The product  is formed by the chemical reaction and is given by .

Where  is a constant.

(a)

Rate of reaction at time  is defined as  .

Consider .

Differentiate on each side  with respect to .

.

Quotient rule of derivatives: .

(b )

Prove that .

Consider the left hand part .

.

We have, .

Substitute  in .

Substitute  in above expression.

,

If , then .

Therefore, .

(c)

Consider the product concentration .

As , then .

.

As , then .

(d)

Consider rate of reaction .

As ,

Rate of reaction is zero as .

(e)

As , that means reaction goes for a long time then concentration of the product tends to a certain point, which is initial value of reactants.

As , the rate of reaction tends to equilibrium , where no more reactions should occurs.

(a).

(b) 

(c) .

(d) Rate of reaction is zero as .

(e)

As , that means reaction goes for a long time then concentration of the product tends to a certain point, which is initial value of reactants.

As , the rate of reaction tends to equilibrium , where no more reactions should occurs.