Problem 86 - Chemistry The Molecular Science

Question

Calculate how many water molecules are in one drop of water. (One drop of water is \(\frac{1}{20} \mathrm{~mL},\) and the density of water is \(1.0 \mathrm{~g} / \mathrm{mL}\).)

Step-by-Step Solution

Answer

Approximately \( 1.67 \times 10^{21} \) water molecules are in one drop of water.

Step 1: Determine Mass of Water in a Drop

A drop of water is \( \frac{1}{20} \) mL. Since the density of water is \( 1.0 \, \text{g/mL} \), the mass of one drop of water is also \( \frac{1}{20} \, \text{g} \).

Step 2: Calculate Number of Moles of Water

The molar mass of water (\( \text{H}_2\text{O} \)) is \( 18.02 \, \text{g/mol} \). To find the number of moles in \( \frac{1}{20} \) g of water, use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Thus, the number of moles of water in one drop is \( \frac{\frac{1}{20}}{18.02} \approx 0.00277 \) moles.

Step 3: Find Number of Molecules in Water Moles

Use Avogadro's number, \( 6.022 \times 10^{23} \) molecules per mole, to calculate the total number of molecules. Multiplying the number of moles by Avogadro's number gives: \( 0.00277 \times 6.022 \times 10^{23} \approx 1.67 \times 10^{21} \) molecules.

Key Concepts

Moles

Moles are a fundamental concept in chemistry that allow us to quantify the amount of a substance. A mole is a unit of measurement used to express the amount of a chemical substance. One mole is defined as exactly 6.022 x 10^{23} elementary entities, which may be atoms, molecules, ions, or other particles. This number is known as Avogadro's number, but we'll get to that later.

Why do we use moles instead of directly counting molecules or atoms? Because the numbers are typically very large! Dealing with these tiny particles in direct amounts would be cumbersome. A mole helps bridge the gap between the world we can see and measure directly and the molecular world we cannot.

To calculate moles, you divide the mass of a substance by its molar mass, which tells you how many moles of that substance you have. This is a crucial step in converting laboratory measurements into meaningful chemical information.

Molecular Mass

The molecular mass (also called molar mass when related to one mole of a substance) is an important concept for understanding the composition of compounds. It represents the mass of one molecule of a substance and is usually expressed in daltons (atomic mass units) or grams per mole.

To calculate the molecular mass of a compound, you add up the atomic masses of all the atoms in a molecule of that compound. For instance, water (H2O) has a molecular mass of about 18.02 g/mol. This amount comes from the sum of the masses of two hydrogen atoms and one oxygen atom:

• Hydrogen: 2 (atoms) x 1.01 g/mol = 2.02 g/mol
• Oxygen: 1 (atom) x 16.00 g/mol = 16.00 g/mol
• Total: 2.02 + 16.00 = 18.02 g/mol

This calculation is critical when you're trying to find out how many moles of a substance you have. By dividing the mass you have by the molecular mass, you determine the number of moles, which is essential for further calculations in chemistry.

Avogadro's Number

Avogadro's number, 6.022 x 10^{23}, is a fundamental constant used to quantify the number of particles in a substance. It serves as the bridge between the macroscopic world that we can measure directly and the atomic or molecular scale.

Named after scientist Amedeo Avogadro, this number allows chemists to count particles by weighing them. When you have one mole of a substance, it contains exactly 6.022 x 10^{23} of its basic units, whether those are atoms, molecules, ions, etc. This makes it possible to calculate and predict the behavior of atoms and molecules in chemical reactions.

For example, when you calculated that there are 0.00277 moles of water in one drop, you use Avogadro's number to determine how many molecules that corresponds to, resulting in approximately 1.67 x 10^{21} water molecules. This connection between quantity and scale is fundamental in chemical calculations.