Question

The ordered pairs (R, t) of concentration of R (molar) in the reaction R → P with time (min) are given as (1, 0), (0.75, 0.05), (0.4, 0.12) and (0.1, 0.18). The order of the reaction is?

Answer 1

The reaction is zero-order.

When you have ordered pairs (`R,t`) of concentration and time and want to determine the order of reaction, you try to plot a graph that gives a straight line.

Thus, you use the integrated rate laws for each reaction order and see which plot gives the best result.

Zero-order reactions

The integrated rate law is

`"[R] = [R]"_0 - kt`

A plot of `"[R]"` vs `t` should be a straight line with `"slope = -"k`.

First-order reactions

The integrated rate law is

`"ln[R] = ln[R]"_0 - kt`

A plot of `"ln[R]"` vs `t` should be a straight line with `"slope = -"k`.

Second-order reactions

The integrated rate law is

`1/["R"] = 1/["R"]_0 + kt`

A plot of `1/["R"]` vs `t` should be a straight line with `"slope" = k`.

To determine the order, we plot the three different graphs and see which one gives the best straight line.

I used your data to generate the points for plotting in Excel.

Here are the graphs.

Only the first plot gives a good straight line. The best-fit straight line goes through all the points.

The reaction is zero-order.