Chapter 18, Problem 41QAP

Interpretation Introduction

Interpretation:

The age of the rockshould be determined.

Concept introduction:

The relation between half-life and first order rate constant is given by:

$\text{k=}\frac{\text{0}\text{.693}}{{\text{t}}_{\text{1/2}}}$

Where, k = first order rate constant and ${\text{t}}_{\text{1/2}}$ = half-life

The activity of sample is directly proportional to the amount of C-14. The mathematical expression is given by:

$\ln \frac{A_o}{A}=kt$

Where, $A_o$ = original activity

$A$ = measured activity

t= age of the sample

The expression for calculating the original amount of compound is given by:

$m_o=m_A+\frac{M_A}{M_B}\times m_B$

Where, $m_o$ = original mass

$m_A$ = given mass of compound A

$m_B$ = given mass of compound B

$M_A$ = molar mass of compound A

$M_B$ = molar mass of compound B