Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine the amount of heat produced during the combustion of hexane in a bomb calorimeter, we need to use the formula for heat transfer:
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where [tex]\( q \)[/tex] is the heat produced in Joules, [tex]\( m \)[/tex] is the mass of the calorimeter, [tex]\( C_p \)[/tex] is the specific heat capacity of the calorimeter, and [tex]\( \Delta T \)[/tex] is the change in temperature.
Let's break this down step-by-step:
1. Given Data:
- Mass of the calorimeter ([tex]\( m \)[/tex]): 1.900 kg. Since the specific heat is given in J/gK, we need to convert this mass to grams:
[tex]\[ m = 1.900 \, \text{kg} \times 1000 \frac{g}{kg} = 1900 \, \text{g} \][/tex]
- Specific heat capacity ([tex]\( C_p \)[/tex]): 3.21 J/gK
- Change in temperature ([tex]\( \Delta T \)[/tex]): 4.542 K
2. Calculate the heat produced:
Using the formula [tex]\( q = m \cdot C_p \cdot \Delta T \)[/tex]:
[tex]\[ q = 1900 \, \text{g} \times 3.21 \, \frac{J}{gK} \times 4.542 \, \text{K} \][/tex]
3. Perform the multiplication:
[tex]\[ q = 1900 \times 3.21 \times 4.542 = 27701.658 \, \text{Joules} \][/tex]
4. Convert Joules to kilojoules:
[tex]\[ q_{\text{kJ}} = \frac{27701.658 \, \text{J}}{1000} = 27.701658 \, \text{kJ} \][/tex]
5. Round to appropriate number of significant figures (based on the precision of the given data):
Given data indicates significant figures up to 4 decimal places (4.542 K), so:
[tex]\[ q_{\text{kJ}} \approx 27.7 \, \text{kJ} \][/tex]
Thus, the amount of heat produced during the combustion of hexane is approximately [tex]\( 27.7 \, \text{kJ} \)[/tex], which matches one of the provided answers. Therefore, the correct answer is:
[tex]\[ \boxed{27.7 \, \text{kJ}} \][/tex]
[tex]\[ q = m \cdot C_p \cdot \Delta T \][/tex]
where [tex]\( q \)[/tex] is the heat produced in Joules, [tex]\( m \)[/tex] is the mass of the calorimeter, [tex]\( C_p \)[/tex] is the specific heat capacity of the calorimeter, and [tex]\( \Delta T \)[/tex] is the change in temperature.
Let's break this down step-by-step:
1. Given Data:
- Mass of the calorimeter ([tex]\( m \)[/tex]): 1.900 kg. Since the specific heat is given in J/gK, we need to convert this mass to grams:
[tex]\[ m = 1.900 \, \text{kg} \times 1000 \frac{g}{kg} = 1900 \, \text{g} \][/tex]
- Specific heat capacity ([tex]\( C_p \)[/tex]): 3.21 J/gK
- Change in temperature ([tex]\( \Delta T \)[/tex]): 4.542 K
2. Calculate the heat produced:
Using the formula [tex]\( q = m \cdot C_p \cdot \Delta T \)[/tex]:
[tex]\[ q = 1900 \, \text{g} \times 3.21 \, \frac{J}{gK} \times 4.542 \, \text{K} \][/tex]
3. Perform the multiplication:
[tex]\[ q = 1900 \times 3.21 \times 4.542 = 27701.658 \, \text{Joules} \][/tex]
4. Convert Joules to kilojoules:
[tex]\[ q_{\text{kJ}} = \frac{27701.658 \, \text{J}}{1000} = 27.701658 \, \text{kJ} \][/tex]
5. Round to appropriate number of significant figures (based on the precision of the given data):
Given data indicates significant figures up to 4 decimal places (4.542 K), so:
[tex]\[ q_{\text{kJ}} \approx 27.7 \, \text{kJ} \][/tex]
Thus, the amount of heat produced during the combustion of hexane is approximately [tex]\( 27.7 \, \text{kJ} \)[/tex], which matches one of the provided answers. Therefore, the correct answer is:
[tex]\[ \boxed{27.7 \, \text{kJ}} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.