Chapter 2, Problem 1Q

Summary Introduction

To analyze: Whether water in the Pacific Ocean contains at least one molecule of ancient water.

Given: The cup contains 18 g (1 mole) of water. The volume of the Pacific Ocean is $\text{1}\text{.5}\text{×}{\text{10}}^9{\text{km}}^{\text{3}}$ or $\text{1}\text{.5}\text{×}{\text{10}}^{\text{24}}{\text{cm}}^{\text{3}}$.

Introduction: A mole can be defined as the molecular weight of a particular atom, molecule, or compound. According to Avogadro’s law, one mole contains $6\text{×}{\text{10}}^{\text{23}}$ molecules in it. Molecular weight of every molecule is its mass relative to that of a hydrogen atom. The concept of mole is just a way to represent the number of molecules that participating in a chemical reaction. The molecular weight of water is 18g or 1mole and it contains $6\text{×}{\text{10}}^{\text{23}}$ molecules.

Explanation of Solution

Molecular weight of water is 18 g or 1 mole. It contains $6\text{×}{\text{10}}^{\text{23}}$ molecules in it. The volume of oceanic water, when converted into cubic centimeters, is $\text{1}\text{.5}\text{×}{\text{10}}^{\text{24}}{\text{cm}}^{\text{3}}$. The cup contains exactly one mole of water and it holds $6\text{×}{\text{10}}^{\text{23}}$ molecules in it. When it comes to the mixing of one mole of ancient water ( $6\text{×}{\text{10}}^{\text{23}}$ molecules) with the oceanic water of volume of $\text{1}\text{.5}\text{×}{\text{10}}^{\text{24}}{\text{cm}}^{\text{3}}$, there would be a chance of $\frac{6\times {10}^{23}}{1.5\times {10}^{24}}$ or 7.2 molecules in 18g of oceanic water.

Conclusion

There is a great chance of having 7.2 molecules of ancient water in 18gm of oceanic water as Avogadro’s number ( $6\text{×}{\text{10}}^{\text{23}}$) is such a huge quantity.