## Calculating slope

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

Ashley Garcia 2L
Posts: 33
Joined: Fri Sep 29, 2017 7:05 am

### Calculating slope

For a first order reaction, why does the slope = -k? Why do we need a negative sign in front of k?

Clarisse Wikstrom 1H
Posts: 63
Joined: Fri Sep 29, 2017 7:05 am

### Re: Calculating slope

It would make sense that as time increases, ln[A] should decrease as well. However, the rate constant, k, is always a positive number, therefore a negative sign must be put in front to make the slope of the line negative.

Andrea ORiordan 1L
Posts: 52
Joined: Fri Sep 29, 2017 7:04 am
Been upvoted: 2 times

### Re: Calculating slope

Remember that [A] is the concentration of the reactants, so, as Clarisse said, ln[A] will decrease over time. The fact that we're able to get k from the graph of ln[A] for a first order reaction is actually super neat.

Julia Campbell 2F
Posts: 31
Joined: Sat Jul 22, 2017 3:00 am

### Re: Calculating slope

It is also because, when graphed, the slope is negative (going to the right and down). So, for the slope to equal k, k must be negative as well.

Sarah Sharma 2J
Posts: 33
Joined: Fri Sep 29, 2017 7:05 am

### Re: Calculating slope

The slope is negative because it will indicate which direction the gradient/slope will. You will see that when deriving the equation for the second order reaction, the negatives can cancel, making the gradient positive.