(a)

Step 1:

Initial concentration of A is .

First half life time is 25 min .

Second half life time is 50 min .

Observe that , each successive half–life is double the preceding one.

So the given reaction is second order reaction.

The rate law for second order reaction is . \ \

Where k = rate constant ,

              [A] = concentration of A at time t.

Solution:

The rate law of reaction is .

(b)

Step 1:

Initial concentration of A is .

First half life time is 25 min .

Second half life time is 50 min .

Find the rate constant k .

Use the second order half life formula : .

Where k = rate constant ,

              [A]₀ = initial concentration of A .

Substitute and min .

Solution:

The rate constant is .

(c)

Step 1:

Initial concentration of A is .

First half life time is 25 min .

Second half life time is 50 min .

Find the  [A] at t = 525 min .

Use the second order Integrated rate law  : .

Where k = rate constant ,

              [A]₀ = initial concentration of A,

              t is time.

Substitute , and min .

Solution:

The concentration at min  is .