A sample contains 3.011×10 23 molecules of CO 2 ​ . Calculate its mass and the total number of oxygen atoms present.

📘 Complete Solution

📌 Given Data

Number of CO₂ molecules = 3.011 × 10²³

Atomic mass of C = 12
Atomic mass of O = 16

N_A = 6.022 × 10²³ mol⁻¹

🔵 Step 1: Calculate Number of Moles

We know:

Number of molecules = Number of moles × N_A

Therefore,

Number of moles = Number of molecules ÷ N_A

= (3.011 × 10²³) ÷ (6.022 × 10²³)

= 0.5 mole

✅ Number of moles of CO₂ = 0.5 mol

🟢 Step 2: Calculate Molar Mass of CO₂

Molar Mass of CO₂

= Atomic mass of C + (2 × Atomic mass of O)

= 12 + (2 × 16)

= 12 + 32

= 44 g mol⁻¹

🟠 Step 3: Calculate Mass of CO₂

Use:

Mass = Number of moles × Molar Mass

Mass = 0.5 × 44

= 22 g

✅ Mass of the sample = 22 g

🟣 Step 4: Calculate Total Number of Oxygen Atoms

Each CO₂ molecule contains 2 oxygen atoms.

Oxygen atoms = Number of CO₂ molecules × 2

= 3.011 × 10²³ × 2

= 6.022 × 10²³ oxygen atoms

✅ Total oxygen atoms = 6.022 × 10²³

🎬 3D-Style CO₂ Molecular Animation

One CO₂ molecule contains one carbon atom and two oxygen atoms.

O C O

1 CO₂ molecule → 2 Oxygen atoms

3.011 × 10²³ CO₂ molecules → 6.022 × 10²³ Oxygen atoms

⚡ Quick Shortcut

3.011 × 10²³ molecules
↓
0.5 mole CO₂
↓
Molar Mass = 44 g mol⁻¹
↓
Mass = 22 g

Each CO₂ molecule has 2 O atoms
↓
O atoms = 6.022 × 10²³

✅ Final Answer

Number of moles = 0.5 mol

Mass of CO₂ = 22 g

Total number of oxygen atoms = 6.022 × 10²³

🎯 Formula Revision

Moles = Molecules ÷ N_A
Mass = Moles × Molar Mass
Oxygen Atoms = CO₂ Molecules × 2