## Textbook question 7B.3

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

Paige Lee 1A
Posts: 136
Joined: Sat Sep 07, 2019 12:16 am

### Textbook question 7B.3

For part C, could someone please explain how to get [A]= 0.085 mols/L? I understand how to get 0.068mols/L, but I don't understand why you subtract it from the starting amount 0.153mol/L for A concentration

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 S B, given that the concentration of A decreases to one-half its initial value in 1000. s; (b) A S B, given that the concentration of A decreases from 0.67 molL21 to 0.53 molL21 in 25 s; (c) 2 A S B 1 C, given that [A]0 5 0.153 molL21 and that after 115 s the concentration of B rises to 0.034 molL21.

Betania Hernandez 2E
Posts: 107
Joined: Fri Aug 02, 2019 12:15 am

### Re: Textbook question 7B.3

$[A]_{t}$ represents the concentration of reactant A that remains at time t. The problem states that the concentration of product B rises to 0.034 M. This means that the concentration of reactant A decreased by 0.068 M. You would need to subtract this number from the initial concentration given to find the concentration of reactant A that remains.

AKatukota
Posts: 100
Joined: Thu Jul 25, 2019 12:18 am

### Re: Textbook question 7B.3

Thank you! I was wondering this also and I see the relation in why you would subtract.

BeylemZ-1B
Posts: 95
Joined: Thu Jul 25, 2019 12:17 am

### Re: Textbook question 7B.3

after you get the new concentration [A]t = 0.085, you can set up the equation to solve for the rate constant:

ln[0.085] = -k*(115 seconds) + ln[.153]

so I got k=5.1E-3, but what would the units be and how do I differentiate the units on k for first and second order reactions?

Rida Ismail 2E
Posts: 139
Joined: Sat Sep 07, 2019 12:16 am

### Re: Textbook question 7B.3

The units are s-1

Brooke Yasuda 2J
Posts: 102
Joined: Sat Jul 20, 2019 12:17 am

### Re: Textbook question 7B.3

This may be the longer way, but it works. To find the units of the rate constant, you just want to remember that your rate needs to have units of (mol/L/s). So when you have your expression which is something like rate = k*[x]^n[y]^m, you can determine that k multiplied by the rest of the expression has to produce units of mol/L/s.