Answer :
Let's work through each part step-by-step:
### 1.a. Mass of 44.8 dm³ of hydrogen chloride (HCl) at s.t.p.
Step 1: Determine the molar volume at s.t.p.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
Step 2: Calculate the number of moles of HCl in 44.8 dm³.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{44.8 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 2 \text{ moles} \][/tex]
Step 3: Calculate the molar mass of HCl.
Hydrogen (H) has a molar mass of 1 g/mol and Chlorine (Cl) has a molar mass of 35.5 g/mol.
[tex]\[ \text{Molar mass of HCl} = 1 \text{ g/mol} + 35.5 \text{ g/mol} = 36.5 \text{ g/mol} \][/tex]
Step 4: Calculate the mass of HCl.
[tex]\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} = 2 \times 36.5 \text{ g} = 73 \text{ g} \][/tex]
Thus, the mass of 44.8 dm³ of hydrogen chloride at s.t.p. is 73 g.
### 1.b. How many molecules are present in 2.24 dm³ of sulphur dioxide (SO₂) at s.t.p.?
Step 1: Determine the molar volume at s.t.p.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
Step 2: Calculate the number of moles of SO₂ in 2.24 dm³.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{2.24 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.1 \text{ moles} \][/tex]
Step 3: Calculate the number of molecules of SO₂.
Using Avogadro's number (6.022 × 10²³ molecules/mol):
[tex]\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} = 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \text{ molecules} \][/tex]
Thus, the number of molecules in 2.24 dm³ of sulphur dioxide at s.t.p. is 6.022 × 10²² molecules.
### 2. Mass and likely formula of a gaseous compound of carbon and hydrogen
Given:
- Mass of compound = 1.5 g
- Volume occupied at STP = 1.12 dm³
Step 1: Calculate the number of moles of the compound in 1.12 dm³.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{1.12 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.05 \text{ moles} \][/tex]
Step 2: Calculate the molar mass of the compound.
[tex]\[ \text{Molar mass} = \frac{\text{Mass of compound}}{\text{Number of moles}} = \frac{1.5 \text{ g}}{0.05 \text{ moles}} = 30 \text{ g/mol} \][/tex]
Step 3: Determine the likely formula.
Considering the compound is a hydrocarbon (contains only carbon and hydrogen), common hydrocarbons and their molar masses include:
- Methane (CH₄): 16 g/mol
- Ethane (C₂H₆): 30 g/mol
- Propane (C₃H₈): 44 g/mol
- Butane (C₄H₁₀): 58 g/mol
Given the molar mass of 30 g/mol, the most likely formula is C₂H₆ (Ethane).
Thus, the mass of 1 mol of the compound is 30 g/mol and its likely formula is C₂H₆ (Ethane).
### 1.a. Mass of 44.8 dm³ of hydrogen chloride (HCl) at s.t.p.
Step 1: Determine the molar volume at s.t.p.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
Step 2: Calculate the number of moles of HCl in 44.8 dm³.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{44.8 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 2 \text{ moles} \][/tex]
Step 3: Calculate the molar mass of HCl.
Hydrogen (H) has a molar mass of 1 g/mol and Chlorine (Cl) has a molar mass of 35.5 g/mol.
[tex]\[ \text{Molar mass of HCl} = 1 \text{ g/mol} + 35.5 \text{ g/mol} = 36.5 \text{ g/mol} \][/tex]
Step 4: Calculate the mass of HCl.
[tex]\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} = 2 \times 36.5 \text{ g} = 73 \text{ g} \][/tex]
Thus, the mass of 44.8 dm³ of hydrogen chloride at s.t.p. is 73 g.
### 1.b. How many molecules are present in 2.24 dm³ of sulphur dioxide (SO₂) at s.t.p.?
Step 1: Determine the molar volume at s.t.p.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
Step 2: Calculate the number of moles of SO₂ in 2.24 dm³.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{2.24 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.1 \text{ moles} \][/tex]
Step 3: Calculate the number of molecules of SO₂.
Using Avogadro's number (6.022 × 10²³ molecules/mol):
[tex]\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} = 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \text{ molecules} \][/tex]
Thus, the number of molecules in 2.24 dm³ of sulphur dioxide at s.t.p. is 6.022 × 10²² molecules.
### 2. Mass and likely formula of a gaseous compound of carbon and hydrogen
Given:
- Mass of compound = 1.5 g
- Volume occupied at STP = 1.12 dm³
Step 1: Calculate the number of moles of the compound in 1.12 dm³.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 dm³/mol.
[tex]\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{1.12 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.05 \text{ moles} \][/tex]
Step 2: Calculate the molar mass of the compound.
[tex]\[ \text{Molar mass} = \frac{\text{Mass of compound}}{\text{Number of moles}} = \frac{1.5 \text{ g}}{0.05 \text{ moles}} = 30 \text{ g/mol} \][/tex]
Step 3: Determine the likely formula.
Considering the compound is a hydrocarbon (contains only carbon and hydrogen), common hydrocarbons and their molar masses include:
- Methane (CH₄): 16 g/mol
- Ethane (C₂H₆): 30 g/mol
- Propane (C₃H₈): 44 g/mol
- Butane (C₄H₁₀): 58 g/mol
Given the molar mass of 30 g/mol, the most likely formula is C₂H₆ (Ethane).
Thus, the mass of 1 mol of the compound is 30 g/mol and its likely formula is C₂H₆ (Ethane).
