How many molecules are present in 4.61 × 10^(-2) mol of O2
The Correct Answer and Explanation is:
To find the number of molecules in 4.61 × 10⁻² mol of O₂, we use Avogadro’s number, which is:
6.022 × 10²³ molecules/mol
Step-by-Step Solution:
We are given:
- Amount of oxygen gas (O₂) = 4.61 × 10⁻² mol
- Avogadro’s number = 6.022 × 10²³ molecules/mol
To find the number of O₂ molecules, multiply the number of moles by Avogadro’s number:Number of molecules=(4.61×10−2 mol)×(6.022×1023 molecules/mol)\text{Number of molecules} = (4.61 \times 10^{-2} \text{ mol}) \times (6.022 \times 10^{23} \text{ molecules/mol})Number of molecules=(4.61×10−2 mol)×(6.022×1023 molecules/mol)=2.777×1022 molecules= 2.777 \times 10^{22} \text{ molecules}=2.777×1022 molecules
✅ Final Answer:
2.78 × 10²² molecules of O₂ (rounded to three significant figures)
📘 Explanation
In chemistry, the concept of the “mole” is essential for relating microscopic particles like atoms and molecules to measurable quantities in the laboratory. One mole of any substance contains 6.022 × 10²³ representative particles, whether those are atoms, molecules, ions, or electrons. This large number is known as Avogadro’s number.
In this case, we are dealing with oxygen gas (O₂), which is made up of diatomic molecules—each molecule contains two oxygen atoms. The question asks how many molecules are present in 4.61 × 10⁻² moles of oxygen gas.
To determine this, we use a direct multiplication:
We take the number of moles and multiply by Avogadro’s number. This gives us the total number of molecules, not atoms. Since each O₂ molecule consists of two oxygen atoms, if the question had asked for atoms, we would have multiplied the result by 2. But since we are only asked for molecules, the answer remains at 2.78 × 10²² molecules.
This type of calculation is foundational in stoichiometry, where chemists use balanced chemical equations to calculate the amounts of reactants and products. Understanding how to convert between moles and number of particles is essential for mastering concepts like gas laws, molar masses, and chemical reactions.
