15.23 c

[Melissa Per 2J]

Determine the rate constant for 2A ----> B+C given that [A]0 = 0.153 molxL^-1 and that after 115 s the concentration of B rises to 0.034 molxL^-1.
I keep getting it wrong. Please help.

[Thuy-Anh Bui 1I]

First, find [A]_t. The reaction starts with [A]₀ = 0.153 mol A and produces [B]_t = 0.034 mol B during some time interval. Using the stoichiometric ratios in the given reaction, [A]₀ must have reacted at a rate of (2 mol A/1 mol B) to end up with [A]_t = 0.153 mol/L A - (2 mol A/1 mol B)(0.034 mol/L B) = 0.085 mol/L A.

Then, use [A]_t, [A]₀ and time (115 seconds) and the 1st order integrated rate law to find k.
k = ln([A]₀ / [A]_t) / t = ln(0.153 mol/L / 0.085 mol/L) / 115 s = 5.1 x 10^-3 s^-1

[Nehal Banik]

You can also do the ln(.083/.115)/-115s and you would get the same rate law just know that you have to divide by a negative time to find the rate constant.