Question

Number of atoms in \(560 \mathrm{~g}\) of Fe (atomic mass \(56 \mathrm{~g}\). \(\mathrm{mol}^{-1}\) ) is: (a) Twice that of \(70 \mathrm{~g} \mathrm{~N}\) (b) Half that of \(20 \mathrm{~g} \mathrm{H}\) (c) Both are correct (d) None is correct

Short answer

Option (c) Both are correct.

Step-by-step solution

Calculate Moles of Fe

To find the number of moles of Fe in 560 g, use the formula: \( \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} \). Plug in the values: \( \frac{560 \text{ g}}{56 \text{ g/mol}} = 10 \text{ mol} \).

Calculate Number of Atoms in Fe

Use Avogadro's number to find the number of atoms: \( \text{Number of atoms in Fe} = \text{moles of Fe} \times 6.022 \times 10^{23} \text{ atoms/mol} = 10 \times 6.022 \times 10^{23} = 6.022 \times 10^{24} \) atoms.

Calculate Moles of N

First, find the molar mass of nitrogen \( \text{(N)} \), which is 14 g/mol. Calculate the moles of N in 70 g: \( \text{moles of N} = \frac{70 \text{ g}}{14 \text{ g/mol}} = 5 \text{ mol} \).

Calculate Number of Atoms in N

Use Avogadro's number: \( \text{Number of atoms in N} = 5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} \) atoms.

Calculate Moles of H

The molar mass of hydrogen \( \text{(H)} \) is 1 g/mol. Calculate the moles of H in 20 g: \( \text{moles of H} = \frac{20 \text{ g}}{1 \text{ g/mol}} = 20 \text{ mol} \).

Calculate Number of Atoms in H

Use Avogadro's number: \( \text{Number of atoms in H} = 20 \times 6.022 \times 10^{23} = 1.2044 \times 10^{25} \) atoms.

Compare Results

Compare the number of atoms: Fe has \( 6.022 \times 10^{24} \) atoms, N has \( 3.011 \times 10^{24} \) atoms, and H has \( 1.2044 \times 10^{25} \) atoms. Thus, \( 6.022 \times 10^{24} \) is twice \( 3.011 \times 10^{24} \) and half \( 1.2044 \times 10^{25} \).

Key concepts

Avogadro's Number

Avogadro's Number is one of the most fundamental constants in chemistry. It represents the number of atoms or molecules in one mole of a substance. Avogadro's Number is often denoted as \( 6.022 \times 10^{23} \). This enormous number allows chemists to relate the macroscopic amounts of materials we can see and measure, to the microscopic quantities of atoms and molecules.
When you have a mole of any element, it contains \( 6.022 \times 10^{23} \) of its atoms. This makes calculations involving reactions and stoichiometry consistent and predictable. Whether you are dealing with carbon, oxygen, or copper, one mole will consistently have Avogadro's Number of atoms.

• Think of Avogadro's Number as a bridge between the atomic scale and the practical scale.
• It provides a way to count atoms by weighing them.

Atomic Mass

Atomic Mass is a measure of the mass of an atom, typically expressed in atomic mass units (amu) or grams per mole (g/mol). It accounts for the average mass of all the isotopes of an element, based on their abundance in nature.
For instance, the atomic mass of iron (Fe) is approximately 56 g/mol. This means one mole of iron atoms weighs 56 grams. When working with chemical reactions, knowing the atomic mass allows you to convert between the mass of elements and moles. This is practical because it's nearly impossible to count atoms, but we can easily measure mass.

• Atomic Mass links the measurable world of grams to the countable world of moles.
• It is crucial for stoichiometry and determining the quantities of reactants and products.

Number of Atoms

The Number of Atoms in a given sample can be determined from the moles of the element using Avogadro's Number. Calculating the number of atoms involves a straightforward conversion from macroscale quantities to an atomic scale understanding using this fundamental relationship:
The number of atoms in a sample = (moles of the element) \( \times 6.022 \times 10^{23} \).
This relationship enables calculations around reactions, balancing equations, and understanding the composition of compounds. Let's consider the example of 560 g of iron (Fe) from the exercise. The number of moles of Fe is determined by dividing its mass by its atomic mass, yielding 10 moles. Since one mole equals Avogadro's Number of atoms, the result is \(10 \times 6.022 \times 10^{23} = 6.022 \times 10^{24}\) atoms.

• This principle ensures precise chemical formulations and reactions.
• It's an essential tool for chemists in measuring and predicting chemical behavior.