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Ideal Gas Law and Kinetic Theory

Ideal Gas Law and Kinetic Theory. Chapter 14. Atoms. helium.

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Ideal Gas Law and Kinetic Theory

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  1. Ideal Gas Law and Kinetic Theory Chapter 14

  2. Atoms helium Atomic number - the number of protonsAll atoms of an element have same number of protonsAtomic mass - mass of an atom Unified atomic mass units, 1 u = 1.6605 x 10-27kg 1 u = (1/12) mass of a C12 atom 1 u is about the mass of one proton or neutron

  3. number of particles number of moles Avogadro's number Amount of substance mole (mol) is the SI unit for the amount substance. One mole of a substance contains 6.02 x 1023 particles which is the number of atoms in 12 grams of C12 The number of particles in one mole is known as Avogadro’s number, NA.

  4. Calculating number of moles The grams of mass in one mole has the same numerical value as the substance's atomic mass or molecular mass in atomic mass units. How many moles are there in 36 grams of water H2O?One mole of water has a mass of 1g+1g+16g = 18 grams.

  5. Properties of an ideal gas constant volume An ideal gasis an idealized model for real gases. Real gases are very nearly ideal gases. For a constant volume, the pressure is proportional to the temperature. For a constant temperature, the pressure is inversely proportional to the volume. constant temperature The pressure is proportional to the amount of gas.

  6. N particles n moles R is the ideal gas constant k is Boltzmann’s constant Ideal gas law P absolute pressure in PaV absolute volume in m3T absolute temperature in Kn number of moles of gasN number of particles of gas

  7. Ideal gas law For cases where the amount of the gas remains constant. P in pascals V in meter3 T in kelvins You can find any missing value if you know the other 5 values. Variables that stay the same, mathematically cancel out . Knowing a variable stays the same reduces the number of things you need to know by two values, one initial value and one final value.

  8. Example Argon gas in a rigid container is heated from 20 °C to 80 °C. The initial absolute pressure was 150,000 Pa. What was the final pressure? (assume n is constant) Idea gas law Ti = 20 °C + 273 = 293 K and Tf = 80 °C + 273 = 353 K Since the container is rigid, Vf = Vi Increasing the temperature makes the pressure go up.

  9. Example A container with a moveable piston is filled with helium gas. Initially the gas has a volume of 0.2 m3, an absolute pressure of 200 kPa, and a temperature of 300 K. The gas is expanded to a volume of 0.8 m3. Then the gas is heated to a temperature of 600 K. What is the final pressure of the gas? (assume n is constant) Idea gas law An increase in the volume by a factor of 4 reduces the pressure by a factor of 4 from 200 kPa to 50 kPa, but an increase in the temperature by a factor of 2 increases the pressure by a factor of 2 from 50 kPa to 100 kPa.

  10. Kinetic theory of gases The particles in a gas are in constant, random motion and are colliding with each other and with the walls of the container. Each collision changes a particle’s speed. As a result, the atoms and molecules all have different speeds and different kinetic energies. The average kinetic energy of the particles is proportional to the absolute temperature of the gas. Kinetic Theory Average KE of particles Internal energy of a gas

  11. The End

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