Question

For 3a-3d, consider the elementary reaction A → B. The reaction has a rate constant of 5.76×10-2 s-1.

3a. What is the half-life of this reaction in seconds?

3b. What fraction of the starting concentration of A is present after 2 min? Multiply your answer by 104 before submitting.

3c. What is the velocity of the reaction, in mM/s, immediately after it is initiated with 20 mM A?

3d. What is the instantaneous velocity, in mM/s, of the reaction in (c) after 1 min?

Answer 1

3a

this is 1st order therefore:

Half life = ln(2)/(k) = ln(2)/(5.76*10^-2) = 12.033 seconds

b)

fraction of A after t =2 min = 120 s

ln(A) = ln(A0) - k*t

let A0 = 1

ln(A) = -(5.76*10^-2)*120

A = exp( -(5.76*10^-2)*120) = 0.00099576 M

fraction of A = A/A0 = 0.00099576 left

3c

velocity after [A] = 20*10^-3 M used

Rate = k*[A]

Rate = (5.76*10^-2)(20*10^-3) = 0.001152 M/s

3d

after t = 1 min = 60 s

find [A] at t = 60

ln(A) = ln(A0) - k*t

ln(A) = 0 - (5.76*10^-2)(60)

A = exp(-(5.76*10^-2)(60)) = 0.03155

Rate = K*[A]

Rate = (5.76*10^-2)(0.03155) = 0.00181728 M/s