What percentage of reactant A will react for a first order reaction after three half lives?

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]….Half-Lives and Radioactive Decay Kinetics.

How do you calculate first order decay?

Calculations Using the First Order Rate Equation: r = k[N] Since the rate of radioactive decay is first order we can say: r = k[N]1, where r is a measurement of the rate of decay, k is the first order rate constant for the isotope, and N is the amount of radioisotope at the moment when the rate is measured.

How do you find the rate constant for radioactive decay?

Suppose N is the size of a population of radioactive atoms at a given time t, and dN is the amount by which the population decreases in time dt; then the rate of change is given by the equation dN/dt = −λN, where λ is the decay constant.

What is the first order reaction?

A first-order reaction can be defined as a chemical reaction in which the reaction rate is linearly dependent on the concentration of only one reactant. In other words, a first-order reaction is a chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants.

What is first order decay?

First order decay simply means that for a population of atoms (e.g. radioactive), molecules (our example of A –> B), or anything else, a constant fraction/unit time is converted to something else. The actual fraction/unit time is expressed as k (the rate constant, in units of time ). Plot of [A]/[Ao] vs time.

What is the half-life for a first order reaction?

The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t1/2 = 0.693/k. Radioactive decay reactions are first-order reactions. The rate of decay, or activity, of a sample of a radioactive substance is the decrease in the number of radioactive nuclei per unit time.

What is the equation for first order reaction?

The integrated rate law for the first-order reaction A → products is ln[A]_t = -kt + ln[A]_0. Because this equation has the form y = mx + b, a plot of the natural log of [A] as a function of time yields a straight line.

What is the amount of reactant left after half-lives?

As you can see from this table, the amount of reactant left after n half-lives of a first-order reaction is (1/2) n times the initial concentration. For a first-order reaction, the concentration of the reactant decreases by a constant with each half-life and is independent of [A].

How do you find the half-life of a first order reaction?

We can derive an equation for determining the half-life of a first-order reaction from the alternate form of the integrated rate law as follows: If we set the time t equal to the half-life, t1/2 t 1 / 2, the corresponding concentration of A at this time is equal to one-half of its initial concentration.

How do you determine the Order of reaction in a reaction?

From these measurements, we determine the order of the reaction in each reactant. Integrated rate laws are determined by integration of the corresponding differential rate laws. Rate constants for those rate laws are determined from measurements of concentration at various times during a reaction.

What is the relationship between rate constant and half life?

We can see that the half-life of a first-order reaction is inversely proportional to the rate constant k. A fast reaction (shorter half-life) will have a larger k; a slow reaction (longer half-life) will have a smaller k. Example 5 Calculation of a First-order Rate Constant using Half-Life