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Worksheet 4C: Kinetic Molecular Theory

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    What are the primary assumptions underlying the ideal gas laws? Are these assumptions always true?


    For the following speed measured for individual gas molecules, calculate the root mean square speed and the average speed:

    30.4 m/s, 32.1 m/s, 38.2 m/s, 42.5 m/s, 29.0 m/s, 39.1 m/s, 12.6 m/s, 40.1 m/s, 101 m/s


    Consider two gases, \(A\) and \(B\), in separate 1.0 L containers at the same temperature and pressure. The total mass of gas \(A\) in the container is 0.25 g and the mass of gas \(B\) in the container is 0.51 g.

    1. Which sample has the most number of molecules?
    2. Which sample has the largest average kinetic energy?
    3. Which sample has the fastest average speed?
    4. How can the pressure in the two containers be equal to each other since the larger gas \(B\) molecules collide with the container walls more forcefully?


    Complete the following table. In general, how does the root mean square speed and average translational kinetic energy change with increasing molecular mass of the gas and increasing temperature of the gas?

    Gas Molecular Mass Temperature Average Translational Kinetic Energy Root Mean Square Speed
    \(CH_4\) 5°C
    \(CH_4\) 112°C
    \(N_2\) 5°C
    \(N_2\) 112°C


    A 100 L flask contains a mixture of methane and argon at 27°C. The mass of the argon present is 245 g and the mole fraction of methane in the mixture is 0.623. Calculate the total kinetic energy of the gaseous mixture.


    Identify if the following statements are true or false in regards to the following distributions of speeds found for different gasses at different temperatures.

    BoltzDist.png BolzDist-MW.gif

    Figure: (left) The distributions of \(N_2\) at differing temperatures. (right) The distribution of different gasses at the room temperature.

    1. The distributions are symmetrical
    2. The more massive the particle the faster the speeds.
    3. The lower the temperature the slower the average speed.
    4. Broader distributions are caused by higher temperatures and heavier particles.


    Draw examples and explain effusion and diffusion.


    Freon-12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass = 137.4 g/mol) is 1.07:1. Which formula is correct for Freon-12: \(CF_4\), \(CF_3Cl\), \(CF_2Cl_2\), \(CFCl_3\), or \(CCl_4\). Hint: use Graham's Law of Effusion.


    The rate of effusion of a particular gas was measured to be 27.2 mL/min. Under the same conditions, the rate effusion of pure methane gas (\(CH_4\)) is 47.8 mL/min. What is the molar mass of the unknown gas? (Hint: Use Graham's Law of Effusion).

    Worksheet 4C: Kinetic Molecular Theory is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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