Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
![**Problem Statement:**
A 50.0 g sample of Chromium metal was heated to 103 degrees Celsius and then dropped into a beaker containing 76.0 g of water at 25.0 degrees Celsius. If the specific heat of Chromium metal is 0.110 cal/g°C, what will be the equilibrium temperature of the Chromium-Water mixture? (C_water = 1 cal/g°C)
---
In this physics and chemistry problem, you're asked to find the final equilibrium temperature when a hot metal (Chromium) is mixed with cooler water. Below are the relevant details extracted from the problem for clarity:
- Mass of Chromium (m_Cr): 50.0 g
- Initial temperature of Chromium (T_initial_Cr): 103°C
- Specific heat of Chromium (C_Cr): 0.110 cal/g°C
- Mass of water (m_water): 76.0 g
- Initial temperature of water (T_initial_water): 25°C
- Specific heat of water (C_water): 1 cal/g°C
The goal is to determine the final equilibrium temperature (T_final) of the combined Chromium-Water mixture.
To solve this, you would typically use the formula for heat transfer and assume that the heat lost by the Chromium equals the heat gained by the water:
\[ q_{Cr} = -q_{water} \]
Where:
- \( q = mc\Delta T \)
- \( \Delta T = T_{final} - T_{initial} \)
### Detailed Solution Process:
1. Write the heat loss equation for Chromium:
\[ q_{Cr} = m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) \]
2. Write the heat gain equation for water:
\[ q_{water} = m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}}) \]
3. Set the heat loss equal to the heat gain and solve for \( T_{final} \):
\[ m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) = - (m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}})) \]
### Substitute the given values and solve:
\[ (50.0](https://content.bartleby.com/qna-images/question/b71b0d5b-4c2e-49d2-b5c8-1f8a009c1755/7e40df0f-8f6c-4bc0-8e15-1a044efffdf1/pudgvuj_processed.jpeg)
Transcribed Image Text:**Problem Statement:**
A 50.0 g sample of Chromium metal was heated to 103 degrees Celsius and then dropped into a beaker containing 76.0 g of water at 25.0 degrees Celsius. If the specific heat of Chromium metal is 0.110 cal/g°C, what will be the equilibrium temperature of the Chromium-Water mixture? (C_water = 1 cal/g°C)
---
In this physics and chemistry problem, you're asked to find the final equilibrium temperature when a hot metal (Chromium) is mixed with cooler water. Below are the relevant details extracted from the problem for clarity:
- Mass of Chromium (m_Cr): 50.0 g
- Initial temperature of Chromium (T_initial_Cr): 103°C
- Specific heat of Chromium (C_Cr): 0.110 cal/g°C
- Mass of water (m_water): 76.0 g
- Initial temperature of water (T_initial_water): 25°C
- Specific heat of water (C_water): 1 cal/g°C
The goal is to determine the final equilibrium temperature (T_final) of the combined Chromium-Water mixture.
To solve this, you would typically use the formula for heat transfer and assume that the heat lost by the Chromium equals the heat gained by the water:
\[ q_{Cr} = -q_{water} \]
Where:
- \( q = mc\Delta T \)
- \( \Delta T = T_{final} - T_{initial} \)
### Detailed Solution Process:
1. Write the heat loss equation for Chromium:
\[ q_{Cr} = m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) \]
2. Write the heat gain equation for water:
\[ q_{water} = m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}}) \]
3. Set the heat loss equal to the heat gain and solve for \( T_{final} \):
\[ m_{Cr} \cdot C_{Cr} \cdot (T_{final} - T_{initial_{Cr}}) = - (m_{water} \cdot C_{water} \cdot (T_{final} - T_{initial_{water}})) \]
### Substitute the given values and solve:
\[ (50.0
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 4 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Similar questions
- A 50.8 g sample of an unknown metal was heated to 700.0 ˚C then placed into 100.0 g of water (specific heat: 4.184) initially at 25.0 ˚C. The water and the unknown metal reach equilibrium when both are at 78.3 ˚C. What was the specific heat of the unknown metal?arrow_forwardPlease help me complete this questionarrow_forwardThe reaction below is a exothermic or endothermic reaction. 2SO3(g) + Heat ⇋ 2SO2(g) + O2(g)arrow_forward
- 1arrow_forward6) A block of rhenium metal (specific heat =0.0329 cal/ gC) is heated to 88.2C and then dropped into 100.0 g of water initially at 26.4 C. The final temperature of the mixture is 32.4C. What was the mass of the block of rhenium?arrow_forwardThe specific heat of the metallic element rhodium is 0.240 J/g-K at 25°C. If 586 J of heat is added to an 80.0 g block of rhodium metal that is initially at 25.0°C, what is the expected final temperature of the block? O 32.3°C O 2470°C O 55.5°C O 30.5°C O 26 8°Carrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning
ChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill Education
Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning 
Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill Education
Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY