Question

Question #c7286

Answer 1

In a 1st order reaction, the rate is directly proportional to the concentration of the reactants.

Explanation:

Hence, the rate is fast at the beginning.

As the reactants get used up the reaction goes slower and slower and slower
and …

We can see this happening in the first order plot shown below.

The blue curve is a plot of a first order reaction in which `[A]_0 = "1 mol/L"` and `k = 1color(white)(l) "s"^"-1"`.

The instantaneous rate at a given time `t` is a line tangent to the curve at that time.

The slope of the line is a measure of the rate (`"slope = -"k`).

Instantaneous rate at `t =0` .

The `color(brown)("brown")` line represents the instantaneous rate at `t = 0`

Since the reaction has just started, [A] is at its maximum and the rate is fastest
(`"1 mol·L"^"-1""s"^"-1"`).

Instantaneous rate at `t color(white)(l)"= 20 s"`

At `t = color(white)(l)"20 s"`, the rate has slowed considerably because `"[A]"` has decreased to 0.135 mol/L and the instantaneous rate (shown by the `color(green)("green")` line) is 0.0135 mol/L.

Average rate

The average rate from 0 s to 20 s (shown by the `color(purple)("purple"` line) is a straight line joining the points, (`"0,[A]"_text(0))` `and ("20,[A]"_text(20))`.

We see that the slope of this line (`"rate" = "0.43 mol·L"^"-1""s"^"-1"`) is between the values at the beginning and end of the 20 s interval.