5. Calculate the approximate final temperature of water in a coffee cup calorimeter if 33.9 kJ of heat is added to 420.0 g of water initially at a temperature of 22.60 °C (the specific heat of water is 4.184 J/g•K).
5. Calculate the approximate final temperature of water in a coffee cup calorimeter if 33.9 kJ of heat is added to 420.0 g of water initially at a temperature of 22.60 °C (the specific heat of water is 4.184 J/g•K).
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Problem Statement:**
5. Calculate the approximate final temperature of water in a coffee cup calorimeter if 33.9 kJ of heat is added to 420.0 g of water initially at a temperature of 22.60 °C (the specific heat of water is 4.184 J/g·K).
**Explanation:**
This problem involves calculating the final temperature of water after a specified amount of heat energy is added to it. The process is done using a coffee cup calorimeter, which is an apparatus used to measure the heat of chemical reactions or physical changes.
**Relevant Formula:**
To find the final temperature, we use the formula:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the heat added (in joules),
- \( m \) is the mass of the water (in grams),
- \( c \) is the specific heat capacity of water (in J/g·K),
- \( \Delta T \) is the change in temperature (in °C or K).
**Steps to Solve:**
1. **Convert Heat Energy to Joules:**
- Since 1 kJ = 1000 J, convert heat from kJ to J.
- \( 33.9 \, \text{kJ} = 33,900 \, \text{J} \)
2. **Apply the Formula:**
- Rearrange the formula to solve for \( \Delta T \):
\[ \Delta T = \frac{q}{m \cdot c} \]
3. **Insert Known Values:**
- \( q = 33,900 \, \text{J} \)
- \( m = 420.0 \, \text{g} \)
- \( c = 4.184 \, \text{J/g·K} \)
- Calculate \( \Delta T \).
4. **Calculate Final Temperature:**
- \( \Delta T = \frac{33,900 \, \text{J}}{420.0 \, \text{g} \times 4.184 \, \text{J/g·K}} \)
- \( \Delta T \approx 19.28 \, \text{K} \)
5. **Determine Final](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30f8b710-1a61-4c05-9269-dd497cde8c1e%2F2ff4eef6-4f06-4006-976f-58404aeadf86%2Fahddhgh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription and explanation suitable for an educational website:
---
**Problem Statement:**
5. Calculate the approximate final temperature of water in a coffee cup calorimeter if 33.9 kJ of heat is added to 420.0 g of water initially at a temperature of 22.60 °C (the specific heat of water is 4.184 J/g·K).
**Explanation:**
This problem involves calculating the final temperature of water after a specified amount of heat energy is added to it. The process is done using a coffee cup calorimeter, which is an apparatus used to measure the heat of chemical reactions or physical changes.
**Relevant Formula:**
To find the final temperature, we use the formula:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the heat added (in joules),
- \( m \) is the mass of the water (in grams),
- \( c \) is the specific heat capacity of water (in J/g·K),
- \( \Delta T \) is the change in temperature (in °C or K).
**Steps to Solve:**
1. **Convert Heat Energy to Joules:**
- Since 1 kJ = 1000 J, convert heat from kJ to J.
- \( 33.9 \, \text{kJ} = 33,900 \, \text{J} \)
2. **Apply the Formula:**
- Rearrange the formula to solve for \( \Delta T \):
\[ \Delta T = \frac{q}{m \cdot c} \]
3. **Insert Known Values:**
- \( q = 33,900 \, \text{J} \)
- \( m = 420.0 \, \text{g} \)
- \( c = 4.184 \, \text{J/g·K} \)
- Calculate \( \Delta T \).
4. **Calculate Final Temperature:**
- \( \Delta T = \frac{33,900 \, \text{J}}{420.0 \, \text{g} \times 4.184 \, \text{J/g·K}} \)
- \( \Delta T \approx 19.28 \, \text{K} \)
5. **Determine Final
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