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If the r. m. s speed of chlorine molecule is 490 \mathrm{~m} / \mathrm{s} at 27^{\circ} \mathrm{C}, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon =39.9 \mathrm{u}, molecular mass of chlorine =70.9 \mathrm{u})

Option: 1

651.7 \mathrm{~m} / \mathrm{s}


Option: 2

451.7 \mathrm{~m} / \mathrm{s}


Option: 3

551.7 \mathrm{~m} / \mathrm{s}


Option: 4

751.7 \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

The molar mass of chlorine = 70.9 u

Atomic mass of argon = 39.9 u

\begin{aligned} & \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{m}}} \\ & \mathrm{V}_{\mathrm{rms}} \propto \sqrt{\frac{1}{\mathrm{~m}}} \\ & \frac{\mathrm{V}_{\text {rms chlorine }}}{\mathrm{V}_{\text {rms argon }}}=\sqrt{\frac{\mathrm{m}_{\text {argon }}}{\mathrm{m}_{\text {chlorine }}}} \\ & \frac{490}{\mathrm{~V}_{\mathrm{rms } \text { argon }}}=\sqrt{\frac{39.9}{70.9}} \\ & \mathrm{~V}_{\text {rms argon }}=490 \times 1.33 \\ & \mathrm{~V}_{\text {rms argon }}=651.7 \mathrm{~m} / \mathrm{sec} \\ & \end{aligned}

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Ritika Kankaria

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