The stagnant liquid B in a container that is 10 cm high (L=10cm) is exposed to the non-reactant gas A at time t=0. The concentration of A, dissolved physically in B, reaches C_(A_o )=0.01 mol/m^3 at the interface instantly and remains constant. The diffusing coefficient of A in B isD_AB=2×(10^(-9) m^2)/s. Determine the evolution of the concentration of A within the container. In the second part, repeat it but this time consider that A reacts with B according to the following reaction

Solution

As shown in the figure physical problem is sketched. The first part of the problem is leads as;

According to the initial and Boundary Conditions:

Initial Condition,        t=0;      for all value of z

Boundary Condition 1;

Z=0    ; 

Boundary Condition 2;

Explicit Method:

Put both the value in above

        Now for the Second case we do this same procedure and the value of K is given that is  this is used for the solving of the equation. We write the initial as well as boundary conditions also determined for two arbitrary step size of space the limit of step size of time