Math Help - What is a "first-order reaction?"

1. What is a "first-order reaction?"

Can someone tell me what a "first-order reaction" is in easy to understand terms please?

2. Say that we're given a chemical reaction: $A + B \to C + D$

And the rate of the reaction is given by: $r = k[A]^m [B]^n$

We say that the order of the reaction with respect to $A$ is $m$ and the order with respect to $B$ is $n$. The total order of the reaction is given by $m + n$.

One thing to note that $m$ and $n$ are determined experimentally. There's no way to predict the order without actually carrying out the experiment itself.

Now for specifics. A first-order reaction means that the rate of the reaction depends only on one of the reactants with order 1, i.e. $r = k[A]^1$

A common form is its integrated form: $\ln [A]_0 = -kt + \ln [A]$ where $[A]_0$ is the initial concentration of our reactant.

3. You went a little ahead of my course by embedding ln into chemistry but I just wanted to ask the following word problem question:

"Consider the decomposition of N2)5 in carbon tetrachloride (CCl4) at 45°C.
2N205(soln)-->4NO2(g)+O2(g)

The reaction is first-order in N205, with the specific rate constant 6.08x10^(-4) per second. Calculate the reaction rate under these conditions.

a) [N2O5] = 0.2 mol/L"

Thanks!

4. Since this is a first-order reaction, we know the rate is given by: $r = k[\text{N}_2\text{O}_5]$

We know the specific rate constant ( $k = 6.08 \times 10^{-4} \ s^{-1}$) and we know $[\text{N}_2\text{O}_5]$.

So simply plug it all in.