43) It takes 10 minutes for the concentration of a radioactive species to decay to its 1/4th value
of its original concentration. What is the rate constant of this radioactive decay reaction?
[Question ID = 750]
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2.
415.8 5-1
[Option ID = 2999)
865.8 s-1
[Option ID = 3000]
0.00231 s-1
[Option ID = 2997)
0.0011555-1
(Option ID = 2998]
3.
4.
Answers
Answer:
id is equal to the answer is yes I am not able to have a great day to all the best teacher in your
Answer:
Another approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value. This period of time is called the half-life of the reaction, written as t1/2. Thus the half-life of a reaction is the time required for the reactant concentration to decrease from [A]0 to [A]0/2. If two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life.
The half-life of a first-order reaction under a given set of reaction conditions is a constant. This is not true for zeroth- and second-order reactions. The half-life of a first-order reaction is independent of the concentration of the reactants. This becomes evident when we rearrange the integrated rate law for a first-order reaction (Equation 14.21) to produce the following equation:
ln[A]0[A]=kt(1)
Substituting [A]0/2 for [A] and t1/2 for t (to indicate a half-life) into Equation 1 gives
ln[A]0[A]0/2=ln2=kt1/2(2)
Substituting ln2≈0.693 into the equation results in the expression for the half-life of a first-order reaction:
t1/2=0.693k(3)
Thus, for a first-order reaction, each successive half-life is the same length of time, as shown in Figure 1 , and is independent of [A].
14.17.jpg
Figure 1 : The Half-Life of a First-Order Reaction. This plot shows the concentration of the reactant in a first-order reaction as a function of time and identifies a series of half-lives, intervals in which the reactant concentration decreases by a factor of 2. In a first-order reaction, every half-life is the same length of time.
If we know the rate constant for a first-order reaction, then we can use half-lives to predict how much time is needed for the reaction to reach a certain percent completion.
Explanation
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