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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### Heat Calculation Problem
**Problem Statement:**
*If the specific heat of iron is 0.460 J/g°C, how much heat is needed to warm 50.0 g of iron from 20.0°C to 100.0°C?*
This question requires you to determine the amount of heat energy needed to raise the temperature of a given mass of iron over a specified temperature range.
**Concepts Involved:**
- **Specific Heat Capacity (c):** The amount of heat required to raise the temperature of 1 gram of a substance by 1°C.
- **Mass (m):** The amount of the substance that is being heated.
- **Temperature Change (ΔT):** The difference in temperature that the substance undergoes.
**Formula:**
To calculate the heat (Q) added or removed, use the formula:
\[ Q = mc\Delta T \]
Where:
- \( Q \) = heat energy (in joules, J)
- \( m \) = mass (in grams, g)
- \( c \) = specific heat capacity (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)
**Given Data:**
- Specific heat of iron, \( c \) = 0.460 J/g°C
- Mass of iron, \( m \) = 50.0 g
- Initial temperature, \( T_{\text{initial}} \) = 20.0°C
- Final temperature, \( T_{\text{final}} \) = 100.0°C
**Steps to Solve:**
1. **Calculate the Temperature Change:**
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]
\[ \Delta T = 100.0°C - 20.0°C \]
\[ \Delta T = 80.0°C \]
2. **Calculate the Heat Energy Required:**
\[ Q = mc\Delta T \]
\[ Q = (50.0 \, \text{g}) \times (0.460 \, \text{J/g°C}) \times (80.0°C) \]
3. **Perform the calculation:**
\[ Q = 50.0 \times 0.460 \times 80.0 \]
\[ Q = 1840 \,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16ab444c-cc67-4b2e-a5c5-3a02b2df29f8%2Fe1fdac51-d9d9-477e-988a-6795df0a181d%2Fnow93h9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Heat Calculation Problem
**Problem Statement:**
*If the specific heat of iron is 0.460 J/g°C, how much heat is needed to warm 50.0 g of iron from 20.0°C to 100.0°C?*
This question requires you to determine the amount of heat energy needed to raise the temperature of a given mass of iron over a specified temperature range.
**Concepts Involved:**
- **Specific Heat Capacity (c):** The amount of heat required to raise the temperature of 1 gram of a substance by 1°C.
- **Mass (m):** The amount of the substance that is being heated.
- **Temperature Change (ΔT):** The difference in temperature that the substance undergoes.
**Formula:**
To calculate the heat (Q) added or removed, use the formula:
\[ Q = mc\Delta T \]
Where:
- \( Q \) = heat energy (in joules, J)
- \( m \) = mass (in grams, g)
- \( c \) = specific heat capacity (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)
**Given Data:**
- Specific heat of iron, \( c \) = 0.460 J/g°C
- Mass of iron, \( m \) = 50.0 g
- Initial temperature, \( T_{\text{initial}} \) = 20.0°C
- Final temperature, \( T_{\text{final}} \) = 100.0°C
**Steps to Solve:**
1. **Calculate the Temperature Change:**
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]
\[ \Delta T = 100.0°C - 20.0°C \]
\[ \Delta T = 80.0°C \]
2. **Calculate the Heat Energy Required:**
\[ Q = mc\Delta T \]
\[ Q = (50.0 \, \text{g}) \times (0.460 \, \text{J/g°C}) \times (80.0°C) \]
3. **Perform the calculation:**
\[ Q = 50.0 \times 0.460 \times 80.0 \]
\[ Q = 1840 \,
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