Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine the heat of the reaction for the dissociation of [tex]\( KNO_3 \)[/tex] in water in a coffee cup calorimeter, we need to follow several steps involving the specific heat capacities of the solution and the calorimeter, as well as the temperature change.
### Step-by-Step Solution:
1. Given Data:
- Mass of [tex]\( KNO_3 \)[/tex]: [tex]\( 7.5 \, \text{g} \)[/tex]
- Mass of water: [tex]\( 49.0 \, \text{g} \)[/tex]
- Initial temperature: [tex]\( 20.4^\circ \mathrm{C} \)[/tex]
- Final temperature: [tex]\( 9.7^\circ \mathrm{C} \)[/tex]
- Specific heat capacity of solution ([tex]\( C_{\text{soln}} \)[/tex]): [tex]\( 4.18 \, \text{J/g}^\circ \mathrm{C} \)[/tex]
- Heat capacity of the calorimeter ([tex]\( C_{\text{cal}} \)[/tex]): [tex]\( 6.5 \, \text{J/}^\circ \mathrm{C} \)[/tex]
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = \text{Final Temperature} - \text{Initial Temperature} = 9.7^\circ \mathrm{C} - 20.4^\circ \mathrm{C} = -10.7^\circ \mathrm{C} \][/tex]
3. Calculate the heat absorbed by the solution ([tex]\( q_{\text{soln}} \)[/tex]):
The total mass of the solution is the sum of the mass of [tex]\( KNO_3 \)[/tex] and the mass of water:
[tex]\[ \text{Total mass of solution} = 7.5 \, \text{g} + 49.0 \, \text{g} = 56.5 \, \text{g} \][/tex]
Using the specific heat capacity of the solution and the change in temperature:
[tex]\[ q_{\text{soln}} = \text{Total mass of solution} \times C_{\text{soln}} \times \Delta T \][/tex]
[tex]\[ q_{\text{soln}} = 56.5 \, \text{g} \times 4.18 \, \text{J/g}^\circ \mathrm{C} \times (-10.7^\circ \mathrm{C}) = -2527.019 \, \text{J} \][/tex]
4. Calculate the heat absorbed by the calorimeter ([tex]\( q_{\text{cal}} \)[/tex]):
[tex]\[ q_{\text{cal}} = C_{\text{cal}} \times \Delta T \][/tex]
[tex]\[ q_{\text{cal}} = 6.5 \, \text{J/}^\circ \mathrm{C} \times (-10.7^\circ \mathrm{C}) = -69.55 \, \text{J} \][/tex]
5. Calculate the total heat of reaction ([tex]\( q_{\text{rxn}} \)[/tex]):
The heat of the reaction is the negative sum of the heat absorbed by the solution and the calorimeter. Since the temperature decreased, the system released heat, so [tex]\( q_{\text{rxn}} \)[/tex] should be positive:
[tex]\[ q_{\text{rxn}} = -(q_{\text{soln}} + q_{\text{cal}}) \][/tex]
[tex]\[ q_{\text{rxn}} = -(-2527.019 \, \text{J} - 69.55 \, \text{J}) = 2596.569 \, \text{J} \][/tex]
### Conclusion:
The heat of the reaction, [tex]\( q_{\text{rxn}} \)[/tex], is [tex]\( +2596.569 \, \text{J} \)[/tex].
### Step-by-Step Solution:
1. Given Data:
- Mass of [tex]\( KNO_3 \)[/tex]: [tex]\( 7.5 \, \text{g} \)[/tex]
- Mass of water: [tex]\( 49.0 \, \text{g} \)[/tex]
- Initial temperature: [tex]\( 20.4^\circ \mathrm{C} \)[/tex]
- Final temperature: [tex]\( 9.7^\circ \mathrm{C} \)[/tex]
- Specific heat capacity of solution ([tex]\( C_{\text{soln}} \)[/tex]): [tex]\( 4.18 \, \text{J/g}^\circ \mathrm{C} \)[/tex]
- Heat capacity of the calorimeter ([tex]\( C_{\text{cal}} \)[/tex]): [tex]\( 6.5 \, \text{J/}^\circ \mathrm{C} \)[/tex]
2. Calculate the change in temperature ([tex]\( \Delta T \)[/tex]):
[tex]\[ \Delta T = \text{Final Temperature} - \text{Initial Temperature} = 9.7^\circ \mathrm{C} - 20.4^\circ \mathrm{C} = -10.7^\circ \mathrm{C} \][/tex]
3. Calculate the heat absorbed by the solution ([tex]\( q_{\text{soln}} \)[/tex]):
The total mass of the solution is the sum of the mass of [tex]\( KNO_3 \)[/tex] and the mass of water:
[tex]\[ \text{Total mass of solution} = 7.5 \, \text{g} + 49.0 \, \text{g} = 56.5 \, \text{g} \][/tex]
Using the specific heat capacity of the solution and the change in temperature:
[tex]\[ q_{\text{soln}} = \text{Total mass of solution} \times C_{\text{soln}} \times \Delta T \][/tex]
[tex]\[ q_{\text{soln}} = 56.5 \, \text{g} \times 4.18 \, \text{J/g}^\circ \mathrm{C} \times (-10.7^\circ \mathrm{C}) = -2527.019 \, \text{J} \][/tex]
4. Calculate the heat absorbed by the calorimeter ([tex]\( q_{\text{cal}} \)[/tex]):
[tex]\[ q_{\text{cal}} = C_{\text{cal}} \times \Delta T \][/tex]
[tex]\[ q_{\text{cal}} = 6.5 \, \text{J/}^\circ \mathrm{C} \times (-10.7^\circ \mathrm{C}) = -69.55 \, \text{J} \][/tex]
5. Calculate the total heat of reaction ([tex]\( q_{\text{rxn}} \)[/tex]):
The heat of the reaction is the negative sum of the heat absorbed by the solution and the calorimeter. Since the temperature decreased, the system released heat, so [tex]\( q_{\text{rxn}} \)[/tex] should be positive:
[tex]\[ q_{\text{rxn}} = -(q_{\text{soln}} + q_{\text{cal}}) \][/tex]
[tex]\[ q_{\text{rxn}} = -(-2527.019 \, \text{J} - 69.55 \, \text{J}) = 2596.569 \, \text{J} \][/tex]
### Conclusion:
The heat of the reaction, [tex]\( q_{\text{rxn}} \)[/tex], is [tex]\( +2596.569 \, \text{J} \)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.