Question

How much faster does ethane (C2H6) gas travel compared to chlorine gas?

Answer 1

Answer:

$\large \boxed{\text{54 \, \% faster }}$

Explanation:

$v_{\text{rms}} \propto \sqrt{\dfrac{3RT}{M}$

if temperature is constant.  

$v_{\text{rms}} \propto \sqrt{\dfrac{1}{M}$

if we are comparing two gases,

$\dfrac{v_{2}}{v_{1}} = \sqrt{\dfrac{M_{1}}{M_{2}}}$

Let chlorine be Gas 1 and ethane be Gas 2

Data:

M₁ =  70.91 g/mol

M₂ = 30.07 g/mol

Calculation

$\begin{array}{rcl}\dfrac{v_{2}}{v_{1}} & = & \sqrt{\dfrac{M_{1}}{M_{2}}}\\\\& = & \sqrt{\dfrac{70.91}{30.07}}\\\\& = & \sqrt{2.358}\\\\& = & \mathbf{1.54}\\\end{array}\\\text{Ethane molecules travel at 1.54 times the speed of chlorine molecules}\\\text{or \large \boxed{\textbf{54 \% faster }} than chlorine molecules}$