(LO 37,45) A reaction is 75% complete in 45.0 min. How long after its start will the reaction be 50% complete if it is (A) first order; (B) zero order

A) t = 22.5 min and B) t = 29.94 min

Explanation:

Initial concentration, [A]₀ = 100

Final concentration = 100 -75 = 25

Time = 45 min

A) First order reaction

ln[A] − ln[A]₀ = −kt

Solving for k;

ln[25] − ln[100] = - 45k

-1.386 = -45k

k = 0.0308 min-1

How long after its start will the reaction be 50% complete?

Initial concentration, [A]₀ = 100

Final concentration, [A] = 100 -50 = 50

Time = ?

ln[A] − ln[A]₀ = −kt

Solving for k;

ln[50] − ln[100] = - 0.0308 * t

-0.693 = -0.0308 * t

t = 22.5 min

B) Zero Order

[A] = [A]₀ − kt

Using the values from the initial reaction and solving for k, we have;

25 = 100 - k(45)

-75 = -45k

k = 1.67 M min-1

How long after its start will the reaction be 50% complete?

Initial concentration, [A]₀ = 100

Final concentration, [A] = 100 -50 = 50

Time = ?

[A] = [A]₀ − kt

50 = 100 - (1.67)t

-50 = - 1.67t

t = 29.94 min