Question

A) Find the gas speed of ethane at 200.0 degrees Celsius. ____________

b) What is the rate of effusion of ethane (C2H6) compared to hexane (C6H14) gas at the same temperature? _________________

Answer 1

a. 627.1 m/s

b. the rate of effusion of ethane = 1.7 faster than hexane

Further explanation

Given

T = 200 + 273 = 473 K

Required

a. the gas speed

b. The rate of effusion comparison

Solution

a.

Average velocities of gases can be expressed as root-mean-square averages. (V rms)

`\large {\boxed {\bold {v_ {rms} = \sqrt {\frac {3RT} {Mm}}}}`

R = gas constant, T = temperature, Mm = molar mass of the gas particles

From the question

R = 8,314 J / mol K

T = temperature

Mm = molar mass, kg / mol

Molar mass of Ethane = 30 g/mol = 0.03 kg/mol

`\tt v=\sqrt{(3* 8.314* 473)/(30) }=627.1~m/s`

b. the effusion rates of two gases = the square root of the inverse of their molar masses:

`\rm (r_1)/(r_2)=\sqrt{(M_2)/(M_1) }`

M₁ = molar mass ethane =30

M₂ = molar mass hexane = 86

`\tt (r_1)/(r_2)=\sqrt{(86)/(30) }=1.7`

the rate of effusion of ethane = 1.7 faster than hexane