A system contains 100 g of oxygen. How many moles does it contain? How many molecules?
The correct answer and explanation is:
Correct Answer:
- Moles of oxygen (O₂): 3.125 mol
- Number of molecules: 1.883 × 10²⁴ molecules
Explanation:
To determine the number of moles in 100 grams of oxygen and the number of molecules, start by understanding the molecular form and molar mass of oxygen.
Oxygen gas exists as a diatomic molecule, meaning it appears as O₂ in nature. The atomic mass of a single oxygen atom is 16 grams per mole. Therefore, the molar mass of O₂ is:
Molar mass of O₂ = 16 g/mol × 2 = 32 g/mol
To find the number of moles, divide the given mass by the molar mass:
Moles = Mass ÷ Molar mass = 100 g ÷ 32 g/mol = 3.125 mol
Now that the number of moles is known, calculate the number of molecules using Avogadro’s number. Avogadro’s number is:
6.022 × 10²³ molecules/mol
To find the number of molecules in 3.125 mol of oxygen:
Molecules = Moles × Avogadro’s number
= 3.125 mol × 6.022 × 10²³ molecules/mol
= 1.882 × 10²⁴ molecules (rounded to 3 significant figures)
This calculation shows that 100 grams of oxygen gas contains 3.125 moles, and this corresponds to about 1.883 × 10²⁴ oxygen molecules. These steps are useful in chemistry when converting between mass, moles, and number of particles. Understanding the molar relationship helps in chemical reactions, stoichiometry, and other scientific calculations.