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2.6.7: Kinetic Molecular Theory (Problems)

  • Page ID
    210669
  • PROBLEM \(\PageIndex{1}\)

    Using the postulates of the kinetic molecular theory, explain why a gas uniformly fills a container of any shape.

    Answer

    The first three parts of Kinetic Molecular Theory explain this:

    Gases are composed of molecules that are in continuous motion, travelling in straight lines and changing direction only when they collide with other molecules or with the walls of a container.

    The molecules composing the gas are negligibly small compared to the distances between them.

    The pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls.

    PROBLEM \(\PageIndex{2}\)

    Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.

    Answer

    Yes. At any given instant, there are a range of values of molecular speeds in a sample of gas. Any single molecule can speed up or slow down as it collides with other molecules. The average velocity of all the molecules is constant at constant temperature.

    PROBLEM \(\PageIndex{3}\)

    Describe what happens to the average kinetic energy of ideal gas molecules when the conditions are changed as follows:

    1. The pressure of the gas is increased by reducing the volume at constant temperature.
    2. The pressure of the gas is increased by increasing the temperature at constant volume.
    3. The average velocity of the molecules is increased by a factor of 2.
    Answer a

    Kinetic energy will not change (temperature is unchanged)

    Answer b

    Kinetic energy will increase (temperature is increased)

    Answer c

    The kinetic energy will increase by a factor of four (velocity is squared in the equation)

    PROBLEM \(\PageIndex{4}\)

    The distribution of molecular velocities in a sample of helium is shown in the photo below (Figure 7.4.4). If the sample is cooled, will the distribution of velocities look more like that of H2 or of H2O? Explain your answer.

    A graph is shown with four positively or right-skewed curves of varying heights. The horizontal axis is labeled, “Velocity v ( m divided by s ).” This axis is marked by increments of 500 beginning at 0 and extending up to 3000. The vertical axis is labeled, “Fraction of molecules.” The tallest and narrowest of these curves is labeled, “X e.” Its right end appears to touch the horizontal axis around 600 m per s. It is followed by a slightly wider curve which is labeled, “A r,” that is about half the height of the initial curve. Its right end appears to touch the horizontal axis around 900 m per s. The third curve is significantly wider and just over a third of the height of the initial curve. It is labeled, “N e.” Its right end appears to touch the horizontal axis around 1200 m per s. The final curve is only about one fourth the height of the initial curve. It is much wider than the others, so much so that its right reaches the horizontal axis around 2500 m per s. This curve is labeled, “H e.”

    Answer

    H2O. Cooling slows the velocities of the He atoms, causing them to behave as though they were heavier.

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