A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 10.0 kg of water at 23.4 °C. During the reaction 139. kJ of heat flows out of the bath and into the flask. Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18 Jg K. Round your answer to 3 significant digits. X

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### Thermodynamics in Chemical Reactions

#### Scenario:
A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 10.0 kg of water at an initial temperature of 23.4°C. During the reaction, 139. kJ of heat flows out of the bath and into the flask.

#### Task:
Calculate the new temperature of the water bath. Use the specific heat capacity of water, which is 4.18 J·g⁻¹·K⁻¹. Ensure to round your answer to three significant digits.

#### Solution:
1. Convert the mass of the water bath from kg to grams:
\[10.0 \, \text{kg} = 10,000 \, \text{g}\]

2. Convert the heat energy lost from kJ to J:
\[139 \, \text{kJ} = 139,000 \, \text{J}\]

3. Use the formula for heat transfer:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the heat energy (139,000 J)
- \( m \) is the mass of the water (10,000 g)
- \( c \) is the specific heat capacity (4.18 J·g⁻¹·K⁻¹)
- \( \Delta T \) is the change in temperature

4. Calculate the change in temperature (\(\Delta T\)):
\[ \Delta T = \frac{q}{m \cdot c} = \frac{139,000 \, \text{J}}{10,000 \, \text{g} \cdot 4.18 \, \text{J·g⁻¹·K⁻¹}} = 3.32 \, °C \]

5. Determine the new temperature:
Initial temperature - Change in temperature
= 23.4°C - 3.32°C
= 20.1°C (rounded to 3 significant digits)

#### Answer:
The new temperature of the water bath will be approximately **20.1°C**.

#### Diagrams:
There is one diagram in the image which is a text input box for the final temperature with the unit "°C" next to it. Beneath the text input box, there are buttons for submitting or resetting the input.

#### Interactive Elements:
- Textbox for inputting the
Transcribed Image Text:### Thermodynamics in Chemical Reactions #### Scenario: A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 10.0 kg of water at an initial temperature of 23.4°C. During the reaction, 139. kJ of heat flows out of the bath and into the flask. #### Task: Calculate the new temperature of the water bath. Use the specific heat capacity of water, which is 4.18 J·g⁻¹·K⁻¹. Ensure to round your answer to three significant digits. #### Solution: 1. Convert the mass of the water bath from kg to grams: \[10.0 \, \text{kg} = 10,000 \, \text{g}\] 2. Convert the heat energy lost from kJ to J: \[139 \, \text{kJ} = 139,000 \, \text{J}\] 3. Use the formula for heat transfer: \[ q = m \cdot c \cdot \Delta T \] Where: - \( q \) is the heat energy (139,000 J) - \( m \) is the mass of the water (10,000 g) - \( c \) is the specific heat capacity (4.18 J·g⁻¹·K⁻¹) - \( \Delta T \) is the change in temperature 4. Calculate the change in temperature (\(\Delta T\)): \[ \Delta T = \frac{q}{m \cdot c} = \frac{139,000 \, \text{J}}{10,000 \, \text{g} \cdot 4.18 \, \text{J·g⁻¹·K⁻¹}} = 3.32 \, °C \] 5. Determine the new temperature: Initial temperature - Change in temperature = 23.4°C - 3.32°C = 20.1°C (rounded to 3 significant digits) #### Answer: The new temperature of the water bath will be approximately **20.1°C**. #### Diagrams: There is one diagram in the image which is a text input box for the final temperature with the unit "°C" next to it. Beneath the text input box, there are buttons for submitting or resetting the input. #### Interactive Elements: - Textbox for inputting the
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