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### 1. Number of Moles of Citric Acid Used
We are given:
- The mass of citric acid is 10 grams.
- The molar mass of citric acid is 192.13 grams/mole.
The number of moles of citric acid can be calculated using the formula:
[tex]\[ \text{Number of moles} = \frac{\text{Mass of citric acid}}{\text{Molar mass of citric acid}} \][/tex]
Substituting the given values:
[tex]\[ \text{Number of moles} = \frac{10 \text{ grams}}{192.13 \text{ grams/mole}} \][/tex]
[tex]\[ \text{Number of moles} \approx 0.0520480924374 \text{ moles} \][/tex]
### 2. Heat Absorbed by the Water (Q)
We are given:
- The mass of water ([tex]\( m \)[/tex]) is 15.0 grams.
- The specific heat capacity of water ([tex]\( C \)[/tex]) is 4.186 joules/gram degree Celsius.
- The temperature change ([tex]\( \Delta T \)[/tex]) is 10 degrees Celsius.
The heat absorbed by the water can be calculated using the formula:
[tex]\[ Q = m \cdot C \cdot \Delta T \][/tex]
Substituting the given values:
[tex]\[ Q = 15.0 \text{ grams} \times 4.186 \text{ J/g°C} \times 10 \text{ °C} \][/tex]
[tex]\[ Q = 627.9 \text{ joules} \][/tex]
### 3. Change in Internal Energy of the Mixture
We assume that the energy absorbed by the mixture of citric acid and sodium bicarbonate is released by the water. Therefore, the change in internal energy of the mixture is equal to the heat absorbed by the water.
Thus, the change in internal energy of the mixture ([tex]\( \Delta U_{\text{mixture}} \)[/tex]) is:
[tex]\[ \Delta U_{\text{mixture}} = Q \][/tex]
[tex]\[ \Delta U_{\text{mixture}} = 627.9 \text{ joules} \][/tex]
### 4. Reaction Enthalpy, in Joules/Mole
The reaction enthalpy is the heat absorbed per mole of citric acid. It can be calculated using the formula:
[tex]\[ \text{Reaction Enthalpy} = \frac{Q_{\text{water}}}{\text{Number of moles of citric acid}} \][/tex]
Substituting the known values:
[tex]\[ \text{Reaction Enthalpy} = \frac{627.9 \text{ joules}}{0.0520480924374 \text{ moles}} \][/tex]
[tex]\[ \text{Reaction Enthalpy} \approx 12063.8427 \text{ joules/mole} \][/tex]
### Summary
- The number of moles of citric acid used: [tex]\( 0.0520480924374 \)[/tex] moles.
- The heat absorbed by the water: [tex]\( 627.9 \)[/tex] joules.
- The change in internal energy of the mixture: [tex]\( 627.9 \)[/tex] joules.
- The reaction enthalpy: [tex]\( 12063.8427 \)[/tex] joules/mole.
### 1. Number of Moles of Citric Acid Used
We are given:
- The mass of citric acid is 10 grams.
- The molar mass of citric acid is 192.13 grams/mole.
The number of moles of citric acid can be calculated using the formula:
[tex]\[ \text{Number of moles} = \frac{\text{Mass of citric acid}}{\text{Molar mass of citric acid}} \][/tex]
Substituting the given values:
[tex]\[ \text{Number of moles} = \frac{10 \text{ grams}}{192.13 \text{ grams/mole}} \][/tex]
[tex]\[ \text{Number of moles} \approx 0.0520480924374 \text{ moles} \][/tex]
### 2. Heat Absorbed by the Water (Q)
We are given:
- The mass of water ([tex]\( m \)[/tex]) is 15.0 grams.
- The specific heat capacity of water ([tex]\( C \)[/tex]) is 4.186 joules/gram degree Celsius.
- The temperature change ([tex]\( \Delta T \)[/tex]) is 10 degrees Celsius.
The heat absorbed by the water can be calculated using the formula:
[tex]\[ Q = m \cdot C \cdot \Delta T \][/tex]
Substituting the given values:
[tex]\[ Q = 15.0 \text{ grams} \times 4.186 \text{ J/g°C} \times 10 \text{ °C} \][/tex]
[tex]\[ Q = 627.9 \text{ joules} \][/tex]
### 3. Change in Internal Energy of the Mixture
We assume that the energy absorbed by the mixture of citric acid and sodium bicarbonate is released by the water. Therefore, the change in internal energy of the mixture is equal to the heat absorbed by the water.
Thus, the change in internal energy of the mixture ([tex]\( \Delta U_{\text{mixture}} \)[/tex]) is:
[tex]\[ \Delta U_{\text{mixture}} = Q \][/tex]
[tex]\[ \Delta U_{\text{mixture}} = 627.9 \text{ joules} \][/tex]
### 4. Reaction Enthalpy, in Joules/Mole
The reaction enthalpy is the heat absorbed per mole of citric acid. It can be calculated using the formula:
[tex]\[ \text{Reaction Enthalpy} = \frac{Q_{\text{water}}}{\text{Number of moles of citric acid}} \][/tex]
Substituting the known values:
[tex]\[ \text{Reaction Enthalpy} = \frac{627.9 \text{ joules}}{0.0520480924374 \text{ moles}} \][/tex]
[tex]\[ \text{Reaction Enthalpy} \approx 12063.8427 \text{ joules/mole} \][/tex]
### Summary
- The number of moles of citric acid used: [tex]\( 0.0520480924374 \)[/tex] moles.
- The heat absorbed by the water: [tex]\( 627.9 \)[/tex] joules.
- The change in internal energy of the mixture: [tex]\( 627.9 \)[/tex] joules.
- The reaction enthalpy: [tex]\( 12063.8427 \)[/tex] joules/mole.
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