The Density Of Water Is 1 Gram Per Ml What Is The Volume Occupied By One Molecule Of Water

5 min read Jun 26, 2024
The Density Of Water Is 1 Gram Per Ml What Is The Volume Occupied By One Molecule Of Water

The Density of Water: A Key to Unlocking the Volume of a Single Molecule

Introduction

Water is a ubiquitous substance that covers over 70% of the Earth's surface. It's a vital component of life, and its unique properties make it essential for various biological, chemical, and physical processes. One of the fascinating aspects of water is its density, which is approximately 1 gram per milliliter (g/mL). But have you ever wondered what this density means in terms of the volume occupied by a single molecule of water?

The Density of Water

The density of a substance is defined as its mass per unit volume. In the case of water, its density is 1 g/mL, which means that a volume of 1 milliliter (mL) of water has a mass of 1 gram. This value is a fundamental constant in physics and chemistry, and it's used extensively in various calculations and applications.

The Molecular Weight of Water

To calculate the volume occupied by a single molecule of water, we need to know its molecular weight. The molecular formula for water is H2O, and its molecular weight is approximately 18.02 grams per mole (g/mol). A mole is a unit of measurement that represents 6.022 x 10^23 particles (atoms or molecules).

Calculating the Volume of a Single Molecule of Water

Now, let's use the density of water and its molecular weight to calculate the volume occupied by a single molecule of water. We'll follow these steps:

  1. Calculate the mass of a single molecule of water:

Using the molecular weight of water, we can calculate the mass of a single molecule:

Mass of a single molecule = Molecular weight / Avogadro's number = 18.02 g/mol / 6.022 x 10^23 particles/mol โ‰ˆ 3 x 10^-23 grams

  1. Calculate the volume of a single molecule of water:

Now, we can use the density of water to calculate the volume of a single molecule:

Volume of a single molecule = Mass of a single molecule / Density of water = 3 x 10^-23 grams / 1 g/mL โ‰ˆ 3 x 10^-23 mL

Conversion to Cubic Nanometers

To make the result more meaningful, let's convert the volume from milliliters to cubic nanometers (nm^3). There are 1,000,000 cubic nanometers in 1 milliliter.

Volume of a single molecule (nm^3) = 3 x 10^-23 mL x (1,000,000 nm^3 / 1 mL) โ‰ˆ 0.03 nm^3

Conclusion

In conclusion, the volume occupied by a single molecule of water is approximately 0.03 cubic nanometers. This value may seem incredibly small, but it's a testament to the remarkable properties of water that make it so essential for life on Earth. The density of water, which is 1 gram per milliliter, plays a crucial role in this calculation and is a fundamental constant in physics and chemistry.