Question

The rate law for the reaction A → products is rate = 4.36 × 10-2 M-1s-1 [A]2. What is the half-life of the reaction if the initial concentration of A is 0.250 M?

Answer 1

The half-life of the reaction is 18 seconds.

Step-by-step explanation:

The half-life of a reaction can be determined using the half-life equation, which is different depending on the order of the reaction. In this case, the reaction is second order, so the half-life equation is: t1/2 = 1 / (k[A]). Given that the rate constant (k) is 4.36 × 10-2 M-1s-1 and the initial concentration of A is 0.250 M, we can substitute these values into the equation to calculate the half-life:

t1/2 = 1 / (4.36 × 10-2 M-1s-1 * (0.250 M)2)

t1/2 = 18 seconds

Answer 2

The formula for the half life is simply:

t1/2 = ln 2 / k

where k is the rate constant and can be calculated from the formula:

rate = k [A]

where [A] is the initial concn = 0.25 M

k = 4.36 × 10-2 M s-1 / 0.25 M = 0.1744 s-1

t1/2 = ln 2 / 0.1744 s-1

t1/2 = 3.97 s