Answer :
Sure, let's solve the problem step by step, providing detailed calculations for each part.
### (a) Atoms of Aluminium in 0.2 Moles of Aluminium
We are given 0.2 moles of aluminium (Al). Using Avogadro's number (6.022 × 10²³ particles/mol), we can calculate the number of aluminium atoms.
[tex]\[ \text{Number of atoms of Al} = \text{moles of Al} \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of atoms of Al} = 0.2 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of atoms of Al} \approx 1.2044 \times 10^{23} \][/tex]
### (b) Molecules of [tex]\(CO_2\)[/tex] in 0.4 Moles of [tex]\(CO_2\)[/tex]
We are given 0.4 moles of carbon dioxide (CO₂). Similarly, we use Avogadro's number to find the number of molecules.
[tex]\[ \text{Number of molecules of } CO_2 = \text{moles of } CO_2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of molecules of } CO_2 = 0.4 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of molecules of } CO_2 \approx 2.4088 \times 10^{23} \][/tex]
### (c) Oxygen Atoms in 8 g of Oxygen
We are given 8 grams of oxygen (O₂). First, we need to calculate the moles of oxygen.
The molar mass of O₂ is 32 g/mol (since each O atom is 16 g and O₂ has 2 atoms).
[tex]\[ \text{Moles of } O_2 = \frac{\text{mass of O}_2}{\text{molar mass of O}_2} \][/tex]
[tex]\[ \text{Moles of } O_2 = \frac{8}{32} = 0.25 \text{ mol} \][/tex]
Each molecule of O₂ consists of 2 atoms of oxygen. Therefore, the number of oxygen atoms is given by:
[tex]\[ \text{Number of oxygen atoms} = \text{moles of } O_2 \times \text{Avogadro's number} \times 2 \][/tex]
[tex]\[ \text{Number of oxygen atoms} = 0.25 \times 6.022 \times 10^{23} \times 2 \][/tex]
[tex]\[ \text{Number of oxygen atoms} \approx 3.011 \times 10^{23} \][/tex]
### (d) Oxygen Molecules in 8 g of Oxygen
Using the same 8 grams of oxygen, we previously determined that it corresponds to 0.25 moles of O₂.
The number of oxygen molecules can be found by:
[tex]\[ \text{Number of oxygen molecules} = \text{moles of } O_2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of oxygen molecules} = 0.25 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of oxygen molecules} \approx 1.505 \times 10^{23} \][/tex]
### (e) Hydrogen and Sulphate Ions in 4.9 g of Sulphuric Acid (H₂SO₄)
We are given 4.9 grams of sulphuric acid (H₂SO₄). First, we calculate the molar mass of H₂SO₄:
[tex]\[ \text{Molar mass of } H_2SO_4 = 2 \times 1 + 32 + 4 \times 16 = 98 \text{ g/mol} \][/tex]
Next, we calculate the number of moles of H₂SO₄:
[tex]\[ \text{Moles of } H_2SO_4 = \frac{\text{mass of } H_2SO_4}{\text{molar mass of } H_2SO_4} \][/tex]
[tex]\[ \text{Moles of } H_2SO_4 = \frac{4.9}{98} = 0.05 \text{ mol} \][/tex]
Each mole of H₂SO₄ yields 2 moles of hydrogen ions (H⁺) and 1 mole of sulphate ions (SO₄²⁻).
[tex]\[ \text{Number of hydrogen ions} = \text{moles of } H_2SO_4 \times 2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of hydrogen ions} = 0.05 \times 2 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of hydrogen ions} \approx 6.022 \times 10^{22} \][/tex]
[tex]\[ \text{Number of sulphate ions} = \text{moles of } H_2SO_4 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of sulphate ions} = 0.05 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of sulphate ions} \approx 3.011 \times 10^{22} \][/tex]
In summary:
(a) The number of atoms of aluminium in 0.2 moles is [tex]\(1.2044 \times 10^{23}\)[/tex].
(b) The number of molecules of [tex]\(CO_2\)[/tex] in 0.4 moles is [tex]\(2.4088 \times 10^{23}\)[/tex].
(c) The number of oxygen atoms in 8 g of oxygen is [tex]\(3.011 \times 10^{23}\)[/tex].
(d) The number of oxygen molecules in 8 g of oxygen is [tex]\(1.505 \times 10^{23}\)[/tex].
(e) The number of hydrogen ions in 4.9 g of H₂SO₄ is [tex]\(6.022 \times 10^{22}\)[/tex] and the number of sulphate ions is [tex]\(3.011 \times 10^{22}\)[/tex].
