Question

a student makes a graph of initial rate vs. concentration in order to determine the order of a reaction. if the reaction is second order, what would she see on the graph?
a straight, horizontal line at the initial rate
a straight line slowly going down to zero
a straight line beginning at the origin and gradually increasing
a curved line showing an increase in rate with concentration
a curved line showing an decrease in rate with concentration

Explanation:

For a second - order reaction, the rate law is \( rate = k[A]^2 \). When we plot the initial rate (\( rate \)) versus concentration (\( [A] \)), if \( rate = k[A]^2 \), this is a quadratic relationship (\( y = ax^{2}\) where \( y=\text{rate}\), \(x = [A]\), and \(a = k\)). A quadratic relationship is a curved line. Since the rate is proportional to the square of the concentration (\( rate\propto[A]^2\)), as the concentration increases, the rate will increase.

Answer:

a curved line showing an increase in rate with concentration