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Sagot :
Sure! Let's go through the calculations step-by-step based on the given information.
1. The number of moles of citric acid used:
- Given the molar mass of citric acid [tex]\( (C_6H_8O_7) \)[/tex] is [tex]\( 192.13 \)[/tex] grams/mole.
- Suppose we have [tex]\( 20 \)[/tex] grams of citric acid.
- The number of moles ([tex]\( n \)[/tex]) is calculated as:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{20 \ \text{grams}}{192.13 \ \text{grams/mole}} \approx 0.1041 \ \text{moles} \][/tex]
2. The heat absorbed by the water (in joules):
- Given:
- The mass of the water [tex]\( (m) \)[/tex] is [tex]\( 15.0 \)[/tex] grams.
- The specific heat capacity of water [tex]\( (C) \)[/tex] is [tex]\( 4.186 \)[/tex] joules/gram degree Celsius.
- The change in temperature [tex]\( (\Delta T) \)[/tex] is [tex]\( 10 \)[/tex] degrees Celsius.
- The heat absorbed ([tex]\( Q \)[/tex]) is calculated as:
[tex]\[ Q = m \cdot C \cdot \Delta T = 15.0 \ \text{grams} \cdot 4.186 \ \text{joules/gram°C} \cdot 10 \ \text{°C} = 627.9 \ \text{joules} \][/tex]
3. The change in internal energy of the mixture of citric acid and sodium bicarbonate ([tex]\(\Delta U\)[/tex]):
- Assuming that the energy absorbed by the mixture of citric acid and sodium bicarbonate is released by the water, the change in internal energy of the mixture is the negative of the heat absorbed by water:
[tex]\[ \Delta U = -Q = -627.9 \ \text{joules} \][/tex]
4. The reaction enthalpy (in joules/mole):
- The reaction enthalpy ([tex]\(\Delta H\)[/tex]) is calculated by dividing the change in internal energy ([tex]\(\Delta U\)[/tex]) by the number of moles of citric acid used:
[tex]\[ \Delta H = \frac{\Delta U}{\text{moles of citric acid}} = \frac{-627.9 \ \text{joules}}{0.1041 \ \text{moles}} \approx -6031.92 \ \text{joules/mole} \][/tex]
To summarize:
| Quantity | Value |
|---------------------------------------------------|------------------------------|
| Number of moles of citric acid used | [tex]\( 0.1041 \ \text{moles} \)[/tex] |
| Heat absorbed by the water | [tex]\( 627.9 \ \text{joules} \)[/tex] |
| Change in internal energy of the mixture | [tex]\( -627.9 \ \text{joules} \)[/tex] |
| Reaction enthalpy | [tex]\( -6031.92 \ \text{joules/mole} \)[/tex] |
These values provide the detailed quantitative insight into the reaction process and energy changes involved.
1. The number of moles of citric acid used:
- Given the molar mass of citric acid [tex]\( (C_6H_8O_7) \)[/tex] is [tex]\( 192.13 \)[/tex] grams/mole.
- Suppose we have [tex]\( 20 \)[/tex] grams of citric acid.
- The number of moles ([tex]\( n \)[/tex]) is calculated as:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{20 \ \text{grams}}{192.13 \ \text{grams/mole}} \approx 0.1041 \ \text{moles} \][/tex]
2. The heat absorbed by the water (in joules):
- Given:
- The mass of the water [tex]\( (m) \)[/tex] is [tex]\( 15.0 \)[/tex] grams.
- The specific heat capacity of water [tex]\( (C) \)[/tex] is [tex]\( 4.186 \)[/tex] joules/gram degree Celsius.
- The change in temperature [tex]\( (\Delta T) \)[/tex] is [tex]\( 10 \)[/tex] degrees Celsius.
- The heat absorbed ([tex]\( Q \)[/tex]) is calculated as:
[tex]\[ Q = m \cdot C \cdot \Delta T = 15.0 \ \text{grams} \cdot 4.186 \ \text{joules/gram°C} \cdot 10 \ \text{°C} = 627.9 \ \text{joules} \][/tex]
3. The change in internal energy of the mixture of citric acid and sodium bicarbonate ([tex]\(\Delta U\)[/tex]):
- Assuming that the energy absorbed by the mixture of citric acid and sodium bicarbonate is released by the water, the change in internal energy of the mixture is the negative of the heat absorbed by water:
[tex]\[ \Delta U = -Q = -627.9 \ \text{joules} \][/tex]
4. The reaction enthalpy (in joules/mole):
- The reaction enthalpy ([tex]\(\Delta H\)[/tex]) is calculated by dividing the change in internal energy ([tex]\(\Delta U\)[/tex]) by the number of moles of citric acid used:
[tex]\[ \Delta H = \frac{\Delta U}{\text{moles of citric acid}} = \frac{-627.9 \ \text{joules}}{0.1041 \ \text{moles}} \approx -6031.92 \ \text{joules/mole} \][/tex]
To summarize:
| Quantity | Value |
|---------------------------------------------------|------------------------------|
| Number of moles of citric acid used | [tex]\( 0.1041 \ \text{moles} \)[/tex] |
| Heat absorbed by the water | [tex]\( 627.9 \ \text{joules} \)[/tex] |
| Change in internal energy of the mixture | [tex]\( -627.9 \ \text{joules} \)[/tex] |
| Reaction enthalpy | [tex]\( -6031.92 \ \text{joules/mole} \)[/tex] |
These values provide the detailed quantitative insight into the reaction process and energy changes involved.
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