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 $=70.9 \mathrm{u}$ )
Solution
The correct relationship between the rms speeds of the two gases is:
<br/><br/>
$$\frac{v_{\mathrm{Ar}}}{v_{\mathrm{Cl}}} = \sqrt{\frac{M_{\mathrm{Cl}}}{M_{\mathrm{Ar}}}}$$
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Given the molar masses for argon and chlorine:
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$M_{\mathrm{Ar}} = 39.9 \mathrm{u}$<br/><br/>
$M_{\mathrm{Cl}_2} = 70.9 \mathrm{u}$
<br/><br/>
And the rms speed of chlorine molecules:
<br/><br/>
$v_{\mathrm{Cl}} = 490 \mathrm{~m} / \mathrm{s}$
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We can now solve for the rms speed of argon molecules:
<br/><br/>
$v_{\mathrm{Ar}} = \sqrt{\frac{70.9}{39.9}} \times 490$
<br/><br/>
$v_{\mathrm{Ar}} \approx 651.7 \mathrm{~m} / \mathrm{s}$
<br/><br/>
The rms speed of argon molecules at the same temperature as the chlorine molecules is approximately $651.7 \mathrm{~m} / \mathrm{s}$.
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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