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

Short Answer

Expert verified
In 500 grams of iron, there are approximately 8.95 moles of Fe atoms and \(5.39 \times 10^{24}\) individual Fe atoms.

Step by step solution

01

Find the molar mass of iron (

Begin by finding the molar mass of iron, which is the mass of one mole of iron atoms. Based on the periodic table, the molar mass of iron (Fe) is approximately 55.84 g/mol.
02

Calculate the amount of iron in moles

Next, divide the mass of iron by the molar mass to find the amount of iron in moles: moles of Fe = (mass of Fe) / (molar mass of Fe) moles of Fe = \( \frac{500}{55.84} \) Now, calculate the moles of Fe: moles of Fe = \( \frac{500}{55.84} \) 鈮 8.95 moles
03

Calculate the number of iron atoms using Avogadro's number

Avogadro's number (N鈧) is the number of atoms (or molecules, ions, etc.) in one mole of a substance, which is approximately \(6.022 \times 10^{23} \) entities per mole. To find the number of iron atoms, multiply the moles of iron by Avogadro's number: Number of Fe atoms = (moles of Fe) 脳 (Avogadro's number) Number of Fe atoms = (8.95 moles) 脳 \(6.022 \times 10^{23}\) atoms/mol Now, calculate the number of Fe atoms: Number of Fe atoms 鈮 5.39 脳 \(10^{24}\) iron atoms To summarize, there are approximately 8.95 moles of Fe atoms and \(5.39 \times 10^{24}\) individual Fe atoms in 500 grams of iron.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass
When you study chemistry, molar mass is a fundamental concept you will encounter frequently. It is essential for converting between the mass of a substance and the amount in moles. The molar mass of an element or compound is the mass of one mole of its entities (atoms, molecules, formula units). For any element, you can find its molar mass on the periodic table. The units are typically expressed in grams per mole (g/mol).

Let's take the example of iron (Fe). If you look at the periodic table, iron has a molar mass of approximately 55.84 g/mol. This means that one mole of iron atoms weighs 55.84 grams. Knowing this property helps in determining the amount of substance present in a given mass.
  • Molar mass is needed to convert grams to moles.
  • It serves as a bridge between the mass of a sample and the number of molecules or atoms in it.
  • You can find molar mass in the periodic table, with each element having a unique value.
By understanding molar mass, it becomes easier to carry out various chemical calculations, such as determining the number of entities in a sample.
Avogadro's Number
Avogadro's number is incredibly important in chemistry as it allows chemists to convert between the mass of a substance to the precise number of its particles. It is the number of entities, such as atoms or molecules, present in one mole of a substance. Avogadro's Number is approximately \(6.022 \times 10^{23}\), a very large number due to the minuscule size of atoms and molecules.

Why do we use Avogadro's number? Since dealing with atoms and molecules individually would be impractical given their size, chemists use Avogadro's number as a collective way to express quantities at a macroscopic scale. When you have one mole, you have exactly \(6.022 \times 10^{23}\) of whatever kind of particle you are considering.
  • It allows for the translation of atomic scale measurements to a size we can work with in a lab.
  • Using this number, you can convert from moles to individual atoms or molecules.
  • Facilitates understanding and application of chemical equations and stoichiometry.
Avogadro's number essentially acts as a useful conversion factor for moving between the amount in moles and the actual number of atoms or molecules.
Chemical Calculations
Chemical calculations often involve several steps, integrating concepts like molar mass and Avogadro's number to achieve a practical and accurate result. Whether you are calculating the number of atoms in a sample or determining the reaction yields, these calculations form the core of many laboratory and theoretical work in chemistry.

Let's revisit our exercise of finding out how many iron atoms are in 500 grams of iron. Initially, you need the molar mass of iron to convert from grams to moles. Then, using Avogadro's number, you calculate the number of atoms.
  • Identify the molar mass of the element from the periodic table.
  • Use the relation: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).
  • Once moles are known, convert to atoms with \(\text{Atoms} = \text{moles} \times 6.022 \times 10^{23}\).
These steps are repetitive across various problems in chemistry, highlighting the importance of mastering chemical calculations. Understanding each step thoroughly will enable you to tackle complex chemistry problems with confidence and precision.

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Most popular questions from this chapter

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What number of atoms of nitrogen are present in \(5.00 \mathrm{~g}\) of each of the following? a. glycine, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{~N}\) b. magnesium nitride c. calcium nitrate d. dinitrogen tetroxide

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