using t 1/2

[emmaferry2D]

Determine the rate constant for each of the following first-order reactions, in each case expressed for the rate of loss of A: (a) A → B, given that the concentration of A decreases to one-half its initial value in 1000. s; (b) A → B, given that the concentration of A decreases from
0.67
mol⋅L−1 to 0.53 mol⋅L−1
in 25 s; (c) 2 A → B + C, given that [A]0=0.153 mol⋅L−1 and that after 115 s the concentration of B rises to 0.034mol⋅L−1

I understand how to find the half life for a first order reaction but I am confused how to calculate when a different portion of the concentration is decreased like in parts b and c of this question.
I anyone could explain this to me that would be great!

[Kaihan_Danesh_2J]

Those values go into the integrated rate law for a first order reaction. In part B, the values of [A] and [A]0 are directly given and in part c you subtract two times the decrease in compound B from [A]0 to get [A] because compound A decomposes two times faster than compound B forms. From there, you calculate k since you also know the t value for each reaction.

[JonathanM]

Hey! So when its not decreasing by half you can just use the equation Ln(A)=-kt+Ln(A_o) and solve for k. You can just plug the numbers in for part B, but for part C you have to find the final concentration of A by converting the amount of B produced to the amount of A lost using just normal stoichiometry and the stoichiometric coefficients. Hope this helps!