Finding [A] when looking for the velocity constant Some reaction of first order on $[A]$ has the data:
  
  
  
  What is the velocity constant for this reaction? The units are
  $s^{-1}$.




Well, since the units are $s^{-1}$, then the reaction must be of global order one. Meaning that $A$ is the only reagent, yes?

Anyway, the velocity equation is

$$V = k \cdot [A]^1$$

Let's pick the first experiment...

$$\left (-\frac{0.40 - 1.60}{10} \right ) = k \cdot [A]$$

Huh. I don't actually know how to find $[A]$. Should I add $1.6 + 0.40$? Subtract them maybe? Or pick just one?

I tried all three of them and still couldn't get the answer. The options were


$0.030$
$3.1x10^{-3}$
$0.013$
$3.0$
$0.14$
For a first-order reaction, the half-life is constant and is given by the equation 

$$t_{1/2} = \frac{\ln 2}{k}$$

In $10~\mathrm{s}$, two half-lives have passed (the concentration of $\ce{A}$ drops to a quarter), so $t_{1/2} = 5~\mathrm{s}$. Accordingly,

$$\begin{align}
k &amp;= \frac{\ln 2}{5~\mathrm{s}} \\
&amp;= 0.1386~\mathrm{s^{-1}}
\end{align}$$