Question

For the simple decomposition reaction ab(g) → a(g) + b(g), the rate is given by rate = k[ab]² and k = 0.15 L/mol·s. How long will it take for [ab] to reach 1/3 of its initial concentration of 1.50 M?

Answer 1

It will take approximately 4.29 seconds for [ab] to reach 1/3 of its initial concentration.

Step-by-step explanation:

The given decomposition reaction is ab(g) → a(g) + b(g) with the rate equation rate = k[ab]², where k = 0.15 L/mol·s. To find how long it will take for [ab] to reach 1/3 of its initial concentration, we can use the integrated rate law for a second-order reaction. The integrated rate law is 1/[ab]t - 1/[ab]0 = kt. We can plug in the values and solve for time to find that it will take approximately 4.29 seconds for [ab] to reach 1/3 of its initial concentration.