Question

The atomic weight of iron is \(55.847\) amu. If one has \(6.02 \mathrm{~g}\) of iron, how many atoms are present?

Short answer

In \(6.02 \mathrm{~g}\) of iron, there are approximately \(6.49 \times 10^{22}\) atoms.

Step-by-step solution

Convert the mass of iron into moles

To convert the mass of iron into moles, we will use the following formula: Number of moles = \(\frac{Mass \; of \; iron}{Atomic \; weight \; of \; iron}\) We are given that the atomic weight of iron is 55.847 amu and the mass of iron is 6.02 grams. Number of moles = \(\frac{6.02}{55.847}\) Use a calculator to find the number. Number of moles ≈ 0.1078 moles

Use Avogadro's number to find the number of atoms

Avogadro's number is approximately \(6.022 \times 10^{23}\) atoms or molecules per mole. So, to find the number of atoms in the given mass of iron, we can use the following formula: Number of atoms = Number of moles × Avogadro's number Number of atoms = 0.1078 × \(6.022 \times 10^{23}\) Use a calculator to find the number. Number of atoms ≈ \(6.49 \times 10^{22}\) So, there are approximately \(6.49 \times 10^{22}\) atoms of iron in 6.02 grams of iron.

Key concepts

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry and physics. It represents the number of atoms or molecules in one mole of a substance. This number is approximately \(6.022 \times 10^{23}\). It was named after the Italian scientist Amedeo Avogadro, who was instrumental in establishing the usefulness of this constant in chemical calculations.

Knowing Avogadro's number allows scientists to convert between the mass of a substance and the amount of substance, which is crucial for performing chemical reactions and understanding the properties of matter. For example, when you know the number of moles of iron, you can calculate the number of iron atoms by multiplying the moles by Avogadro's number. This makes Avogadro's number an invaluable tool for chemists working with atoms on a small scale.

Moles

The concept of a mole is central to chemistry, providing a bridge between the atomic world and the macroscopic world we can measure. One mole of any substance contains Avogadro’s number of atoms or molecules. This standard unit allows chemists to count particles by weighing them.

A mole is defined by the number of carbon atoms in exactly 12 grams of carbon-12, which is \(6.022 \times 10^{23}\) atoms per mole. This is why every element's atomic weight, as listed on the periodic table, is expressed in terms of grams per mole (g/mol).

• To convert mass into moles, divide the mass of the sample by the atomic weight of the element.

This calculation gives you the number of moles, which you can then use to deduce information such as the number of atoms in a given sample.

Atoms

Atoms are the basic units of matter and the defining structure of elements. Everything in the universe is made up of atoms, which consist of a nucleus of protons and neutrons, surrounded by electrons in various energy levels. Despite their minuscule size, they are crucial components of all chemical substances.

Atoms combine in countless ways to form molecules and compounds. When discussing the number of atoms in a substance, it's generally more practical to consider them in large quantities, such as moles, due to their extremely small size.

• In chemical calculations, you can determine the number of atoms in a sample by first finding the moles and then using Avogadro's number.

This is why understanding the relationship between moles and atoms is crucial for students and professionals dealing with material sciences.

Iron

Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series and is by far the most common element on Earth by mass, forming much of Earth's outer and inner core. Iron is crucial in biology and important in many industrial applications, including construction, manufacturing, and tool-making.

The atomic weight of iron is 55.847 amu. This value is critical when converting between the mass of iron and the number of moles. The understanding of iron's atomic weight allows chemists to calculate how many atoms are present in a given mass of iron.

• For instance, calculating the number of moles by dividing the mass by the atomic weight and then using Avogadro's number helps find how many iron atoms are present.

Iron's properties and roles make it an essential element for numerous scientific and practical applications.