10.5: Kinetic Molecular Theory of Gases

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Kinetic Molecular Theory

Exercise \(\PageIndex{1}\)

Which of the following statements is/are postulates of the kinetic–molecular theory of gases?

Gas particles are in constant, random motion.
The distance between gas particles is large in comparison to their size.
The average kinetic energy of gas particles is proportional to the kelvin temperature of the gas.

a. 1 only b. 2 only c. 3 only d. 1 and 2 e. 1, 2, and 3

Answer: e. 1, 2, and 3

Exercise \(\PageIndex{2}\)

Calculate the root-mean-square velocity for the O₂ molecules in a sample of O₂ gas at 35.9°C. (R = 8.3145 J/K⋅mol)

Answer

2.41*10⁵ J*kg^-1

\(v = \sqrt{\frac{3RT}{M}}\)

R = 8.314 J/K*mol; T = 35.9 + 273.15 = 309.05 K; M = (O₂) = 32*10^-3 kg/mol

\(v = \sqrt{\frac{3*8.3145*309.05}{32*10-3}}=2.408*10^{5}\;J*kg^{-1}\)

Exercise \(\PageIndex{3}\)

Place the following gases in order of increasing average velocity at 300 K: Ar, CH₄, N₂, and N₂O.

Answer: N₂O < Ar < N₂ < CH₄

Exercise \(\PageIndex{4}\)

At STP, as the molar mass of the molecules that make up a pure gas increases, the

root mean square speed of the molecules increases.
root mean square speed of the molecules decreases.
root mean square speed of the molecules remains constant.
root mean square speed increases to a maximum, then decreases.
none of the above.

Answer: b. root mean square speed of the molecules decreases.