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Q)

The average kinetic energy of 1.6 g $CH_4$ molecules at $27^{\large\circ}C$ is:

$(a)\;6.21\times10^{-15}erg\qquad(b)\;6.21\times10^{-15}J\qquad(c)\;6.21\times10^{-15}Cal\qquad(d)\;\text{None of these}$

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A)
Toolbox:
  • The behaviour of gases has been expressed in terms of various gas laws obtained experimentally i.e Boyle's law , Charles law , Pressure-temperature law , Dalton's law of partial pressure , Graham's law of diffusion and Avogadro's hypothesis . Later on Maxwell derived kinetic equation $PV = \large\frac{1}{3}mnu^2$ , theoretically by assuming the concept of molecules and their motion . The term u represents root mean square speed of molecule.
Average Kinetic Energy = $\large\frac{3\times n\times R\times T}{2\times Av.No}$
$=\large\frac{3\times0.1\times8.314\times10^7\times300}{2\times6.023\times10^{23}}$
$=6.21\times10^{-15} erg$
Hence Answer is (A)
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