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).

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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
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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