Q16.118 CP - Chemistry: Molecular Nature Of Matter And Change

Question

The molecular scenes below represent the first-order reaction as cyclopropane (red) is converted to propene (green):

Determine (a) the half-life and (b) the first-order rate constant.

Step-by-Step Solution

Answer

Half-life is $0.60s^{-1}$

b. Rate constant for a reaction is  $K=1.163s^{-1}$

Step 1: Half-life

Half-life is defined as the period to convert half of the reactant to the product

As per the diagram given half of the red balls are converted into the green balls.

Let the time taken convert these balls as x

So, the rest half will take some time that is x so that the half-life becomes 2x 

Let x=0.30

Then half-life is 0.60 $s^{-1}$ 

Step 2: Rate constant

For the first-order kinetic the half-life is inversely proportional to the rate constant 

 $t_{1/2}=\frac{0.698}{K}$

So, 

$$\begin{gathered} t_{1/2}=\frac{0.698}{K} \\ K=\frac{0.698}{t_{1/2}} \\ K=\frac{0.693}{0.60} \\ K=1.163s^{-1} \end{gathered}$$ 

The rate constant for a reaction is  $K=1.163s^{-1}$