Question

How many moles of atoms are there in each of the following? a. 40.1 \(\mathrm{g} \mathrm{Ca}\) b. 11.5 \(\mathrm{g} \mathrm{Na}\) c. 5.87 \(\mathrm{g} \mathrm{Ni}\) d. 150 \(\mathrm{gS}\) e. 2.65 \(\mathrm{g} \mathrm{Fe}\) f. 0.00750 \(\mathrm{g} \mathrm{Ag}\) g. \(2.25 \times 10^{25}\) atoms \(\mathrm{Zn}\) h. 50 atoms \(\mathrm{Ba}\)

Short answer

a. 1.00 molb. 0.500 molc. 0.100 mold. 4.68 mole. 0.0475 molf. 0.0000695 molg. 37.4 molh. 8.30 × 10⁻²³ mol

Step-by-step solution

Convert grams to moles for each element

Use the formula: \[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass of element}} \]Look up the molar masses: \( \text{Ca} = 40.08 \frac{\text{g}}{\text{mol}} \), \( \text{Na} = 22.99 \frac{\text{g}}{\text{mol}} \), \( \text{Ni} = 58.69 \frac{\text{g}}{\text{mol}} \), \( \text{S} = 32.07 \frac{\text{g}}{\text{mol}} \), \( \text{Fe} = 55.85 \frac{\text{g}}{\text{mol}} \), \( \text{Ag} = 107.87 \frac{\text{g}}{\text{mol}} \).

Calculate moles for each element

a. For 40.1 g Ca:\[ \text{Moles of Ca} = \frac{40.1 \text{ g}}{40.08 \frac{\text{g}}{\text{mol}}} \ \text{Moles of Ca} \approx 1.00 \text{ mol} \]b. For 11.5 g Na:\[ \text{Moles of Na} = \frac{11.5 \text{ g}}{22.99 \frac{\text{g}}{\text{mol}}} \ \text{Moles of Na} \approx 0.500 \text{ mol} \]c. For 5.87 g Ni:\[ \text{Moles of Ni} = \frac{5.87 \text{ g}}{58.69 \frac{\text{g}}{\text{mol}}} \ \text{Moles of Ni} \approx 0.100 \text{ mol} \]d. For 150 g S:\[ \text{Moles of S} = \frac{150 \text{ g}}{32.07 \frac{\text{g}}{\text{mol}}} \ \text{Moles of S} \approx 4.68 \text{ mol} \]e. For 2.65 g Fe:\[ \text{Moles of Fe} = \frac{2.65 \text{ g}}{55.85 \frac{\text{g}}{\text{mol}}} \ \text{Moles of Fe} \approx 0.0475 \text{ mol} \] f. For 0.00750 g Ag:\[ \text{Moles of Ag} = \frac{0.00750 \text{ g}}{107.87 \frac{\text{g}}{\text{mol}}} \ \text{Moles of Ag} \approx 0.0000695 \text{ mol} \]

Convert atoms to moles for each element

Use Avogadro's number: \( 6.022 \times 10^{23} \) atoms/mol.g. For \(2.25 \times 10^{25}\) atoms Zn:\[ \text{Moles of Zn} = \frac{2.25 \times 10^{25} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \ \text{Moles of Zn} \approx 37.4 \text{ mol} \]h. For 50 atoms Ba:\[ \text{Moles of Ba} = \frac{50 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \ \text{Moles of Ba} \approx 8.30 \times 10^{-23} \text{ mol} \]

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, defined as the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol). The molar mass is determined by the atomic or molecular weight of an element or compound.
For example, the molar mass of Calcium (Ca) is \[40.08 \frac{grams}{mole} \] while the molar mass of Sodium (Na) is \[22.99 \frac{grams}{mole} \].
Knowing the molar mass allows us to convert between the mass of a substance and the number of moles, using the formula: \[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass of the element}} \]. This conversion is essential for many chemical calculations.

Avogadro's Number

Avogadro's Number is another key concept in chemistry. It provides a way to understand the quantity of atoms or molecules in a mole. Avogadro's Number is \[ 6.022 \times 10^{23} \] atoms or molecules per mole. This number allows chemists to convert between the number of atoms or molecules and the number of moles.
For example, 1 mole of any substance always contains \[ 6.022 \times 10^{23} \] entities (atoms or molecules).
When we know the number of atoms, Avogadro's Number can help us calculate the number of moles using the formula: \[ \text{Moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} \].

Moles to Atoms Conversion

The conversion of moles to atoms is frequently required in chemistry problems. This conversion utilizes Avogadro's Number, allowing us to understand the relationship between the macroscopic and microscopic quantities.
For instance, if we have 1 mole of zinc (Zn), we know it contains \[ 6.022 \times 10^{23} \] atoms. Conversely, if we start with \[2.25 \times 10^{25} \] atoms of Zn, the number of moles can be calculated using: \[ \text{Moles of Zn} = \frac{2.25 \times 10^{25} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \text{Moles of Zn} \approx 37.4 \text{ mol} \].
This relationship is crucial for stoichiometric calculations and understanding the scale of chemical reactions.

Stoichiometry

Stoichiometry is the study of the quantitative aspects of chemical reactions. It involves calculations based on balanced chemical equations to determine the amounts of reactants and products involved.
For instance, when converting grams to moles, we follow these steps:

• Determine the molar mass of each element or compound
• Use the formula: \[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass}} \]
• Apply the concept for each reactant and product

In a reaction, if given 11.5 grams of Na with a molar mass of \[ 22.99 \frac{grams}{mole} \], we calculate: \[ \text{Moles of Na} = \frac{11.5 \text{ grams}}{22.99 \frac{grams}{mole}} \approx 0.500 \text{ mol} \]. Understanding stoichiometry allows chemists to forecast the course of reactions, determine yields, and prepare chemical compounds efficiently.