Question

The half-life of a reaction, t1/2, is the time required for one-half of a reactant to be consumed. It is the time during which the amount of reactant or its concentration decreases to one-half of its initial value.

Determine the half-life for the reaction in Part B using the integrated rate law, given that the initial concentration is 1.90mol?L?1 and the rate constant is 0.0016mol?

Answer 1

Answer: The half life of the reaction is 593.8 seconds

Explanation:

We are given:

Rate constant = $0.0016mol/L.s$

The formula for determining the unit of 'k' is:

$\text{Unit}=\frac{(Concentration)^{1-n}}{Time}$

where, n = order of reaction

The unit of concentration is, M or mole/L

The unit of time is, second or 's'

Evaluating the value of 'n' from above equation:

$mol.L^{-1}s^{-1}=\frac{(mol/L)^{1-n}}{s}\\\\n=0$

The reaction is zero order reaction.

The equation used to calculate half life for zero order kinetics:

$t_{1/2}=\frac{[A_o]}{2k}$

where,

k = Rate constant = $0.0016mol/L.s$

$[A_o]$ = initial concentration = 1.90 mol/L

Putting values in above equation, we get:

$t_{1/2}=\frac{1.90mol/L}{2\times 0.0016mol/L.s}=593.8s$

Hence, the half life of the reaction is 593.8 seconds

Answer 2

The half life of the reaction has been 593.8 sec.

The half life has been defined as the time taken by the sample to reduce to half of its initial concentration. The half-life of the sample has been determined with respect to the rate of the reaction.

Computation of Half-life of reaction:

The rate law has been used for the determination of the order of reaction. The rate law has been given as:

$\rm rate\;constant=\dfrac{(concentration)^{1-n}}{Time}$

The n has been the representation of the order of reaction. Substituting the values for the determination of the rate of reaction.

$\rm 0.0016\;mol.L^-^1.s^-^1=\dfrac{(1.90\;mol.L^-^1)^{n-1}}{t\;s}\\n-1=1\\n=0$

The order of reaction has been a zero order reaction.

The half life for zero order reaction has been given by:

$\rm Half\;life=\dfrac{[\AA]}{2\textit k}$

Where, the initial concentration of the reactant has been, $\rm\AA=1.90\;mol\;L^-^1$

The rate constant for the reaction, $k=0.0016\;\rm mol.L^-^1.s^-^1$

Substituting the values for calculation of half life:

$\rm Half\;life=\dfrac{1.90}{2\;\times\;0.0016}\\Half \;life=593.8\;s$

The half life of the reaction has been 593.8 sec.

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

https://brainly.com/question/24710827