Kinetics Assignment - Reaction Orders

[sltungle]

Homework Statement

The concentration of the reactant A has been studied as a function of time. By a suitable plot of the data below, show that the reaction is first order, and determine the rate constant, k, and the half-life, t_1/2. Use the integrated rate equation to determine [A] when t = 600s.

t (seconds) 100 200 300 400 500

[A] (mol/L) 0.344 0.314 0.286 0.261 0.238

Homework Equations

-d[A]/dt = k*[A]

The Attempt at a Solution

The main part that's confusing me is the bolded part. I've done the first part in showing that the reaction is first order by plotting the concentration on the Y-axis against time on the X-axis. My linear trend line has an R² value of 0.997 so I'd say it's a safe bet to assume just from the geometry of the graph that the reaction is a first order one.

The second part (the bolded part) is what is stumping me, because I KNOW it's insanely simple but for some reason I can't do it.

I took the gradient of my graph (2.65*10^-4) which is the reaction rate (d[A]/dt) and set that to equal k[A], but here's where I'm getting frustrated and things don't seem to be working out.

My gradient is a constant value (which makes sense - it's a linear graph); it doesn't depend on any variables. My [A] value is constantly changing as the reaction progresses over time.

If d[A]/dt = k*[A] and the left hand side is constant, while on the right hand side [A] is changing over time, then does k not also have to be a changing value in order to keep the whole equation constant? But that makes no sense, because k is a reaction rate constant. I need a solid value for it.

Any help would be greatly appreciated. I'm getting myself in a really bad mood over this and I get the feeling that by focusing too much on this one aspect of the problem that I'm blinding myself to alternate methods.

 

[Borek]

$\frac {d[A]} {dt}$ is not constant. Concentration changes by 0.030M in the first 100 sec and by 0.023M in the last 100 sec.