Find the best answers to your questions with the help of IDNLearn.com's knowledgeable users. Get step-by-step guidance for all your technical questions from our dedicated community members.
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 using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.