Answer :
Sure! Let's address each part of the question one by one, providing explanations and results:
1. Atoms in 8.00 moles of sodium sulphate (Na₂SO₄):
To find the number of atoms, we multiply the number of moles by Avogadro's number (approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mol). Sodium sulphate contains multiple atoms in each molecule.
[tex]\[
\text{Number of atoms} = 8.00 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 4.8176 \times 10^{24} \text{ atoms}
\][/tex]
2. Nitrogen atoms in 0.510 moles of nitrogen gas (N₂):
Since nitrogen gas is diatomic (N₂), each mole of nitrogen gas contains 2 moles of nitrogen atoms.
[tex]\[
\text{Nitrogen atoms} = 0.510 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 3.07122 \times 10^{23} \text{ atoms}
\][/tex]
3. Molecules in 6.74 grams of aluminum nitrate (Al(NO₃)₃):
First, convert grams to moles using the molar mass of aluminum nitrate. Then multiply by Avogadro's number.
[tex]\[
\text{Number of molecules} \approx 1.9055530516431925 \times 10^{22} \text{ molecules}
\][/tex]
4. Atoms in 9.6 grams of alumina (Al₂O₃):
Convert grams to moles using the molar mass and then find the number of atoms, considering the formula of alumina.
[tex]\[
\text{Number of atoms} \approx 5.669988230678698 \times 10^{22} \text{ atoms}
\][/tex]
5. Oxygen atoms in 20.0 grams of rubidium nitrate (RbNO₃):
Convert grams to moles, then find the number of oxygen atoms. Rubidium nitrate has three oxygen atoms per molecule.
[tex]\[
\text{Oxygen atoms} \approx 2.449959316517494 \times 10^{23} \text{ atoms}
\][/tex]
6. Atoms in 5 molecules of aluminum chloride (AlCl₃):
Aluminum chloride has four atoms per molecule (one aluminum and three chlorine), so:
[tex]\[
\text{Number of atoms} = 5 \text{ molecules} \times 4 \approx 25 \text{ atoms}
\][/tex]
7. Atoms in 0.82 moles of sodium sulphide (Na₂S):
Convert moles to atoms (each molecule contains three atoms: 2 sodium, 1 sulfur).
[tex]\[
\text{Number of atoms} \approx 4.93804 \times 10^{23} \text{ atoms}
\][/tex]
8. Atoms in 20.0 moles of nitrogen gas (N₂):
Each molecule of nitrogen gas contains two nitrogen atoms.
[tex]\[
\text{Nitrogen atoms} \approx 2.4088 \times 10^{25} \text{ atoms}
\][/tex]
9. Atoms in 5.00 moles of oxygen (O₂):
Oxygen gas is diatomic, so each mole contains two moles of oxygen atoms.
[tex]\[
\text{Oxygen atoms} \approx 3.011 \times 10^{24} \text{ atoms}
\][/tex]
10. Molecules in 8.24 grams of lead(II) oxide (PbO):
Convert grams to moles and then calculate molecules.
[tex]\[
\text{Number of molecules} \approx 2.223175627240144 \times 10^{22} \text{ molecules}
\][/tex]
11. Hydrogen atoms in 182.3 grams of ammonium sulphate ((NH₄)₂SO₄):
Convert grams to moles, accounting for hydrogen atoms per formula unit.
[tex]\[
\text{Hydrogen atoms} \approx 6.646348418344181 \times 10^{24} \text{ atoms}
\][/tex]
These calculations will help you understand how the number of atoms or molecules can be derived from given masses or moles of substances through stoichiometric conversions and Avogadro's number.
1. Atoms in 8.00 moles of sodium sulphate (Na₂SO₄):
To find the number of atoms, we multiply the number of moles by Avogadro's number (approximately [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mol). Sodium sulphate contains multiple atoms in each molecule.
[tex]\[
\text{Number of atoms} = 8.00 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 4.8176 \times 10^{24} \text{ atoms}
\][/tex]
2. Nitrogen atoms in 0.510 moles of nitrogen gas (N₂):
Since nitrogen gas is diatomic (N₂), each mole of nitrogen gas contains 2 moles of nitrogen atoms.
[tex]\[
\text{Nitrogen atoms} = 0.510 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 3.07122 \times 10^{23} \text{ atoms}
\][/tex]
3. Molecules in 6.74 grams of aluminum nitrate (Al(NO₃)₃):
First, convert grams to moles using the molar mass of aluminum nitrate. Then multiply by Avogadro's number.
[tex]\[
\text{Number of molecules} \approx 1.9055530516431925 \times 10^{22} \text{ molecules}
\][/tex]
4. Atoms in 9.6 grams of alumina (Al₂O₃):
Convert grams to moles using the molar mass and then find the number of atoms, considering the formula of alumina.
[tex]\[
\text{Number of atoms} \approx 5.669988230678698 \times 10^{22} \text{ atoms}
\][/tex]
5. Oxygen atoms in 20.0 grams of rubidium nitrate (RbNO₃):
Convert grams to moles, then find the number of oxygen atoms. Rubidium nitrate has three oxygen atoms per molecule.
[tex]\[
\text{Oxygen atoms} \approx 2.449959316517494 \times 10^{23} \text{ atoms}
\][/tex]
6. Atoms in 5 molecules of aluminum chloride (AlCl₃):
Aluminum chloride has four atoms per molecule (one aluminum and three chlorine), so:
[tex]\[
\text{Number of atoms} = 5 \text{ molecules} \times 4 \approx 25 \text{ atoms}
\][/tex]
7. Atoms in 0.82 moles of sodium sulphide (Na₂S):
Convert moles to atoms (each molecule contains three atoms: 2 sodium, 1 sulfur).
[tex]\[
\text{Number of atoms} \approx 4.93804 \times 10^{23} \text{ atoms}
\][/tex]
8. Atoms in 20.0 moles of nitrogen gas (N₂):
Each molecule of nitrogen gas contains two nitrogen atoms.
[tex]\[
\text{Nitrogen atoms} \approx 2.4088 \times 10^{25} \text{ atoms}
\][/tex]
9. Atoms in 5.00 moles of oxygen (O₂):
Oxygen gas is diatomic, so each mole contains two moles of oxygen atoms.
[tex]\[
\text{Oxygen atoms} \approx 3.011 \times 10^{24} \text{ atoms}
\][/tex]
10. Molecules in 8.24 grams of lead(II) oxide (PbO):
Convert grams to moles and then calculate molecules.
[tex]\[
\text{Number of molecules} \approx 2.223175627240144 \times 10^{22} \text{ molecules}
\][/tex]
11. Hydrogen atoms in 182.3 grams of ammonium sulphate ((NH₄)₂SO₄):
Convert grams to moles, accounting for hydrogen atoms per formula unit.
[tex]\[
\text{Hydrogen atoms} \approx 6.646348418344181 \times 10^{24} \text{ atoms}
\][/tex]
These calculations will help you understand how the number of atoms or molecules can be derived from given masses or moles of substances through stoichiometric conversions and Avogadro's number.
