Question

If ch4 and c4h8 are released simultaneously at ends of a 50.0cm long glass tube, at what distance from the left end of the tube will they meet

Answer 1

Answer:

They meet at the distance of 32.5 cm

Explanation:

The rate of diffusion is inversely proportional to the molar mass of gases.

If diffusion is represented as d and mass of gases as M. Then , rate is given as:

$d=k\sqrt{\frac{1}{M}}$

For , two gases

$\frac{d_{1}}{d_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}$

First , Calculate the ,molar mass of each gas :

CH4 = 1 (mass of C) + 4(mass of H)

= 1(12)+4(1)

= 12 + 4 = 16 gram

M1 = 16 gram

C4H8 = 4(mass of C) + 8(Mass of H)

= 4(12) + 8(1)

= 48 + 8

M2 = 56 grams

d1 is diffusion of CH4

d2 = diffusion of C4H8

$\frac{d_{1}}{d_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}$

$\frac{d_{1}}{d_{2}}=\sqrt{\frac{56}{16}$}

$\frac{d_{1}}{d_{2}} = 1.87$

This means CH4 diffuse 1.87 times faster than C4H8

Now, the mathematical part

If velocity of C4H8 = 1 cm/sec , then velocity of CH4 = 1.87 cm/sec

v1 = 1.87 cm/sec

v2 = 1 cm/sec

Let both meet at time "t". If distance travelled by CH4(s1) = x , then remaining(s2) distance (50-x) is travelled by C4H8

(see the attached image)

$time =\frac{distance}{speed}$

since both meet at same time so t = constant.

$\frac{s1}{v1}=\frac{s2}{v2}$

$\frac{x}{1.87}\frac{50-x}{1.00}$

on solving for x we get,

x = 17.42 cm

from the other side the distance is (50 - x)

= 50 - 17.42 = 32.5 cm