Respuesta :
The correct answer is: 6.173 seconds.
Explanation:
The formula for half life (of reaction) is:
Half-life = [tex]\frac{1}{K*I}[/tex] --- (A)
Where,
K = Rate constant = 0.54 [tex]\frac{1}{ms}[/tex]
I = Initial concentration = 0.30 m
Plug in the values in equation (A):
Half-life = [tex]\frac{1}{0.54*0.30} = 6.173[/tex]
Hence, the half life is 6.173 seconds.
The half-life of a second-order reaction is [tex]\boxed{{\text{6}}{\text{.173 seconds}}}[/tex]
Further explanation:
Second-order reaction:
A reaction is said to be of second-order if its rate is proportional to the square of the concentration of one reactant. The general example of second-order reaction is,
[tex]2{\text{A}}\to{\text{P}}[/tex]
Here,
A is the reactant.
P is the product.
The rate is calculated by using the following equation:
[tex]{\text{Rate}}={\text{k}}{\left[{\text{A}}\right]^2}[/tex]
Another form of second-order reaction is as follows:
[tex]{\text{A}}+{\text{B}}\to{\text{P}}[/tex]
Here,
A and B are the two different reactants.
P is the product.
The rate is calculated by using the following equation:
[tex]{\text{Rate}}={\text{k}}\left[{\text{A}}\right]\left[{\text{B}}\right][/tex]
Half-life:
Half-life is defined as the time required to reduce the concentration of reactant to half of its initial value. It is denoted by [tex]{{\text{t}}_{1/2}}[/tex] . The general expression to calculate [tex]{{\text{t}}_{1/2}}[/tex] of second-order reaction is,
[tex]{{\text{t}}_{1/2}}=\frac{1}{{{\text{k}}{{\left[{\text{A}}\right]}_{\text{0}}}}}[/tex] …… (1)
Here,
[tex]{{\text{t}}_{1/2}}[/tex] is the half-life of the reaction.
k is the rate constant for the reaction.
[tex]{\left[ {\text{A}}\right]_{\text{0}}}[/tex] is the initial concentration of the reactant.
The rate constant for the given reaction is [tex]0.54\;{{\text{M}}^{-1}}{{\text{s}}^{-1}}[/tex] .
The initial concentration of the given reaction is 0.30 M.
Substitute these values in equation (1).
[tex]\begin{aligned}{{\text{t}}_{1/2}}&=\frac{1}{{\left({0.54\;{{\text{M}}^{ - 1}}{{\text{s}}^{ - 1}}}\right)\left( {{\text{0}}{\text{.30 M}}}\right)}}\\&=\frac{1}{{0.162\;{{\text{s}}^{ - 1}}}}\\&=6.1728\;{\text{s}}\\&\approx 6.173\;{\text{s}}\\\end{aligned}[/tex]
So, the half-life of a second-order reaction is 6.173 seconds.
Learn more:
1. Calculate the moles of chlorine in 8 moles of carbon tetrachloride: https://brainly.com/question/3064603
2. Calculate the moles of ions in the solution: https://brainly.com/question/5950133
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Chemical Kinetics
Keywords: second-order reaction, half-life, initial, half, 6.173 seconds, 0.30 m, k, A0, A, B, P, 2A, reactant, product, t1/2.
