Kinetic Molecular Theory Gas!

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The average speeds are the same If you have a bottle with Helium (red) & Nitrogen (blue) at room temperature, how do the speed of the particles compare? All have same speed The average speeds are the same Helium particles have greater average speed Nitrogen particles have greater average speed Use Gas Properties to show C is correct

Light and heavy gas at same temperature 300K Speed of each particle varies!!

What happens if you add energy using the heater? All atoms speed up All atoms speed up about the same The lighter ones speed up more The heavier ones speed up more A is the best answer, b is not true, the other options depend on how you define “more”, see next slide

687-411= 276 1516-1172= 344 nor does it just add. 687/411=1.67 1516/1172= 1.3 So the light species doesn’t change by the same factor 687-411= 276 1516-1172= 344 nor does it just add. answer

Which is most likely oxygen gas? C discussion how do you know? A B C

Kinetic Theory is based on an ideal gas model Kinetic Theory is based on an ideal gas model. The following statements about the ideal gas are true EXCEPT: All molecules move with the same speed The average molecular kinetic energy is directly proportional to the absolute temperature All molecules make elastic collisions with each other and the walls of the container The attractive force between the molecules can be ignored Two boxes of equal volume each contain the same quantity of an ideal gas. The first box is much warmer than the second box. Which of the following statements MUST be true? (select 2 answers) The pressure in the first box is greater than the pressure in the second box There are more molecules in the first box than in the second box The boxes contain different types of gasses The molecules in the first box have a higher average kinetic energy than those in the second box

Kinetic Molecular Theory summary: Matter is made up of particles having negligible mass are in constant random motion (vibrate, rotate, translate) The particles are separated by great distances The particles collide perfectly elastically (there are no forces acting except during the collision) The temperature of a substance is related to the molecular velocity.

What about the speeds of the molecules in an ideal gas…… This molecule has an average speed This one has a different average speed What about the Kinetic Energy of a gas molecule? m v KE = ½mv2 What about the average Kinetic Energy of a group of gas molecules? KE = ½mvrms2

Kinetic Theory B Average KE of an ideal gas molecule Temperature is a measure of the average molecular kinetic energy (k = Boltzmann’s constant = 1.38 x 10-23 J/K) Kelvin temperature So now you can relate the mass, speed, and temperature of molecules in an ideal gas: B Temperature is simply a measure of the average Kinetic Energy of the molecules of a substance. A single molecule has no temperature since temperature is an averaging effect.

Helium gas is sealed in a container Helium gas is sealed in a container. The container is heated, causing the temperature to increase at a constant rate. Which of the following statements is NOT true? The pressure of the gas increases at a constant rate Temperature of the gas increases at a constant rate The average kinetic energy of the gas particles increases at a constant rate The average speed of the gas particles increases at a constant rate

Maxwell Distribution Curves

The internal energy of an ideal gas depends only on its temperature The internal energy of an ideal gas depends only on its temperature. Therefore, the change in internal energy of a fixed amount of ideal gas (n moles) is given by: Units: Joules (J) R = 8.31 J/mol K (U  T for any ideal gas)

Three containers are filled with 1 kg of each: water, ice, and water vapor at the same temperature T = 0°C. Which of the following is true about the internal energy of the substances? (A) U water > U ice > U vapor (B) U water = U ice = U vapor (C) U water < U ice < U vapor (D) U ice < U water < U vapor

Or solve using (easier) ~ Suppose you want the Vrms speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? What is the total random kinetic energy of all the molecules in one mole of hydrogen at a temperature of 300 K. Or solve using (easier) ~

If 2. 0 mol of an ideal gas are confined to a 5 If 2.0 mol of an ideal gas are confined to a 5.0 L vessel at a pressure of 8.0 x 105 Pa, what is the average kinetic energy of a gas molecule? Temperature of the gas: Kinetic energy:

At 300 K could any He atoms have kinetic energy greater than their potential energy due to Earth's gravity? Yes No This is the reason why there is very little helium left in Earth’s atmosphere