Question

What number of Fe atoms and what amount (moles) of Fe atoms are in \(500.0 \mathrm{~g}\) of iron?

Short answer

In 500.0 g of iron, there are 8.951 moles of Fe atoms and 5.385 × 10^24 Fe atoms.

Step-by-step solution

Calculate moles of Fe in 500 grams

To calculate the amount of iron (Fe) in moles, we need to divide the given mass (500 grams) by the molar mass of iron (55.845 g/mol). Using the formula: Moles of Fe = (mass of Fe) / (molar mass of Fe) Moles of Fe = \( \frac{500.0}{55.845} \)

Perform the division

Now we simply perform the division operation to get the amount (moles) of Fe atoms: Moles of Fe = 8.951 moles (rounded to three decimal places)

Calculate the number of Fe atoms

We know that 1 mole consists of Avogadro's number (6.022 × 10^23 atoms/mol) of atoms. To calculate the number of Fe atoms in 8.951 moles, we simply multiply the moles by Avogadro's number: Fe atoms = (moles of Fe) × (Avogadro's number) Fe atoms = (8.951 moles) × (6.022 × 10^23 atoms/mol)

Perform the multiplication

Now, we perform the multiplication to get the total number of Fe atoms: Fe atoms = 5.385 × 10^24 atoms (rounded to three decimal places) So, there are 5.385 × 10^24 Fe atoms and 8.951 moles of Fe atoms in 500.0 g of iron.

Key concepts

Avogadro's Number

In the world of chemistry, Avogadro's number is a fundamental constant. It allows us to relate different atoms and molecules to a measurable quantity known as a mole. Avogadro's number is defined as 6.022 × 10^23, which is the number of atoms, molecules, or particles found in one mole of a substance. This large number makes it possible to count tiny particles, which would otherwise be impossible to handle due to their minuscule size.

For example, when you have one mole of iron atoms, you actually have 6.022 × 10^23 iron atoms. This relationship is essential for converting moles to atoms, and vice versa, a fundamental aspect of many chemistry calculations. In exercises like determining the number of atoms in 500g of iron, Avogadro's number becomes incredibly useful as it assists in converting between the moles of iron and the actual number of iron atoms.

Molar Mass

Molar mass is a key concept in chemistry that denotes the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). Each element has a specific molar mass, which is essentially the mass of its atoms averaged over the isotopes found naturally.

For iron (Fe), the molar mass is about 55.845 g/mol. This value can be found on the periodic table and is used to convert between mass and the number of moles. When you're tasked with solving a problem involving 500g of iron, you'll first need to convert that mass into moles using the molar mass. By dividing the mass of the substance by its molar mass, we can find out how many moles of the substance we have. This step is critical for further conversions, like the number of individual atoms or molecules present in that mass.

Chemical Composition

Understanding chemical composition involves knowing what elements make up a substance and in what proportions. Every compound or element has its unique chemical composition, which affects its properties and reactions.

• Individual elements like iron (Fe) have simple compositions consisting of only one type of atom.
• Compounds consist of a combination of different elements bonded together in specific ratios.

For the calculation of atoms in iron, the chemical composition is relatively simple since iron is a pure element. However, knowing the molar mass and Avogadro’s number allows you to analyze its composition accurately.

In more complex scenarios involving compounds, understanding the chemical composition is vital. You'd need to consider the molar masses of all constituent elements and their ratios. For iron, being a pure element, you focus solely on its own molar mass. This ensures that you accurately perform conversions between grams, moles, and the actual count of atoms, based on the chemical composition of the element in question.