## First and Second Order Reaction Graphs

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

Emilie Flores 2G
Posts: 15
Joined: Fri Sep 25, 2015 3:00 am

### First and Second Order Reaction Graphs

In lecture today, Lavelle graphed the first order reaction ln[A] vs time and it was downward sloping and linear. The second order reaction is 1/[A] vs time and is ALSO linear, but upward sloping. Are the slopes for a first order always negative and the slopes for the second order reactions always positive? If not, how can I differentiate the graphs?

Shaye Busse 3B
Posts: 20
Joined: Fri Sep 25, 2015 3:00 am

### Re: First and Second Order Reaction Graphs

In the derivation for the first order equation, the negative remains throughout. This makes the final graph of ln[A] vs. time negative and linear. In the derivation for the second order reaction, the negative is phased out. The result of this is a final graph of 1/[A] vs. time positive and linear.