Write the differential equation for steady-state diffusion and homogeneous chemical reaction at constant reaction rate K in a cylindrical rod. Determine the solution for the HCl concentration in the rod.

J = - K*∆p/∆x * A = Cm²/s. atm * atm. cm²/cm = cm³/s

Explanation:

On the basis of the above considerations, Fick's First Law may be formulated as:

J = - ∆ (dc/dx)

In words: The diffusive flux is

proportional to the

existing concentration

gradient.

The negative sign in this relationship indicates that particle flow occurs in a "down"

gradient direction.

J (moles/cm²s)

= - D (dc/dx)

Thus: D = cm2/s

We can now set up the diffusion equation:

J = - K (dp/dx)

Jdx = KdP

(operates with pressures instead

of concentrations)

We may now formally separate the variables and integrate:

Jdx = - KdP

We can forego the integration since (dP/dx) = (∆P/dx) and we may immediately write:

J = - K*∆p/∆x * A = Cm³/s