Question

In a homogeneous chemical reaction the conversion of A to B follows first order kinetics in a batch process .After 6 mins 55% of A is converted. Find out the percentage conversion of A after 10 mins​

Answer 1

Given info : in a homogeneous chemical reaction the conversion of A to B follows first order kinetics in a batch process. After 6 mins, 55 % of A is converted.

To find : find percentage of conversion of A after 10 mins.

Solution : equation of first order reaction is given by,

k = 1/t ln([A]₀/[A])

Where [A]₀ is initial amount , [A] is final amount of substance remained unreactive and k is rate constant.

Case 1 : t = 6 mins , [A]₀ = 100 , [A] = 100 - 55 = 45

so, k = 1/6 ln(100/45) = 1/6 ln(20/9) ....(1)

Case 2 : t = 10 mins , [A]₀ = 100 , [A] = ?

k = 1/10 ln(100/[A]) .......(2)

From equations (1) and (2) we get,

1 = 10/6 ln(20/9)/ln(100/[A])

⇒3 ln(100/[A]) = 5ln(20/9)

⇒(100)³/[A]³ = (20/9)⁵

⇒[A]³ = 10⁶/(20/9)⁵ = 18452.8125

⇒[A] = 26.42

So the conversion of A after 10 mins = 100 - 26.42 = 73.58 %