Q.Show that the rms velocity of an oxygen molecule is $\sqrt{2}$ times that of a sulfur dioxide molecule at S.T.P.

[!TLDR] v_rms ∝ 1/√M, and SO₂'s molar mass (64) is twice O₂'s (32). [!ANSWER] v_rms(O₂) = √ …

The rms speed of a gas is v_rms = sqrt(3RT/M0), where M0 is its molar mass. At the same temperature and pressure (S.T.P.), the ratio of rms speeds of two different gases depends only on the inverse square root of their molar masses: v_rms(O2)/v_rms(SO2) = sqrt(M0(SO2)/M0(O2)). The molar mass of O2 is 32 g/mol, and the molar mass of SO2 is 32 + 2(16) = 64 g/mol (S=32, two O at 16 each). So v_rms(O2)/v_rms(SO2) = sqrt(64/32) = sqrt(2). This confirms that the rms …

Use v_rms ∝ 1/√M0 at a fixed temperature, and compute the molar masses of O₂ (3 …

Using the wrong molar mass for SO₂ (forgetting it contains ONE sulfur plus TWO oxygen atoms …