Chapter 13, Problem 13.141IME

Interpretation Introduction

Interpretation:

The shortest and longest times (in years) that can be estimated by carbon-14 dating has to be determined.

Concept introduction:

Rate equation for the general reaction $\text{A+B}\to \text{Product}$ is,

Then the rate equation becomes,

$Rate=k{\left[A\right]}^x{\left[B\right]}^y$

Order of a reaction:  The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.

$\text{Order}\text{= }\text{x+y}$

Half-life is the time required for one half of a reactant to react.

For first order reaction $-kt=\ln \left(\frac{\left[A\right]}{\left[A_0\right]}\right)$

$\left[A\right]$ is the concentration of reactant A at time t ${\left[A\right]}_0$ is the  initial concentration of reactant, k is the rate constant.

All nuclear reactions follow first order kinetics.