Question

The reaction of compound A to give compounds C and D was found to be second-order in A. The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t_1/2?

Short answer

Half-life periods may be defined as the time period at which half the concentration of reactant converts into the product. The half-life period of the second-order decomposition of the A is 10.33×10^-2seconds which has a rate constant 2.42L/mole/s.

Step-by-step solution

Reaction Rate

The reaction involved the effective collision of two reactants to produce the desired products. Reactions can be natural, which occur in the surrounding environment, whereas it can be artificially done in the laboratory to form a desired required product.

The reaction rate can be defined as the reaction speed to produce the products. The reaction rate can be slow, fast or moderate. The reaction can take less than a millisecond to produce products, or it can take years to produce the desired product.

The half-life period can be defined as the time period at which half the concentration of the reactants gets converted into a product.

Explanation

The half-life period of the second-order decomposition of the A is:

$\mathbf{H}\mathbf{a}\mathbf{l}\mathbf{f}\mathbf{-}\mathbf{l}\mathbf{i}\mathbf{f}\mathbf{e}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\frac{\left(\mathbf{A}\right){}^{\circ }}{\mathbf{2}\mathbf{k}}$

Where $\left(\mathbf{A}\right){}^{\circ }$ = initial concentration of reactant

K = Rate constant

Initial concentration of reactant,$\left(\mathbf{A}\right){}^{\circ }$ =0.500 mole/L

Rate constant for the decomposition of ${\mathbf{O}}_{\mathbf{3}}$= 2.42L/mol/s

.$\begin{array}{rl}Half-lifeperiod& =\frac{0.500mole/L}{2\times \left(2.42L/mole/s\right)}\\ Half-lifeperiod& =\frac{0.500mole/L}{4.84L/mole/s}\\ Half-lifeperiod& =10.33\times {10}^{-2}\sec ond\end{array}$.

Half-life period = 10.33×10^-2 second.

Therefore, the half-life period of the second-order decomposition of the A is 10.33×10^-2 seconds which has a rate constant is 2.42 L/mol/s.