Question

Write the relationships between rate
constant and half life of first order and
zeroth order reactions,​

Answer 1

Answer:

FIRST-ORDER REACTIONS

An equation relating the rate constant kto the initial concentration [A]0 and the concentration [A]t present after any given time t can be derived for a first-order reaction and shown to be:

ln([A]t[A]0)=−ktln([A]t[A]0)=−kt

or

ln([A]0[A]t)=ktln([A]0[A]t)=kt

or

[A]=[A]0e−kt

SECOND-ORDER REACTIONS

The equations that relate the concentrations of reactants and the rate constant of second-order reactions are fairly complicated. We will limit ourselves to the simplest second-order reactions, namely, those with rates that are dependent upon just one reactant’s concentration and described by the differential rate law:

Rate=k[A]2Rate=k[A]2

For these second-order reactions, the integrated rate law is:

1[A]=kt+1[A]01[A]=kt+1[A]0

where the terms in the equation have their usual meanings as defined earlier

ZERO-ORDER REACTIONS

For zero-order reactions, the differential rate law is:

Rate=k[A]0=kRate=k[A]0=k

A zero-order reaction thus exhibits a constant reaction rate, regardless of the concentration of its reactants.

The integrated rate law for a zero-order reaction also has the form of the equation of a straight line:

[A]−kt+[A]0ymx+b[A]−kt+[A]0ymx+b

A plot of [A] versus t for a zero-order reaction is a straight line with a slope of −k and an intercept of [A]0. Figure 3shows a plot of [NH3] versus t for the decomposition of ammonia on a hot tungsten wire and for the decomposition of ammonia on hot quartz (SiO2). The decomposition of NH3 on hot tungsten is zero order; the plot is a straight line. The decomposition of NH3 on hot quartz is not zero order (it is first order). From the slope of the line for the zero-order decomposition, we can determine the rate constant:

slope=−k=1.3110−6mol/L/s