1 mole = 6.02 x 10²³ particles. Particles can be: atoms, molecules, ions, or formula units.

1 mole = 22.4 L at STP. Liter is a measure of volume.

1 mole = Formula mass in grams. Formula mass uses the atomic masses of elements to calculate.

2-step mole problems: have moles and a conversion factor in the question.

1-step mole problems: have either moles, grams, particles, or liters in the question.

1. To find the number of moles in 25.0g of O₂, we use the formula:
Moles = Mass / Molar mass
The molar mass of O₂ is 32 g/mol.
Moles = 25.0g / 32 g/mol = 0.78125 mol

2. To find the number of particles in 100.0g of gold, we use the formula:
Particles = Moles * Avogadro's number
The molar mass of gold (Au) is 197 g/mol.
Moles = 100.0g / 197 g/mol ≈ 0.5076 mol
Particles = 0.5076 mol * 6.02 x 10²³ particles/mol ≈ 3.06 x 10²³ particles

3. To find the number of liters in 3 moles of carbon dioxide (CO₂) at STP, we use the fact that 1 mole of any gas occupies 22.4 L at STP.
Liters = 3 moles * 22.4 L/mol = 67.2 L

4. To find the number of particles in 50.0L of NO₂, we use the formula:
Particles = Moles * Avogadro's number
First, we need to find the number of moles. Since the volume is given, we convert it to moles using the ideal gas law.
Moles = Volume / 22.4 L/mol = 50.0L / 22.4 L/mol ≈ 2.23 mol
Particles = 2.23 mol * 6.02 x 10²³ particles/mol ≈ 1.34 x 10²⁴ particles

5. To find the number of grams in 5.0 x 10²⁵ molecules of water (H₂O), we use the formula:
Grams = Moles * Molar mass
The molar mass of water (H₂O) is 18 g/mol.
Moles = (5.0 x 10²⁵ molecules) / (6.02 x 10²³ molecules/mol) ≈ 8.31 mol
Grams = 8.31 mol * 18 g/mol ≈ 149.58 g

6. To find the number of grams in 6.00 moles of C₅H₁₂O₅, we use the formula:
Grams = Moles * Molar mass
The molar mass of C₅H₁₂O₅ is 92.1 g/mol.
Grams = 6.00 mol * 92.1 g/mol = 552.6 g

7. To find the number of moles in 22.4L of H₂S, we use the formula:
Moles = Volume / 22.4 L/mol = 22.4L / 22.4 L/mol = 1 mol

8. To find the number of moles in 3.00 x 10²² atoms
of gold, we use the formula:
Moles = Number of atoms / Avogadro's number
Moles = (3.00 x 10²² atoms) / (6.02 x 10²³ atoms/mol) ≈ 0.498 mol

9. To find the number of particles in 25.0g of carbon (C), we use the formula:
Moles = Mass / Molar mass
The molar mass of carbon (C) is 12 g/mol.
Moles = 25.0g / 12 g/mol ≈ 2.08 mol
Particles = 2.08 mol * 6.02 x 10²³ particles/mol ≈ 1.25 x 10²⁴ particles

10. To find the number of liters in 20.0 moles of carbon dioxide (CO₂) at STP, we use the fact that 1 mole of any gas occupies 22.4 L at STP.
Liters = 20.0 moles * 22.4 L/mol = 448 L

11. To find the number of grams in 44.8L of oxygen (O₂) at STP, we use the fact that 1 mole of any gas occupies 22.4 L at STP and the molar mass of oxygen is 32 g/mol.
Moles = Volume / 22.4 L/mol = 44.8L / 22.4 L/mol = 2 mol
Grams = 2 mol * 32 g/mol = 64 g

12. To find the number of liters in 1.34g of carbon monoxide (CO), we use the fact that 1 mole of any gas occupies 22.4 L at STP and the molar mass of carbon monoxide is 28 g/mol.
Moles = Mass / Molar mass = 1.34g / 28 g/mol ≈ 0.048 mol
Liters = 0.048 mol * 22.4 L/mol ≈ 1.08 L
