Problem 120 - Chemistry Matter and Change

Question

Air contains several gases. When resting, every breath you take contains approximately 0.600 g of air. If argon makes up 0.934% of the air, calculate the number of argon atoms inhaled with each breath.

Step-by-Step Solution

Answer

You inhale approximately \( 8.45 \times 10^{19} \) argon atoms with every breath.

Step 1: Calculate Mass of Argon Per Breath

First, determine how much argon is present in one breath. Since argon makes up 0.934% of the air, multiply the total mass of air in one breath by this percentage: \ \( \text{mass of argon} = 0.934\% \times 0.600\, \text{g} = 0.005604\, \text{g} \).

Step 2: Convert Mass of Argon to Moles

Convert the mass of argon from grams to moles. Use the molar mass of argon, which is approximately 39.95 g/mol: \ \( \text{moles of argon} = \frac{0.005604\, \text{g}}{39.95\, \text{g/mol}} \approx 0.0001403\, \text{mol} \).

Step 3: Calculate Number of Argon Atoms

Use Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) atoms/mol, to find the number of argon atoms: \ \( \text{number of argon atoms} = 0.0001403\, \text{mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 8.45 \times 10^{19} \text{ atoms} \).

Key Concepts

Mole Concept

The mole is an essential unit in chemistry that allows us to relate the microscopic world of atoms and molecules to the macroscopic world we can see and measure. One mole represents a specific number of particles, typically atoms or molecules. This number is known as Avogadro's number, which is defined as \( 6.022 \times 10^{23} \) particles per mole.

When dealing with chemical reactions and quantities, the concept of the mole helps us calculate how much of a substance is involved or needed. For example, in the exercise, we determined the amount of argon in terms of moles before calculating the number of atoms. This is done by converting the mass of the element into moles using its molar mass, which is the mass of one mole of that element, expressed in grams. This allows us to then use Avogadro's number to find the number of individual atoms or molecules.

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. It provides valuable information for identifying the relative amounts of each element within a substance. In the context of gases like air, percent composition helps us understand the proportion of different gases present, such as oxygen, nitrogen, and in our example, argon.

To find the mass of a component within a mixture, we multiply the total mass by the percentage (expressed as a decimal) that component makes up of the whole. In the given exercise, we calculated how much argon is present in the air you breathe by applying its percent composition. We took the mass of air per breath and multiplied it by 0.934% to find the mass of argon inhaled.

• Determine the percentage of the element in the compound.
• Calculate the mass of the element using the mass percentage and total mass of the substance.

This straightforward method provides useful insights for calculating how much of a specific substance is involved in any mixture.

Avogadro's Number

Avogadro's number is a fundamental constant used in chemistry to provide a bridge between the atomic scale and real-world quantities. It is defined as the number of constituent particles, usually atoms or molecules, in one mole of a substance. This number is \( 6.022 \times 10^{23} \, \text{particles/mol} \).

With Avogadro's number, converting between moles of an element and the actual number of atoms becomes simple. For instance, once we determined the moles of argon in a breath of air, we multiplied that by Avogadro's number to discover how many argon atoms are inhaled. This number serves as a key tool in stoichiometry, allowing chemists to use quantities they measure (moles) and easily translate them to the microscopic world (individual atoms or molecules).

• Represents the number of atoms or molecules in one mole.
• Used to convert moles to particles (atoms, molecules).

Understanding and utilizing Avogadro's number is crucial for performing chemical calculations effectively.