# Question 4ee02

Apr 1, 2017

It can be solved like this:

#### Explanation:

1.

This is not a well worded question since the rate of the reaction is not constant. I will assume they are asking for the average rate after 40 min.

Average rate = loss of sulfur / time

Average rate = $\textsf{\frac{0.8 - 0.4}{40} = 0.01 \textcolor{w h i t e}{x} {\text{min}}^{-} 1}$

2.

There are several methods you could use to show this. I will use "The Integral Method".

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

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}$

This means that if the reaction is 1st order then a plot of $\textsf{\ln {\left[A\right]}_{t}}$ against t should be a straight line of the form $\textsf{y = m x + c}$

The gradient of the line will be equal to -k.

Excel is a useful tool to do this (other spreadsheet programmes are available) . Here's what I got:

The straight line confirms that the reaction is 1st order.

Since $\textsf{{R}^{2} = 0.9996}$ this means the correlation coefficient $\textsf{R = \sqrt{0.9996} = 0.9997}$. This indicates an almost perfect fit.

The equation of the line has been added by the programme for you:

$\textsf{y = - 0.0174 x - 0.2268}$

This tells us that $\textsf{- k = - 0.0174 \textcolor{w h i t e}{x} {\text{min}}^{- 1}}$

$\therefore$$\textsf{k = 0.0174 \textcolor{w h i t e}{x} {\text{min}}^{-} 1}$

3.

We now have the rate equation for the reaction:

Rate = sf(kxx%S)#

At the 30th minute the %S = 0.47

$\therefore$$\textsf{{\text{Rate"=0.0174 xx 0.47=0.0082color(white)(x)"min}}^{- 1}}$