 P2V2 ------- = --------- T1 T2

  8. So we can now say: PV a nT Getting the Ideal Gas Law Part 2 The next part is to impart a little logic. Not only does the temperature molecules affect Pressure and Volume, but so should the number of Molecules that make up that gas. We often describe the number of molecules of a substance in moles Mass of substancegrams Moles = n = ----------------------------- Molecular Mass

  9. Getting the Ideal Gas Law part 3 All we need now is a constant to make the equation work. Like many constants it was found through experimentation and is called the universal gas constant (It works for all Ideal gases…it’s universal) universal gas constant = R = 8.315 Joules/(Mole*Kelvin) So the ideal gas law is: Pressure*Volume = Moles*universal gas constant*Temperature Kelvin PV = nRT

  10. Unit Warning • When working the Ideal gas law in PV = nRT form the following units MUST be used (unless you convert R) • Pressure must be in Pa (N/m2) • Volume must be in m3 • Temperature must be in K • When working the ideal gas law in (P1V1/T1) = (P2V2/T2) • Pressure may be in any unit (The conversions cancel) • Volume may be in any unit (The conversions cancel) • Temperature must be in K (The conversions will not cancel)

  11. Reason why P is proportional to T • The higher the temperature a gas is the more kinetic energy each of the gas’s molecules have, this means that they are moving inside the container faster then if they where cool. • These molecules hit the container harder and more often then if they were cool, resulting in a higher pressure on the conation trying to hold the gas.

  12. Kinetic Theory • Kinetic Theory states that the atoms that make up matter are in continual random motion. And for gases the atom’s Kinetic energy is dependant on its Temperature (in Kelvin) • To get this to work we need to make 4 assumptions about the gas.

  13. The Assumptions of Kinetic theory • There are a large number of molecules moving in random directions with varying speeds. • On Average the molecules are very far apart from one another. • The Molecules must obey the classical laws of physics, and are so far way from each other that any attractive/repelling force is negligible. • All collisions involving the gas’s molecules are perfectly elastic.

  14. The EK and T relationship • To find the relationship between the Ek of a single molecule and T we must first put the Ideal gas Law (PV = nRT) in terms of the number of molecules of the gas and not moles. • #molecules =(Moles)(Avogadro's number) • N = (n)(NA) = (n)(6.02*1023 molecules/mole)

  15. k = Boltzmann’s constant PV = nRT [ ] N k = R/NA PV = RT NA [ ] k = 1.38*10-23 J/K R PV = N T NA PV = NkT PV = N(1.38*10-23 J/K)T

  16. 3kT Vrms = m The Ek and T relationship part 2 average kinetic energy of a molecule = (3/2) (1.38*10-23 J/K) T Ek = (3/2)kT Since EK = (1/2) mv2

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