Question

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

Answer 1

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

Step-by-step explanation:

`v_{\text{rms}} \propto \sqrt{(3RT)/(M)`

if temperature is constant.

`v_{\text{rms}} \propto \sqrt{(1)/(M)`

if we are comparing two gases,

`(v_(2))/(v_(1)) = \sqrt{(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}(v_(2))/(v_(1)) & = & \sqrt{(M_(1))/(M_(2))}\\\\& = & \sqrt{(70.91)/(30.07)}\\\\& = & √(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}`