First-order integrated rate law

The deomposition of AIBN in xylene at 77°C was studiedt by measuring the volume of N2 evolved as a function of time. The volumes obtained at time t and t = 00, are and, respectively. Show that the manner of plotting used in Fig. 6.1 is consistent with the integrated first-order rate law and evaluate k j. 

STRATEGY The level of mercury(II) in the urine can be predicted by using the integrated first-order rate law, Eq. 5b. To use this equation, we need the rate constant. Therefore, start by calculating the rate constant from the half-life (Eq. 7) and substitute the result into Eq. 5b. 

We can use an integrated first-order rate law to confirm that a reaction is first order and to measure its rate constant. From Eq. 13a, we can write... 

Recall from Chapter 15 that this is the rate law for a first-order process. The integrated first-order rate law is... 

The half-life (t,/2) of a radioactive sample is defined as the time required for the number of nuclides to reach half of the original value (N0/2). We can use this definition in connection with the integrated first-order rate law (see Section 15.4) to produce the following expression for f1/2 ... 

The problem can be solved using the integrated first-order rate law ... 

Plan (a) We must find the concentration of cyclobutane at time t, [C4H8],. The problem tells us this is a first-order reaction, so we use the integrated first-order rate law ... 

Aii radioactive decay processes foiiow first-order kinetics. What does this mean What happens to the rate of radioactive decay as the number of nuciides is haived Write the first-order rate law and the integrated first-order rate law. Define the terms in each equation. What is the half-life equation for radioactive decay processes How does the half-life depend on how many nuclides are present Are the half-life and rate constant k directly related or inversely related ... 

EXERCISE 14.7 Using the Integrated First-Order Rate Law... 

Show how equation 20.33 reduces to a simplerform of an integrated first-order rate law when the reverse reaction of an equilibrium is negligible. 

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