How many ATOMS of carbon are present in 6.43 grams of carbon dioxide? __atoms of carbon . 2. How many GRAMS of oxygen are present in 2.05 x 10^21 molecules of carbon dioxide? ___grams of oxygen .
The Correct Answer and Explanation is:
Let’s break this down step-by-step:
Question 1: How many atoms of carbon are present in 6.43 grams of carbon dioxide (CO₂)?
- Molar Mass of CO₂:
- Carbon (C) has a molar mass of 12.01 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
- The molar mass of CO₂ = (1 × 12.01) + (2 × 16.00) = 44.01 g/mol.
- Moles of CO₂:
To find the number of moles of CO₂, divide the given mass of CO₂ by the molar mass of CO₂: Moles of CO₂=6.43 g44.01 g/mol≈0.1465 mol\text{Moles of CO₂} = \frac{6.43 \text{ g}}{44.01 \text{ g/mol}} \approx 0.1465 \text{ mol}Moles of CO₂=44.01 g/mol6.43 g≈0.1465 mol - Atoms of Carbon:
Since each molecule of CO₂ contains 1 atom of carbon, the number of moles of carbon atoms is the same as the moles of CO₂.
To find the number of carbon atoms, multiply the moles of carbon by Avogadro’s number (6.022 × 10²³ atoms/mol): Atoms of carbon=0.1465 mol×6.022×1023 atoms/mol≈8.82×1022 atoms\text{Atoms of carbon} = 0.1465 \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 8.82 \times 10^{22} \text{ atoms}Atoms of carbon=0.1465 mol×6.022×1023 atoms/mol≈8.82×1022 atoms
Answer: There are approximately 8.82 × 10²² atoms of carbon in 6.43 grams of CO₂.
Question 2: How many grams of oxygen are present in 2.05 × 10²¹ molecules of CO₂?
- Molecules of CO₂ to Moles of CO₂:
To convert molecules of CO₂ to moles, use Avogadro’s number: Moles of CO₂=2.05×1021 molecules6.022×1023 molecules/mol≈3.41×10−3 mol\text{Moles of CO₂} = \frac{2.05 \times 10^{21} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 3.41 \times 10^{-3} \text{ mol}Moles of CO₂=6.022×1023 molecules/mol2.05×1021 molecules≈3.41×10−3 mol - Moles of Oxygen:
Each molecule of CO₂ contains 2 atoms of oxygen, so the number of moles of oxygen atoms will be twice the moles of CO₂: Moles of oxygen=3.41×10−3 mol CO₂×2=6.82×10−3 mol oxygen\text{Moles of oxygen} = 3.41 \times 10^{-3} \text{ mol CO₂} \times 2 = 6.82 \times 10^{-3} \text{ mol oxygen}Moles of oxygen=3.41×10−3 mol CO₂×2=6.82×10−3 mol oxygen - Mass of Oxygen:
The molar mass of oxygen is 16.00 g/mol, so to find the mass of oxygen: Mass of oxygen=6.82×10−3 mol×16.00 g/mol=0.1091 g\text{Mass of oxygen} = 6.82 \times 10^{-3} \text{ mol} \times 16.00 \text{ g/mol} = 0.1091 \text{ g}Mass of oxygen=6.82×10−3 mol×16.00 g/mol=0.1091 g
Answer: There are approximately 0.109 grams of oxygen in 2.05 × 10²¹ molecules of CO₂.
Summary:
- The number of carbon atoms in 6.43 grams of CO₂ is approximately 8.82 × 10²².
- The mass of oxygen in 2.05 × 10²¹ molecules of CO₂ is approximately 0.109 grams.
