How many atoms are in 4.39 g of CO2?
The Correct Answer and Explanation is:
To find how many atoms are in 4.39 grams of carbon dioxide (CO₂), follow these steps:
Step 1: Calculate the molar mass of CO₂
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol × 2 = 32.00 g/mol
- Total molar mass of CO₂ = 12.01 + 32.00 = 44.01 g/mol
Step 2: Convert grams of CO₂ to moles
Moles of CO₂=4.39 g44.01 g/mol≈0.0998 mol\text{Moles of CO₂} = \frac{4.39 \text{ g}}{44.01 \text{ g/mol}} ≈ 0.0998 \text{ mol}Moles of CO₂=44.01 g/mol4.39 g≈0.0998 mol
Step 3: Use Avogadro’s number to find number of molecules
Number of molecules=0.0998 mol×6.022×1023 molecules/mol≈6.01×1022 molecules\text{Number of molecules} = 0.0998 \text{ mol} × 6.022 × 10^{23} \text{ molecules/mol} ≈ 6.01 × 10^{22} \text{ molecules}Number of molecules=0.0998 mol×6.022×1023 molecules/mol≈6.01×1022 molecules
Step 4: Count atoms per molecule of CO₂
Each molecule of CO₂ contains:
- 1 carbon atom
- 2 oxygen atoms
Total = 3 atoms per molecule
Step 5: Multiply molecules by atoms per molecule
Total atoms=6.01×1022 molecules×3 atoms/molecule≈1.80×1023 atoms\text{Total atoms} = 6.01 × 10^{22} \text{ molecules} × 3 \text{ atoms/molecule} ≈ 1.80 × 10^{23} \text{ atoms}Total atoms=6.01×1022 molecules×3 atoms/molecule≈1.80×1023 atoms
Final Answer:
There are approximately 1.80 × 10²³ atoms in 4.39 grams of CO₂.
Explanation
To determine how many atoms are in a given mass of carbon dioxide, we begin by finding the molar mass of the compound. Carbon dioxide has one atom of carbon and two atoms of oxygen. Carbon has an atomic mass of about 12.01 grams per mole, while oxygen has an atomic mass of about 16.00 grams per mole. Thus, the molar mass of carbon dioxide is 44.01 grams per mole.
Next, we convert the given mass (4.39 grams) of carbon dioxide into moles. This is done by dividing the mass by the molar mass, yielding approximately 0.0998 moles. This step tells us how many moles of carbon dioxide molecules we have.
To determine how many individual molecules this represents, we use Avogadro’s number, which states that one mole of any substance contains approximately 6.022 × 10²³ entities, in this case, molecules. Multiplying the number of moles by Avogadro’s number gives us around 6.01 × 10²² carbon dioxide molecules.
Finally, we must remember that each molecule of carbon dioxide consists of three atoms—one carbon atom and two oxygen atoms. Therefore, to find the total number of atoms, we multiply the number of molecules by three. This results in a total of about 1.80 × 10²³ atoms in 4.39 grams of carbon dioxide.
