## 7B.7

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Gisela F Ramirez 2H
Posts: 61
Joined: Fri Sep 28, 2018 12:27 am

### 7B.7

Substance A decomposes in a first order reaction and its half life is 355 s. How much time must elapse for the concentration of A to decrease to
a) 1/8 of initial concentration
b)1/4 of initial concentration
c) 15% of initial concentration
d) 1/9 of initial concentration

How would I go about solving this problem?

ThomasLai1D
Posts: 61
Joined: Fri Sep 28, 2018 12:17 am

### Re: 7B.7

For part A, because 1/8 = (1/2)^3, you can assume that substance A divided in half three times. Therefore, you can just multiply 355s by a factor of 3. Similarly, in part B, because 1/4 = (1/2)^2, substance A divided in half two times. Therefore you can multiply 355s by a factor of 3. For C and D, you need to determine the rate constant, by using the equation [A] = [A]initial e^-kt. Because the definition of half life is [A] = 1/2[A]initial, by plugging in 1/2[A]initial into the equation for [A] and the time (355s), you get the equation 1/2 = e^-355k. Solve for k, and then for part B, 15% of initial concentration means [A] = 0.15[A]initial. Plug k and 0.15[A]initial into equation and solve for t. The same can be done for 1/9 initial concentration, where [A] = 1/9 [A]initial.