Question

In a gas-phase diffusion mass-transfer process, the steady-state flux of helium in a binary mixture of helium and neon is 3.8 x 10-9 kgmole/cm2 s, and the flux of neon is 0. At a particular point in the diffusion space, the concentration of helium is 0.023 kgmole/m3 and the concentration of neon is 0.045 kgmole/m3 . Estimate the individual net velocities of helium and neon along the direction of mass transfer, the average molar velocity, and the average mass velocity.''

Answer 1

In a gas-phase diffusion mass-transfer process, the individual net velocities of helium and neon can be estimated using Fick's laws of diffusion.

Step-by-step explanation:

In a gas-phase diffusion mass-transfer process, the individual net velocities of helium and neon can be estimated using Fick's laws of diffusion. According to Fick's laws, the net velocity of a gas species is proportional to its concentration gradient. Since the flux of neon is 0, its individual net velocity is also 0.

The individual net velocity of helium can be calculated by dividing its flux by its concentration gradient:

Net Velocity of Helium = Flux of Helium / Concentration Gradient of Helium

The average molar velocity can be calculated by dividing the sum of the individual net velocities of helium and neon by 2:

Average Molar Velocity = (Net Velocity of Helium + Net Velocity of Neon) / 2

The average mass velocity can be calculated by multiplying the average molar velocity by the molar mass of the gas mixture:

Average Mass Velocity = Average Molar Velocity * Molar Mass

Answer 2

Step-by-step explanation:

Let's assume that Helium is He and Neon is Ne

Then, the expression of the steady-state flux of Helium in a binary mixture of Helium and Neon is:

`N_(He) = c_(He)v_(He)`

where;

`c_(He)` = concentration of Helium

`v _ {He}` = net velocity of Helium

Making
`v _ {He}` the subject, we have:

`v_(He)=( N_(He) )/(c_(He))`

`v_(He)=( 3.8 * 10^(-9) \ kg/mol /m^2.s)/(0.023 \ kgmol/m^3)`

`v_(He)= 1.652 * 10^(-7) \ m/s`

The expression for the steady-state flux of Neon

`N_(Ne) = c_(Ne) \ v_(Ne)`

Here;

`c_(Ne)` = Concentration of neon

`v_(Ne)` = net velocity of neon species

`v_(Ne) = (N_(Ne) )/(c_(Ne))`

`v_(Ne) = ( 0 \ kgmole/m^2 .s )/(0.045 \ kgmole/m^3)`

`v_(Ne) = 0 \ m/s`

Thus, the net velocity of species Ne along the direction of mass transfer = 0 m/s

The average velocity V is:

`V _(avg )= (1)/(c)(c_(He)v_(He) + c_(Ne)v_(Ne))`

`= \frac{(N_(He) + N_(Ne))} {(C_(He) + C_(Ne))}`

`V _(avg)= \frac{(3.8 * 10^(-9) + 0) \ kgmole /m^2.s} {(0.023 + 0.045) \ kgmole/m^3}`

`V _(avg)= 5.588 * 10^(-8) \ m/s`

The average mass velocity is:

`V_(mass) = ((0.023 * 4 ) * 1.652* 10^(-7) +0)/((0.023 * 4) + (0.045 * 20) )`

`V_(mass) = 1.532 * 10^(-8) \ m/s`