First and Second Order Reaction Graphs

[Emilie Flores 2G]

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]

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.