Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Given:
Mass of Gold (g) -51.1557 g
Volume of H2O (mL) - 100mL
Mass of H2O (g) - 99.8g
Initial Temperature of H2O (degrees Celsius) - 25 degrees Celsius
Initial Temperature of Gold (degrees Celsius) - 200 degrees Celsius
Max temp of H2O + metal (degrees Celsius) - 27.23 degrees
Calculate:
The change in temperature:
The heat (q) in J gained by the water using the following equation:
The changes in temperature of the metal:
Remembering that the heat gained by the water is equal to the heat lost by the metal, calculate the specific heat of metal in J/g degrees Celsius.
The percent error in the specific heat value that you determined experimentally. The accepted value for the metal is Au= 0.126 J/g degrees Celsius.
![**Calculation of Temperature Change and Specific Heat**
1. **Calculate the Change in Temperature of the Water (\( \Delta T_{\text{water}} \)):**
\[
\Delta T_{\text{water}} = T_p - T_i
\]
2. **Calculate the Heat (\( q \)), in Joules, Gained by the Water:**
Use the equation:
\[
q_{\text{water}} = m_{\text{water}} \times \Delta T_{\text{water}} \times C_{\text{water}}
\]
3. **Calculate the Change in Temperature of the Metal (\( \Delta T_{\text{metal}} \)):**
\[
\Delta T_{\text{metal}} = T_p - T_i
\]
4. **Calculate the Specific Heat of the Metal:**
Since the heat gained by water is equal to the heat lost by the metal:
\[
q_{\text{water}} = -q_{\text{metal}} = m_{\text{metal}} \times \Delta T_{\text{metal}} \times C_{\text{metal}}
\]
Therefore, the specific heat, \( C_{\text{metal}} \), is:
\[
C_{\text{metal}} = q_{\text{metal}} / (m_{\text{metal}} \times \Delta T_{\text{metal}})
\]
5. **Calculate the Percent Error in the Specific Heat Value:**
Compare the experimentally determined specific heat with the accepted value:
\[
\text{Accepted value for the metal is} \, Au = 0.126 \, \text{J/g°C}
\]
This serves as a step-by-step guide for determining the changes in temperature and calculating specific heat, essential in understanding thermal transfer processes.](https://content.bartleby.com/qna-images/question/3dd8c9ac-d087-46bb-b8c4-53ceffa446e7/8ac85e10-f361-4400-86d3-db9e26b4f47e/djl7iqr_processed.jpeg)
Transcribed Image Text:**Calculation of Temperature Change and Specific Heat**
1. **Calculate the Change in Temperature of the Water (\( \Delta T_{\text{water}} \)):**
\[
\Delta T_{\text{water}} = T_p - T_i
\]
2. **Calculate the Heat (\( q \)), in Joules, Gained by the Water:**
Use the equation:
\[
q_{\text{water}} = m_{\text{water}} \times \Delta T_{\text{water}} \times C_{\text{water}}
\]
3. **Calculate the Change in Temperature of the Metal (\( \Delta T_{\text{metal}} \)):**
\[
\Delta T_{\text{metal}} = T_p - T_i
\]
4. **Calculate the Specific Heat of the Metal:**
Since the heat gained by water is equal to the heat lost by the metal:
\[
q_{\text{water}} = -q_{\text{metal}} = m_{\text{metal}} \times \Delta T_{\text{metal}} \times C_{\text{metal}}
\]
Therefore, the specific heat, \( C_{\text{metal}} \), is:
\[
C_{\text{metal}} = q_{\text{metal}} / (m_{\text{metal}} \times \Delta T_{\text{metal}})
\]
5. **Calculate the Percent Error in the Specific Heat Value:**
Compare the experimentally determined specific heat with the accepted value:
\[
\text{Accepted value for the metal is} \, Au = 0.126 \, \text{J/g°C}
\]
This serves as a step-by-step guide for determining the changes in temperature and calculating specific heat, essential in understanding thermal transfer processes.
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