Question

In the reaction, a → products, a plot of ln[a] vs. Time is linear and the slope is equal to -0.860 s-1. How long will it take one-half of the initial amount of a to react?

Answer 1

The reaction is given as follows:

$a\rightarrow product$

The plot of ln[a] verses t is linear with slope $-0.860 s^{-1}$.

The plot for ln[a] verses t is linear for first order reaction. The integrated rate law equation is as follows:

$[A]=[A_{0}]e^{-kt}$

Here, k is rate constant, t is time of the reaction, $[A]$ is concentration of reactant at time t and $[A_{0}]$ is initial concentration of reactant.

Taking ln both sides,

$ln[A]=ln[A_{0}]-kt$...... (1)

Comparing with equation for linear graph, y=mx+c

Thus, slope =-k

Or, $k=0.860 s^{-1}$

Now, if final concentration become half of its initial value,$[A]=\frac{[A_{0}]}{2}$ and t becomes $t_{1/2}$

Putting the values in equation (1)

$ln\frac{[A_{0}]}{2}=ln[A_{0}]-(0.860 s^{-1})t_{1/2}$

On rearranging,

$t_{1/2}=\frac{ln2}{0.860 s^{-1}}=\frac{0.6932}{0.860 s^{-1}}=0.806 sec$

Therefore, it takes 0.806 sec to react half of the reactant a.

Answer 2

The study of chemicals and bonds is called chemistry. There are different types of elements and these are metals and nonmetals.

The correct answer is -0.806sec.

What is half time?

• Halftime definition, the period indicating completion of half the time allowed for an activity.

The plot for ln[a] verses t is linear for a first-order reaction. The integrated rate law equation is as follows:

$[A]=[A_o]e^{-kt}$

Here,

• k is rate constant
• t is a time of the reaction,
• [A] is the concentration of a reactant at time t
• [Ao} is the initial concentration of reactant.

The equation will be:-

$In[A] = In[A_o]-kt$

Compared with the equation for linear graph, y=mx+c

Thus, slope =-k

The value of k will be 0.860

Now, if the final concentration becomes half of its initial value $[A] = \frac{{A_o}}{2}$.

Place all the values and rearrange them.

$T_\frac{1}{2} =\frac{In}{0.860}$

Hence, the correct answer is 0.860.

For more information about the half-life, refer to the link:-

https://brainly.com/question/7932885