Question

Assume the following chemical reactions: ? ⇌ ? ⇀ ?

The rate equations are:

?? ?? = −2? + ?

?? ?? = 2? − 3?

?? ?? = 2?

The initial conditions are ?(0) = ?0, ?(0) = ?(0) = 0.

Obtain the concentrations for each species.

Answer 1

Solution :

Here reaction is :

A. <----> B. ---> C

The rate equations are:

??/ ?? = −2? + ?.............1

?? /?? = 2? − 3?............2

??/ ?? = 2?.......................3

The initial conditions are ?(0) = ?0, ?(0) = ?(0) = 0.

Here B is intermediate, so its quantity is very small so change in B is almost zero.

So from equation 2,

??/?? = 2? − 3? = 0

2A = 3B

B = 2A/3

Put it in equation 1, we will get

dA/dt = -2A + 2A/3

dA/dt = -4A/3

Now doing integration of above equation,

ln(Ao/A) = 4t/3

So A = Ao e-4t/3

So B = 2Ao e-4t/3/3

Put this B in equation 3, we will get,

dC/dt = 4Ao e-4t/3/3

Now integrating above equation

C = -Ao(e-4t/3 - 1)

C = Ao(1 - e-4t/3)