### (a) Atoms of Aluminium in 0.2 Moles of Aluminium
We are given 0.2 moles of aluminium (Al). Using Avogadro's number (6.022 × 10²³ particles/mol), we can calculate the number of aluminium atoms.
[tex]\[ \text{Number of atoms of Al} = \text{moles of Al} \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of atoms of Al} = 0.2 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of atoms of Al} \approx 1.2044 \times 10^{23} \][/tex]
### (b) Molecules of [tex]\(CO_2\)[/tex] in 0.4 Moles of [tex]\(CO_2\)[/tex]
We are given 0.4 moles of carbon dioxide (CO₂). Similarly, we use Avogadro's number to find the number of molecules.
[tex]\[ \text{Number of molecules of } CO_2 = \text{moles of } CO_2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of molecules of } CO_2 = 0.4 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of molecules of } CO_2 \approx 2.4088 \times 10^{23} \][/tex]
### (c) Oxygen Atoms in 8 g of Oxygen
We are given 8 grams of oxygen (O₂). First, we need to calculate the moles of oxygen.
The molar mass of O₂ is 32 g/mol (since each O atom is 16 g and O₂ has 2 atoms).
[tex]\[ \text{Moles of } O_2 = \frac{\text{mass of O}_2}{\text{molar mass of O}_2} \][/tex]
[tex]\[ \text{Moles of } O_2 = \frac{8}{32} = 0.25 \text{ mol} \][/tex]
Each molecule of O₂ consists of 2 atoms of oxygen. Therefore, the number of oxygen atoms is given by:
[tex]\[ \text{Number of oxygen atoms} = \text{moles of } O_2 \times \text{Avogadro's number} \times 2 \][/tex]
[tex]\[ \text{Number of oxygen atoms} = 0.25 \times 6.022 \times 10^{23} \times 2 \][/tex]
[tex]\[ \text{Number of oxygen atoms} \approx 3.011 \times 10^{23} \][/tex]
### (d) Oxygen Molecules in 8 g of Oxygen
Using the same 8 grams of oxygen, we previously determined that it corresponds to 0.25 moles of O₂.
The number of oxygen molecules can be found by:
[tex]\[ \text{Number of oxygen molecules} = \text{moles of } O_2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of oxygen molecules} = 0.25 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of oxygen molecules} \approx 1.505 \times 10^{23} \][/tex]
### (e) Hydrogen and Sulphate Ions in 4.9 g of Sulphuric Acid (H₂SO₄)
We are given 4.9 grams of sulphuric acid (H₂SO₄). First, we calculate the molar mass of H₂SO₄:
[tex]\[ \text{Molar mass of } H_2SO_4 = 2 \times 1 + 32 + 4 \times 16 = 98 \text{ g/mol} \][/tex]
Next, we calculate the number of moles of H₂SO₄:
[tex]\[ \text{Moles of } H_2SO_4 = \frac{\text{mass of } H_2SO_4}{\text{molar mass of } H_2SO_4} \][/tex]
[tex]\[ \text{Moles of } H_2SO_4 = \frac{4.9}{98} = 0.05 \text{ mol} \][/tex]
Each mole of H₂SO₄ yields 2 moles of hydrogen ions (H⁺) and 1 mole of sulphate ions (SO₄²⁻).
[tex]\[ \text{Number of hydrogen ions} = \text{moles of } H_2SO_4 \times 2 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of hydrogen ions} = 0.05 \times 2 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of hydrogen ions} \approx 6.022 \times 10^{22} \][/tex]
[tex]\[ \text{Number of sulphate ions} = \text{moles of } H_2SO_4 \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of sulphate ions} = 0.05 \times 6.022 \times 10^{23} \][/tex]
[tex]\[ \text{Number of sulphate ions} \approx 3.011 \times 10^{22} \][/tex]
In summary:
(a) The number of atoms of aluminium in 0.2 moles is [tex]\(1.2044 \times 10^{23}\)[/tex].
(b) The number of molecules of [tex]\(CO_2\)[/tex] in 0.4 moles is [tex]\(2.4088 \times 10^{23}\)[/tex].
(c) The number of oxygen atoms in 8 g of oxygen is [tex]\(3.011 \times 10^{23}\)[/tex].
(d) The number of oxygen molecules in 8 g of oxygen is [tex]\(1.505 \times 10^{23}\)[/tex].
(e) The number of hydrogen ions in 4.9 g of H₂SO₄ is [tex]\(6.022 \times 10^{22}\)[/tex] and the number of sulphate ions is [tex]\(3.011 \times 10^{22}\)[/tex].
