Volumetric flow rate in a PFR reactor

[dRic2]

Hi pf,

I have a reaction $aA → bB$ in a PFR reactor. The simplest equation to write is:

$\frac {dF_A} {dV} = -R$ where $F$ is the Molar flow rate. $F = C_A*Q$ where $Q$ is the volumetric flow rate and $C_A$ is the molar concentration of A.

My textbooks says that if $a=b$ (the total number of moles doesn't change) $Q$ is constant. I don't understand why, can someone explain me? Moreover, sometimes, in the exercise $Q$ is considered constant even if $a≠b$...
So my question is: "When $Q$ can be considered constant?

Thank you
Ric

 

[BvU]

Do they mention that this is for a gas phase reaction ? And the ideal gas law applies ? And the temperature is constant ?

 

[dRic2]

If temperature (and pressure) are constant and the total number of moles doesn't change, using $PV=nRT$, it's clear to me that the volumetric flow is constant.
If temperature (and pressure) are constant but the total number of moles does change I can still consider the volumetric flow as constant if the change in the total number of moles is very small (eg working with ppm).

Now let's a reaction like $A + E → 2B + C$

In gas phase under which conditions (if possible) $Q$ can be considered constant?
In liquid phase phase under which conditions (if possible) $Q$ can be considered constant?

Thank you
Ric

Ps: I hope my english is good enough

 

[Chestermiller]

If temperature (and pressure) are constant and the total number of moles doesn't change, using $PV=nRT$, it's clear to me that the volumetric flow is constant.
If temperature (and pressure) are constant but the total number of moles does change I can still consider the volumetric flow as constant if the change in the total number of moles is very small (eg working with ppm).

Now let's a reaction like $A + E → 2B + C$

In gas phase under which conditions (if possible) $Q$ can be considered constant?

Yes, if the actual change in the number of moles is small (e.g., if only a small amount of A is available to react)

In liquid phase phase under which conditions (if possible) $Q$ can be considered constant?

Yes again, if the actual change in the specific volume of the mixture is small.

 

[dRic2]

Thank you.