Question 267: Thermodynamics & KTG

Question

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 $$=70.9 \mathrm{u}$$ )

Accepted Answer

The correct relationship between the rms speeds of the two gases is:
$$\frac{v_{\mathrm{Ar}}}{v_{\mathrm{Cl}}} = \sqrt{\frac{M_{\mathrm{Cl}}}{M_{\mathrm{Ar}}}}$$
Given the molar masses for argon and chlorine:
$$M_{\mathrm{Ar}} = 39.9 \mathrm{u}$$
$$M_{\mathrm{Cl}_2} = 70.9 \mathrm{u}$$
And the rms speed of chlorine molecules:
$$v_{\mathrm{Cl}} = 490 \mathrm{~m} / \mathrm{s}$$
We can now solve for the rms speed of argon molecules:
$$v_{\mathrm{Ar}} = \sqrt{\frac{70.9}{39.9}} 	imes 490$$
$$v_{\mathrm{Ar}} \approx 651.7 \mathrm{~m} / \mathrm{s}$$
The rms speed of argon molecules at the same temperature as the chlorine molecules is approximately $$651.7 \mathrm{~m} / \mathrm{s}$$.

Answer

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

Answer

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

Answer

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

Answer

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

Thermodynamics & KTG

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

Choose the correct answer: