Answer:
[tex]\large \boxed{\text{54 $\, \%$ faster }}[/tex]
Explanation:
[tex]v_{\text{rms}} \propto \sqrt{\dfrac{3RT}{M}[/tex]
if temperature is constant.
[tex]v_{\text{rms}} \propto \sqrt{\dfrac{1}{M}[/tex]
if we are comparing two gases,
[tex]\dfrac{v_{2}}{v_{1}} = \sqrt{\dfrac{M_{1}}{M_{2}}}[/tex]
Let chlorine be Gas 1 and ethane be Gas 2
Data:
M₁ = 70.91 g/mol
M₂ = 30.07 g/mol
Calculation
[tex]\begin{array}{rcl}\dfrac{v_{2}}{v_{1}} & = & \sqrt{\dfrac{M_{1}}{M_{2}}}\\\\& = & \sqrt{\dfrac{70.91}{30.07}}\\\\& = & \sqrt{2.358}\\\\& = & \mathbf{1.54}\\\end{array}\\\text{Ethane molecules travel at 1.54 times the speed of chlorine molecules}\\\text{or $\large \boxed{\textbf{54 $\%$ faster }}$ than chlorine molecules}[/tex]
