Question

the r.m.s speed of oxygen molecule at a certain temperature T is C.If the temperature is doubled oxygen gas dissociates in to atomic oxygen what is the changed r.m.s speed?

Answer 1

$$\begin{gathered} \mathbf{RMS}\mathbf{}\mathbf{Speed}\mathbf{}\mathbf{of}\mathbf{}\mathbf{a}\mathbf{}\mathbf{gas}\mathbf{:} \\ \mathrm{The}\mathrm{rms}\mathrm{speed}\mathrm{of}\mathrm{a}\mathrm{gas}\mathrm{is}\mathrm{directly}\mathrm{proportional}\mathrm{to}\mathrm{square}\mathrm{root}\mathrm{of}\mathrm{its}\mathrm{absolute}\mathrm{temperaure}. \\ \mathrm{v}\mathrm{\alpha }\sqrt{\mathrm{T}} \\ \frac{{\mathrm{v}}_2}{{\mathrm{v}}_1}=\sqrt{\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}} \\ {\mathrm{v}}_2={\mathrm{v}}_1\sqrt{\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}} \\ =\mathrm{C}\sqrt{\frac{2{\mathrm{T}}_1}{{\mathrm{T}}_1}} \\ =\sqrt{2}\mathrm{C} \end{gathered}$$