Chapter 4, Problem 5STP

Interpretation Introduction

Interpretation : The number of nitrogen-14 atoms is to be calculated. The method used to determine the answer including calculations is to be explained.

Concept Introduction : According to the rule of conservation of mass, mass is conserved during all physical and chemical processes. There is no formation or destruction of mass.

Answer to Problem 5STP

The number of nitrogen-14 atoms that would need to place on the right pan is 9.

The method adopted for the calculation is according to the law of conservation of mass.

Explanation of Solution

The composition of matter always changes when a chemical reaction takes place.

The mass of the reactants and products are always equal during any chemical reaction.

In the law of conservation of mass, there is no mass lost or gained during the chemical or physical change.

There are three calcium-42 atoms on the left pan.

According to the law of conservation of mass, the mass of the left pan is equal to the mass of the right pan.

Let x be the number of nitrogen-14 atoms. The number of nitrogen-14 atoms is given as

  ${\text{3 }}^{42}\text{Ca}\to x{}^{14}\text{N}$

The mass of three calcium-42 atoms is $3\times 42\text{amu}\text{=}\text{126}\text{amu}$ .

The number of nitrogen-14 atoms is given as:

  $\begin{array}{c}{\text{3 }}^{42}\text{Ca}=x{}^{14}\text{N}\\ \text{126}\text{amu}\text{=}x\left(14\text{amu}\right)\\ x=\frac{126\text{amu}}{14\text{amu}}\\ x=9\end{array}$

The number of nitrogen-14 atoms is 9.