Three closed vessels \(A, B\) and \(C\) are at the same temperature \(T\) and contain gases. Vessel \(A\)…
Three closed vessels \(A, B\) and \(C\) are at the same temperature \(T\) and contain gases. Vessel \(A\) contains only \(\mathrm{O}_2, B\) contains only \(\mathrm{N}_2\) and \(\mathrm{C}\) contains a mixture of equal quantities of \(\mathrm{O}_2\) and \(\mathrm{N}_2\). If the rms speed of \(\mathrm{O}_2\) molecules in vessel \(A\) is \(v_1\) and that of \(\mathrm{N}_2\) molecules in vessel \(B\) is \(v_2\) then the rms speed of \(\mathrm{O}_2\) molecules in vessel \(\mathrm{C}\) is
\(\left(\frac{v_1+v_2}{2}\right)\)
\(v_1\)
\(\left(v_1 v_2\right)\)
\(\frac{v_1}{2}\)
Solution
Key Idea Root mean square velocity of any gas is given by
\(v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}\)
Where, \(M=\) molecular weight.
As, rms speed of any gas is depends on the temperature of gas and molecular weight of gas.
In a mixture of gases (say \(\mathrm{N}_2\) and \(\mathrm{O}_2\) ) at a constant temperature, rms speed is independent to the quantity (moles) of gas present in the gas mixture. So, in this problem the rms speed of \(\mathrm{O}_2\) in vessel \(C\) is \(v_1\).
Hence, the correct option is (b).