Question

the first order reaction is 40% complete in 80 minutes . calculate the value of rate constant (k). in what time will the reaction be 90% complete?
[Given : log 2=0.3010, log 3= 0.4771, log 4 = 0.6021, log 5 = 0.6771, log 6 =0.7782]

Answer 1

Explanation:

Find the value of m so that the quadratic equation px^2 + (p – 1) x +(p – 1) = 0 has equal roots.

Answer 2

The value of the rate constant is approximately 0.00219 min^-1 and the reaction will be 90% complete in approximately 231.7 minutes.

To find,

Time for the reaction to be 90% complete

Given,

The first-order reaction is 40% complete in 80 minutes.

Solution,

We know that for a first-order reaction, the integrated rate law is given by:

ln[A]t = -kt + ln[A]0

Where [A]t is the concentration of a reactant at time t, [A]0 is the initial concentration of the reactant, k is the rate constant, and ln is the natural logarithm.

Now, let's consider the given problem:

At t = 80 minutes, the reaction is 40% complete, which means that [A]t/[A]0 = 0.6. Substituting this value and the given time in the integrated rate law, we get:

ln(0.6) = -k(80) + ln(1)

ln(0.6) = -k(80)

Solving for k, we get:

k = (-ln(0.6))/80

k ≈ 0.00219 min^-1

Now, we need to find the time required for the reaction to be 90% complete. This means that [A]t/[A]0 = 0.1. Substituting this value and the calculated value of k in the integrated rate law, we get:

ln(0.1) = -k(t) + ln(1)

ln(0.1) = -k(t)

Solving for t, we get:

t = (-ln(0.1))/k

t ≈ 231.7 minutes

Therefore, the value of the rate constant is approximately 0.00219 min^-1 and the reaction will be 90% complete in approximately 231.7 minutes.

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