Answer :
To determine the amount of energy it takes to boil [tex]\(100 \, \text{mL}\)[/tex] of water, let's follow these steps:
1. Volume to Mass Conversion:
Since 1 mL of water has a mass of 1 gram, the mass of 100 mL of water is:
[tex]\[ 100 \, \text{mL} \times \frac{1 \, \text{g}}{1 \, \text{mL}} = 100 \, \text{g} \][/tex]
2. Mass to Moles Conversion:
Next, we need to convert the mass of water to moles. The molar mass of water (H₂O) is approximately 18.02 g/mol. Thus, the number of moles of water is:
[tex]\[ \text{Moles of water} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{100 \, \text{g}}{18.02 \, \text{g/mol}} \approx 5.55 \, \text{mol} \][/tex]
3. Energy Required for Each Option:
Now we use the number of moles to calculate the energy based on different energy constants provided for each option:
- Option A:
Energy required per mole = 6.03 kJ/mol
[tex]\[ \text{Energy (A)} = 5.55 \, \text{mol} \times 6.03 \, \text{kJ/mol} \approx 33.46 \, \text{kJ} \][/tex]
- Option B:
Energy required per mole = -285.83 kJ/mol
[tex]\[ \text{Energy (B)} = 5.55 \, \text{mol} \times (-285.83 \, \text{kJ/mol}) \approx -1586.18 \, \text{kJ} \][/tex]
- Option C:
Energy required per mole = 40.65 kJ/mol
[tex]\[ \text{Energy (C)} = 5.55 \, \text{mol} \times 40.65 \, \text{kJ/mol} \approx 225.58 \, \text{kJ} \][/tex]
- Option D:
Energy required per mole = 4.186 kJ/mol
[tex]\[ \text{Energy (D)} = 5.55 \, \text{mol} \times 4.186 \, \text{kJ/mol} \approx 23.23 \, \text{kJ} \][/tex]
Comparing these calculations with the given options:
- Option A: 33.5 kJ is approximately 33.46 kJ.
- Option B: -1586 kJ is approximately -1586.18 kJ.
- Option C: 226 kJ is approximately 225.58 kJ.
- Option D: 23.2 kJ is approximately 23.23 kJ.
The closest match for the calculated energy with the given options is Option A: [tex]\(33.5 \, \text{kJ}\)[/tex].
Therefore, the energy required to boil [tex]\(100 \, \text{mL}\)[/tex] of water is:
A. [tex]\(33.5 \, \text{kJ}\)[/tex].
1. Volume to Mass Conversion:
Since 1 mL of water has a mass of 1 gram, the mass of 100 mL of water is:
[tex]\[ 100 \, \text{mL} \times \frac{1 \, \text{g}}{1 \, \text{mL}} = 100 \, \text{g} \][/tex]
2. Mass to Moles Conversion:
Next, we need to convert the mass of water to moles. The molar mass of water (H₂O) is approximately 18.02 g/mol. Thus, the number of moles of water is:
[tex]\[ \text{Moles of water} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{100 \, \text{g}}{18.02 \, \text{g/mol}} \approx 5.55 \, \text{mol} \][/tex]
3. Energy Required for Each Option:
Now we use the number of moles to calculate the energy based on different energy constants provided for each option:
- Option A:
Energy required per mole = 6.03 kJ/mol
[tex]\[ \text{Energy (A)} = 5.55 \, \text{mol} \times 6.03 \, \text{kJ/mol} \approx 33.46 \, \text{kJ} \][/tex]
- Option B:
Energy required per mole = -285.83 kJ/mol
[tex]\[ \text{Energy (B)} = 5.55 \, \text{mol} \times (-285.83 \, \text{kJ/mol}) \approx -1586.18 \, \text{kJ} \][/tex]
- Option C:
Energy required per mole = 40.65 kJ/mol
[tex]\[ \text{Energy (C)} = 5.55 \, \text{mol} \times 40.65 \, \text{kJ/mol} \approx 225.58 \, \text{kJ} \][/tex]
- Option D:
Energy required per mole = 4.186 kJ/mol
[tex]\[ \text{Energy (D)} = 5.55 \, \text{mol} \times 4.186 \, \text{kJ/mol} \approx 23.23 \, \text{kJ} \][/tex]
Comparing these calculations with the given options:
- Option A: 33.5 kJ is approximately 33.46 kJ.
- Option B: -1586 kJ is approximately -1586.18 kJ.
- Option C: 226 kJ is approximately 225.58 kJ.
- Option D: 23.2 kJ is approximately 23.23 kJ.
The closest match for the calculated energy with the given options is Option A: [tex]\(33.5 \, \text{kJ}\)[/tex].
Therefore, the energy required to boil [tex]\(100 \, \text{mL}\)[/tex] of water is:
A. [tex]\(33.5 \, \text{kJ}\)[/tex].
