Problem 142 - Chemistry Matter and Change

Question

Determine the number of molecules of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in 47.0 \(\mathrm{g}\).

Step-by-Step Solution

Answer

There are approximately \( 6.145 \times 10^{23} \) molecules of ethanol in 47 grams.

Step 1: Find the Molar Mass of Ethanol

To determine the number of molecules, we first need the molar mass of ethanol. Ethanol's chemical formula is \( \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH} \). Calculate its molar mass using the atomic masses: \( \mathrm{C} = 12.01 \, \mathrm{g/mol} \), \( \mathrm{H} = 1.008 \, \mathrm{g/mol} \), and \( \mathrm{O} = 16.00 \, \mathrm{g/mol} \). Thus, the molar mass is calculated as follows: \[ 2 \times 12.01 + 6 \times 1.008 + 16.00 = 46.068 \, \mathrm{g/mol} \].

Step 2: Calculate the Number of Moles of Ethanol

We know the mass of ethanol is \( 47.0 \mathrm{g} \). Use the formula for moles, \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), to find the number of moles of ethanol:\[ \text{moles of ethanol} = \frac{47.0 \, \mathrm{g}}{46.068 \, \mathrm{g/mol}} \approx 1.020 \, \text{moles} \].

Step 3: Convert Moles to Molecules

Now convert the moles of ethanol to molecules using Avogadro's number. Avogadro's number is \( 6.022 \times 10^{23} \) molecules/mol. Multiply the number of moles by Avogadro's number:\[ \text{Number of molecules} = 1.020 \, \text{moles} \times 6.022 \times 10^{23} \, \frac{\text{molecules}}{\text{mol}} \approx 6.145 \times 10^{23} \, \text{molecules} \].

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant used in chemistry to relate the amount of substance in moles to the number of constituent particles, typically atoms or molecules. This constant is defined as \( 6.022 \times 10^{23} \) particles per mole. It essentially states the number of atoms, ions, or molecules in one mole of a given substance.

This concept is incredibly useful for understanding the scale of molecules and helps bridge the microscopic world of atoms to the macroscopic world we can measure and observe. For example, one mole of ethanol contains \( 6.022 \times 10^{23} \) molecules of ethanol.

When performing chemical calculations, Avogadro's number allows us to convert between moles and the actual number of particles. This is crucial in stoichiometry, reaction computations, and understanding chemical compositions.

Moles Calculation

Calculating moles from a given mass is a common problem-solving strategy in chemistry. It allows you to deduce how much of a substance is needed or has reacted based on measured amounts in grams. The formula for moles is:

• \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)

In the case of ethanol (\( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)), the molar mass is calculated by adding together the atomic masses of all the atoms in the chemical formula. Ethanol has a molar mass of approximately 46.068 g/mol. Using this calculation method, if you start with 47.0 g of ethanol, you find that you have about 1.020 moles of ethanol.

This method is very useful not only in laboratory settings but also in industrial applications where precise amounts of chemicals are required to react in a controlled manner.

Chemical Formula

A chemical formula is a symbolic way to represent the composition of a compound. It tells you which elements are present in the compound and in what proportions. For instance, ethanol is represented by \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \), which indicates it contains 2 carbon (C) atoms, 6 hydrogen (H) atoms, and 1 oxygen (O) atom.

Understanding chemical formulas is crucial for several reasons:

• They help in computing the molar mass for use in stoichiometric calculations.
• They reveal the ratio in which atoms are present, which is fundamental to understanding and predicting chemical reactions.
• They allow us to derive other important chemical information like empirical formulas or structural composition.

Chemical formulas serve as a basic language in chemistry, allowing scientists and students to communicate and understand chemical compounds and reactions universally.