Q8 / 180 · KCET 2007 · Chemistry

One mole of oxygen at $273 \mathrm{~K}$ and one mole of sulphur dioxide at $546 \mathrm{~K}$ are taken in two separate containers, then,

  • A
    kinetic energy of $\mathrm{O}_{2}>$ kinetic energy of $\mathrm{SO}_{2}$
  • Correct answer
    B
    kinetic energy of $\mathrm{O}_{2} < $ kinetic energy of $\mathrm{SO}_{2}$
  • C
    kinetic energy of both are equal
  • D
    None of the above

Solution

$\mathrm{KE}=\frac{3}{2} R T$ $\mathrm{KE} \propto T$ $$ \begin{aligned} & \frac{\mathrm{KE}_{\mathrm{O}_{2}}}{\mathrm{KE}_{\mathrm{SO}_{2}}}=\frac{T_{\mathrm{O}_{2}}}{T_{\mathrm{SO}_{2}}}=\frac{273}{546}=\frac{1}{2} \\ \mathrm{KE}_{\mathrm{SO}_{2}} &=2 \mathrm{KE}_{\mathrm{O}_{2}} \\ \therefore \quad \mathrm{KE}_{\mathrm{SO}_{2}} &>2 \mathrm{KE}_{\mathrm{O}_{2}} \end{aligned} $$

Hence, the correct answer is option: 'B'.

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