# Question #e6605

Mar 25, 2017

You can do it like this:

#### Explanation:

I will confine the answer to a 1st order reaction.

Suppose we have:

$\textsf{A \rightarrow \text{products}}$

For a 1st order reaction we have:

$\textsf{\text{Rate} = k {\left[A\right]}^{1}}$

Where k is the rate constant.

This can be expressed in terms of the rate of disappearance of A :

$\textsf{- \frac{d \left[A\right]}{\mathrm{dt}} = k . \mathrm{dt}}$

Rearranging and applying integration between 0 and t gives:

$\textsf{{\int}_{{\left[A\right]}_{0}}^{{\left[A\right]}_{t}} \frac{d \left[A\right]}{\left[A\right]} = - k {\int}_{0}^{t} \mathrm{dt}}$

This gives:

$\textsf{\ln {\left[A\right]}_{t} - \ln {\left[A\right]}_{0} = - k t}$

$\therefore$$\textsf{\ln {\left[A\right]}_{t} = \ln {\left[A\right]}_{0} - k t}$

You can see that this is a straight line graph of the form $\textsf{y = m x + c}$.

This means if we plot $\textsf{\ln {\left[A\right]}_{t}}$ against t the gradient will be equal to -k and the intercept will be $\textsf{\ln {\left[A\right]}_{0}}$.

Here is an example for the breakdown of ozone by light: See if you can measure the gradient yourself to give you -k.

If you read off the intercept i.e the point where the graph cuts the y axis, this will give you the value of $\textsf{\ln {\left[A\right]}_{0}}$.

You can get $\textsf{{\left[A\right]}_{0}}$ from that by selecting the $\textsf{{e}^{x}}$ function on your calculator.