Question

Respiration 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.

Short answer

The number of argon atoms inhaled with each breath can be calculated using the following steps: 1. Calculate the mass of argon inhaled: mass of argon = (0.934/100) × 0.600 g. 2. Convert the mass of argon to moles: moles of argon = mass of argon / 39.95 g/mol. 3. Calculate the number of argon atoms: number of argon atoms = moles of argon × \(6.022 × 10^{23}\) atoms/mol.

Step-by-step solution

Calculate the mass of argon inhaled with each breath

First, we need to find out how much argon is present in each breath, given that the total mass of air inhaled is 0.600 g and argon makes up 0.934% of the air. To do this, multiply the percentage of argon (0.934%) by the total mass of the air (0.600 g): mass of argon = (percentage of argon/100) × total mass of air mass of argon = (0.934/100) × 0.600 g

Convert the mass of argon to moles

To calculate the number of atoms, we first need to convert the mass of argon to moles. We can achieve this by using the molar mass of argon, which is approximately 39.95 g/mol. The formula to calculate the moles of argon is: moles of argon = mass of argon / molar mass of argon

Calculate the number of argon atoms

Now that we have the moles of argon, we can convert it into the number of argon atoms using Avogadro's number, which is approximately \(6.022 × 10^{23}\) atoms/mol. To get the number of argon atoms, simply multiply the moles of argon by Avogadro's number: number of argon atoms = moles of argon × Avogadro's number By following these steps, we can find out the number of argon atoms inhaled in each breath.

Key concepts

Molar Mass

Understanding the molar mass of a substance is like knowing the weight requirement for your recipe. It's defined as the mass in grams of one mole of any substance, be it atom, molecule, or ion. For instance, the molar mass of argon is about 39.95 g/mol. Knowing this allows us to move from the mass of argon in a single breath to the amount in moles, which is a fundamental step before counting the individual atoms. To calculate it, you would divide the actual mass by molar mass. This forms a bridge between the microscopic atoms and our macroscopic measurements.

In the given exercise, you take the small amount of argon from your breath's air mass and convert it into moles. Picture it like converting kilograms into pounds; you're changing units so that they make sense for your next calculation. Utilizing the molar mass in calculations is crucial for chemists when making precise measurements for reactions.

Avogadro's Number

Avogadro's number, often denoted as NA, opens up the world of atoms and molecules by relating the macro world to the micro world. This large constant, approximately equal to \(6.022 \times 10^{23}\), is the number of units (atoms, molecules, etc.) in one mole of a substance, tying together the mole concept and particles. It's named after the scientist Amedeo Avogadro, and it's the secret ingredient for counting atoms as if they were tangible enough to be placed on a scale.

When we talk about inhaling argon atoms, Avogadro's number enables us to calculate the exact number of atoms from the moles we previously figured out by molar mass. It’s like knowing the exact count of marbles in a jar without having to count each individually by simply knowing the volume of one marble and the total volume of marbles in the jar.

Mole Concept

The mole concept is a way to count particles like atoms and molecules. A mole is a unit of measurement that represents a massive amount, specifically Avogadro's number, of these tiny particles. It's like a chemist's dozen, but instead of 12, we're talking about over 600 sextillion! Using the mole concept allows us to measure substances at the particle level by relating mass, which we can easily measure, to the number of particles, which we generally can’t.

In our example with argon, once we have calculated the mass of argon per breath using its percent composition in air, we then use the mole concept to convert this mass to a number of moles. This is akin to converting a large number of items into a more manageable unit, like converting a huge number of grains of rice to bags to understand the quantity in practical terms.

Percent Composition

Percent composition is the chemist's way of breaking down the contribution of individual elements or components in a mixture. It's the portion, by mass, of each element within a compound, or of a component in a mixture, represented as a percentage. Just as a nutrition label tells you how much sugar is in your snack, the percent composition tells you how much of a compound is made up of a particular element.

As per our respiration exercise, air is a mixture that contains a small percentage of argon. Knowing that argon makes up 0.934% of air provides the initial clue to how much of this noble gas we are inhaling with each breath. This percentage helps us find out the mass of just argon in the air we breathe, by applying it to the mass of air inhaled. Once you know the fraction, you can calculate the amount of any substance within your mixture.