Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Given the problem, we need to calculate the change in internal energy, [tex]\(\Delta E\)[/tex], for the combustion reaction of sucrose in a bomb calorimeter. We are provided with the following data:
- Mass of sucrose: 10.0 grams
- Heat capacity of the calorimeter: 7.50 kJ/°C
- Temperature increase: 22.0 °C
- Molar mass of sucrose ([tex]\(\text{C}_{12}\text{H}_{22}\text{O}_{11}\)[/tex]): 342.30 g/mol
We proceed in a step-by-step manner as follows:
1. Calculate the heat absorbed by the calorimeter:
Given the heat capacity of the calorimeter ([tex]\(C\)[/tex]) and the temperature increase ([tex]\(\Delta T\)[/tex]), we use the formula:
[tex]\[ q = C \times \Delta T \][/tex]
Substituting the given values:
[tex]\[ q = 7.50 \, \text{kJ/°C} \times 22.0 \, \text{°C} = 165.0 \, \text{kJ} \][/tex]
Hence, the heat absorbed by the calorimeter is 165.0 kJ.
2. Calculate the number of moles of sucrose burned:
To find the number of moles, we use the molar mass of sucrose and the given mass:
[tex]\[ \text{moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}} \][/tex]
Substituting the values:
[tex]\[ \text{moles of sucrose} = \frac{10.0 \, \text{g}}{342.30 \, \text{g/mol}} \approx 0.0292 \, \text{mol} \][/tex]
So, 10.0 grams of sucrose corresponds to approximately 0.0292 moles.
3. Calculate the change in internal energy per mole of sucrose ([tex]\(\Delta E\)[/tex]):
The heat absorbed by the calorimeter represents the total heat released by the combustion of the given amount of sucrose. To find [tex]\(\Delta E\)[/tex] per mole, we divide the total heat absorbed by the number of moles of sucrose:
[tex]\[ \Delta E \, (\text{per mole}) = \frac{q}{\text{moles of sucrose}} \][/tex]
Substituting in the values:
[tex]\[ \Delta E \, (\text{per mole}) = \frac{165.0 \, \text{kJ}}{0.029214139643587496 \, \text{mol}} \approx 5647.95 \, \text{kJ/mol} \][/tex]
Thus, the change in internal energy [tex]\(\Delta E\)[/tex] for the reaction per mole of sucrose is [tex]\(5647.95\)[/tex] kJ/mol.
Expressing this to three significant figures, we get:
[tex]\[ \Delta E \approx 5650 \, \text{kJ/mol} \][/tex]
Therefore, the change in internal energy for this reaction per mole of sucrose is approximately [tex]\(5650 \, \text{kJ/mol}\)[/tex].
- Mass of sucrose: 10.0 grams
- Heat capacity of the calorimeter: 7.50 kJ/°C
- Temperature increase: 22.0 °C
- Molar mass of sucrose ([tex]\(\text{C}_{12}\text{H}_{22}\text{O}_{11}\)[/tex]): 342.30 g/mol
We proceed in a step-by-step manner as follows:
1. Calculate the heat absorbed by the calorimeter:
Given the heat capacity of the calorimeter ([tex]\(C\)[/tex]) and the temperature increase ([tex]\(\Delta T\)[/tex]), we use the formula:
[tex]\[ q = C \times \Delta T \][/tex]
Substituting the given values:
[tex]\[ q = 7.50 \, \text{kJ/°C} \times 22.0 \, \text{°C} = 165.0 \, \text{kJ} \][/tex]
Hence, the heat absorbed by the calorimeter is 165.0 kJ.
2. Calculate the number of moles of sucrose burned:
To find the number of moles, we use the molar mass of sucrose and the given mass:
[tex]\[ \text{moles of sucrose} = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}} \][/tex]
Substituting the values:
[tex]\[ \text{moles of sucrose} = \frac{10.0 \, \text{g}}{342.30 \, \text{g/mol}} \approx 0.0292 \, \text{mol} \][/tex]
So, 10.0 grams of sucrose corresponds to approximately 0.0292 moles.
3. Calculate the change in internal energy per mole of sucrose ([tex]\(\Delta E\)[/tex]):
The heat absorbed by the calorimeter represents the total heat released by the combustion of the given amount of sucrose. To find [tex]\(\Delta E\)[/tex] per mole, we divide the total heat absorbed by the number of moles of sucrose:
[tex]\[ \Delta E \, (\text{per mole}) = \frac{q}{\text{moles of sucrose}} \][/tex]
Substituting in the values:
[tex]\[ \Delta E \, (\text{per mole}) = \frac{165.0 \, \text{kJ}}{0.029214139643587496 \, \text{mol}} \approx 5647.95 \, \text{kJ/mol} \][/tex]
Thus, the change in internal energy [tex]\(\Delta E\)[/tex] for the reaction per mole of sucrose is [tex]\(5647.95\)[/tex] kJ/mol.
Expressing this to three significant figures, we get:
[tex]\[ \Delta E \approx 5650 \, \text{kJ/mol} \][/tex]
Therefore, the change in internal energy for this reaction per mole of sucrose is approximately [tex]\(5650 \, \text{kJ/mol}\)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.