Answer :
Certainly! Let's tackle each part of the question one at a time.
### Part i: Determining the heaviest molecule
To find out which one weighs the most, we will calculate the molar mass (molecular weight) of each substance (CO₂, H₂O, NH₃, NO₂). The molar mass of a molecule is the sum of the atomic masses of all the atoms in the molecule, given in grams per mole (g/mol).
1. CO₂ (Carbon dioxide):
- Carbon (C): atomic mass ≈ 12 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of CO₂ = 12 + 2 16 = 12 + 32 = 44 g/mol
2. H₂O (Water):
- Hydrogen (H): atomic mass ≈ 1 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of H₂O = 2 1 + 16 = 2 + 16 = 18 g/mol
3. NH₃ (Ammonia):
- Nitrogen (N): atomic mass ≈ 14 g/mol
- Hydrogen (H): atomic mass ≈ 1 g/mol
- Molar mass of NH₃ = 14 + 3 1 = 14 + 3 = 17 g/mol
4. NO₂ (Nitrogen dioxide):
- Nitrogen (N): atomic mass ≈ 14 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of NO₂ = 14 + 2 16 = 14 + 32 = 46 g/mol
Now, let’s compare the molar masses:
- CO₂: 44 g/mol
- H₂O: 18 g/mol
- NH₃: 17 g/mol
- NO₂: 46 g/mol
The heaviest molecule is NO₂ with a molar mass of 46 g/mol.
So, the answer is:
D. 1 mole of \( NO_2 \)
### Part ii: Volume occupied by 7.1 grams of chlorine gas at STP
At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters.
First, we need to find the number of moles of chlorine gas (Cl₂) in 7.1 grams.
1. Chlorine gas (Cl₂):
- Chlorine (Cl): atomic mass ≈ 35.5 g/mol
- Molar mass of Cl₂ = 2 * 35.5 = 71 g/mol
To calculate the number of moles:
[tex]\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{7.1 \text{ g}}{71 \text{ g/mol}} = 0.1 \text{ moles} \][/tex]
Now, we use the fact that 1 mole of gas occupies 22.4 liters at STP:
[tex]\[ \text{Volume of 0.1 moles} = 0.1 \times 22.4 \text{ L} = 2.24 \text{ L} \][/tex]
So, the volume occupied by 7.1 g of chlorine gas at STP is:
B. [tex]\( 2.24 \, \text{L} \)[/tex]
### Part i: Determining the heaviest molecule
To find out which one weighs the most, we will calculate the molar mass (molecular weight) of each substance (CO₂, H₂O, NH₃, NO₂). The molar mass of a molecule is the sum of the atomic masses of all the atoms in the molecule, given in grams per mole (g/mol).
1. CO₂ (Carbon dioxide):
- Carbon (C): atomic mass ≈ 12 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of CO₂ = 12 + 2 16 = 12 + 32 = 44 g/mol
2. H₂O (Water):
- Hydrogen (H): atomic mass ≈ 1 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of H₂O = 2 1 + 16 = 2 + 16 = 18 g/mol
3. NH₃ (Ammonia):
- Nitrogen (N): atomic mass ≈ 14 g/mol
- Hydrogen (H): atomic mass ≈ 1 g/mol
- Molar mass of NH₃ = 14 + 3 1 = 14 + 3 = 17 g/mol
4. NO₂ (Nitrogen dioxide):
- Nitrogen (N): atomic mass ≈ 14 g/mol
- Oxygen (O): atomic mass ≈ 16 g/mol
- Molar mass of NO₂ = 14 + 2 16 = 14 + 32 = 46 g/mol
Now, let’s compare the molar masses:
- CO₂: 44 g/mol
- H₂O: 18 g/mol
- NH₃: 17 g/mol
- NO₂: 46 g/mol
The heaviest molecule is NO₂ with a molar mass of 46 g/mol.
So, the answer is:
D. 1 mole of \( NO_2 \)
### Part ii: Volume occupied by 7.1 grams of chlorine gas at STP
At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters.
First, we need to find the number of moles of chlorine gas (Cl₂) in 7.1 grams.
1. Chlorine gas (Cl₂):
- Chlorine (Cl): atomic mass ≈ 35.5 g/mol
- Molar mass of Cl₂ = 2 * 35.5 = 71 g/mol
To calculate the number of moles:
[tex]\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{7.1 \text{ g}}{71 \text{ g/mol}} = 0.1 \text{ moles} \][/tex]
Now, we use the fact that 1 mole of gas occupies 22.4 liters at STP:
[tex]\[ \text{Volume of 0.1 moles} = 0.1 \times 22.4 \text{ L} = 2.24 \text{ L} \][/tex]
So, the volume occupied by 7.1 g of chlorine gas at STP is:
B. [tex]\( 2.24 \, \text{L} \)[/tex]
