A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.

_{(log 2 = 0.3010)}

Solution

For the given first order reaction the rate constant for 50% completion is given by
$straight i right parenthesis space space straight K equals space fraction numerator 2.303 over denominator straight t end fraction log space fraction numerator left square bracket straight R right square bracket subscript 0 over denominator left square bracket straight R right square bracket end fraction space......1$

Here t= time taken for 50% completion =30 min

[R]₀= initial concentration of the reactant

[R] =final concentration of the reactant

Let [R]₀be 100 and due to 50% completion of the reaction [R] will be 100-50 i.e. 50

Putting value in 1 we get
$straight K equals space fraction numerator 2.303 over denominator straight t space end fraction log space 100 over 50 space equals 0.023 space min to the power of negative 1 end exponent$
For same reaction the time required for 90% completion of the reaction can be computed using the expression $text K= end text fraction numerator 2.303 over denominator straight t end fraction log space fraction numerator left square bracket straight R right square bracket subscript 0 over denominator left square bracket straight R right square bracket end fraction$

Here [R] = final concentration of reactant=100-90 =10

So we have
$straight K equals fraction numerator space 2.303 over denominator straight t end fraction log space 100 over 10 space equals 100.13 space min$
Therefore the time required for 90% completion of the given first order reaction is 100.13min.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

For Daily Free Study Material Join wiredfaculty

Chemical Kinetics

A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.

_{(log 2 = 0.3010)}

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Chemical Kinetics

A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction. (log 2 = 0.3010)

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.

_{(log 2 = 0.3010)}