(a) The average kinetic energy of a molecule of an ideal gas is 6.21 x 10⁻²¹ J.
(b) The total random kinetic energy of the molecule in 1 mole of this gas is 3,741.3 J.
(c) The RMS speed of the oxygen molecule is 215.25 m/s.
Average kinetic energy of ideal gas
The average kinetic energy of a molecule of an ideal gas is calculated as follows;
[tex]K .E = \frac{3}{2} K T[/tex]
Where;
- K is Boltzmann constant = 1.38066 x 10⁻²³ J/K
- T is temperature in Kelvin, = 27°c + 273 = 300 K
[tex]K.E = \frac{3}{2} \times (1.38 066 \times 10^{-23}) \times 300\\\\K.E = 6.21 \times 10^{-21} \ J[/tex]
Total random kinetic energy
The total random kinetic energy of the molecule in 1 mole of this gas is calculated as follows;
[tex]K.E = \frac{3}{2} nRT\\\\K.E = \frac{3}{2} (1) (8.314)(300)\\\\K.E = 3,741.3 \ J[/tex]
RMS of speed of oxygen molecule
The RMS speed of the oxygen molecule is calculated as follows;
[tex]K.E = \frac{1}{2} mV_{rms}^2\\\\V_{rms}^2 = \frac{2K.E}{m} \\\\V_{rms} = \sqrt{\frac{2 K.E}{m} }[/tex]
one mole of oxygen gas = 32 g = 0.032 kg
[tex]V_{rms} = \sqrt{\frac{2 \times 741.3 }{0.032} }\\\\V_{rms} = 215.25 \ m/s[/tex]
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