xv1ll4inx asked:

Can you help me with this problem? Given the general reaction A --> products. provide a rate constant and 3 hypothetical data points in the format ([A],t) that would be consistent with a second order rxn (data should have consistent slope)

Ooh, kinetics is not my strong suit, but I will try! 

Rate laws describe how the rate of the reaction, v(t), depends on the concentrations of the reactants. They are often written in the general form:

v(t) = k[A]^m [B]^n …

[A] and [B] are the concentrations of reactants, the exponents m and n are constants related to the reaction order, and k is the rate constant. The sum of the exponents is the overall order of the reaction.

Since the rate law is time-dependent, the behavior of a reaction over time can be plotted. Each kind of reaction order has a different predictable kinetic plot, which you can see either by physically making the plot from data, or from the rate law. 

You are asked to make a plot for a second order reaction A —> products. Since the reaction is second order, we know that the rate   law’s coefficients must sum to 2. The simplest version would be:

v = k [A]^2

Now, to turn this into a plottable equation, we need to rewrite it as the change in [A] with time: -d[A]/dt = k[A]^2. Then, we rewrite it to separate the concentration and time variables: -d[A] = k[A]^2 dt. Integrating this gives:

(1/[A]) = (1/[A]o) + kt

where [A]o is the concentration of A at t=0. You may notice that this is a linear equation of the form y = mx + b (in our case, y = kt + 1/[A]o). The rate constant k is the slope.

So, for data consistent with a second-order reaction, you would create a linear plot of (1/[A]) vs t. Hope that helps!

For reference, this example is from McQuarrie and Simon’s Physical Chemistry, p. 1148-9.