Calculate the energy required to heat 513.0 mg of mercury from 0 °C to 10.0 °C. Assume the specific heat capacity of mercury under these conditions is 0.139 J-g K Be sure your answer has the correct number of significant digits. ロロ の
Calculate the energy required to heat 513.0 mg of mercury from 0 °C to 10.0 °C. Assume the specific heat capacity of mercury under these conditions is 0.139 J-g K Be sure your answer has the correct number of significant digits. ロロ の
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 Energy Calculation
**Problem Statement:**
Calculate the energy required to heat 513.0 mg of mercury from 0°C to 10.0°C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.
**Inputs and Explanation:**
- **Mass of mercury (m):** 513.0 mg (which needs to be converted to grams because the given specific heat capacity is in J·g⁻¹·K⁻¹)
- **Initial temperature (T₁):** 0°C
- **Final temperature (T₂):** 10.0°C
- **Specific heat capacity (c):** 0.139 J·g⁻¹·K⁻¹
**Conversion:**
1 mg = 0.001 g
So, 513.0 mg = 513.0 * 0.001 g = 0.513 g
**Formula to use:**
The energy required (Q) can be calculated using the formula:
\[ Q = m \cdot c \cdot \Delta T \]
Where:
- \( Q \) is the heat energy (in joules, J)
- \( m \) is the mass (in grams, g)
- \( c \) is the specific heat capacity (J·g⁻¹·K⁻¹)
- \( \Delta T \) is the change in temperature (T₂ - T₁) (in Celsius or Kelvin, K since the difference in temperature in Celsius and Kelvin is the same)
**Calculation:**
1. Calculate the change in temperature (ΔT):
\[ \Delta T = T₂ - T₁ = 10.0°C - 0°C = 10.0 K \]
2. Substitute the values into the formula:
\[ Q = 0.513 \, \text{g} \times 0.139 \, \text{J·g}^{-1} \text{·K}^{-1} \times 10.0 \, \text{K} \]
\[ Q = 0.513 \times 0.139 \times 10.0 \]
\[ Q = 0.71307 \text{ J} \]
**Result:**
\[ Q = 0.713 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd290e29f-bf0a-4e13-893a-d0d06da948d8%2F35133f19-d6e7-468e-a0e6-531d7b890e09%2Fipfr3go_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Heat Energy Calculation
**Problem Statement:**
Calculate the energy required to heat 513.0 mg of mercury from 0°C to 10.0°C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.
**Inputs and Explanation:**
- **Mass of mercury (m):** 513.0 mg (which needs to be converted to grams because the given specific heat capacity is in J·g⁻¹·K⁻¹)
- **Initial temperature (T₁):** 0°C
- **Final temperature (T₂):** 10.0°C
- **Specific heat capacity (c):** 0.139 J·g⁻¹·K⁻¹
**Conversion:**
1 mg = 0.001 g
So, 513.0 mg = 513.0 * 0.001 g = 0.513 g
**Formula to use:**
The energy required (Q) can be calculated using the formula:
\[ Q = m \cdot c \cdot \Delta T \]
Where:
- \( Q \) is the heat energy (in joules, J)
- \( m \) is the mass (in grams, g)
- \( c \) is the specific heat capacity (J·g⁻¹·K⁻¹)
- \( \Delta T \) is the change in temperature (T₂ - T₁) (in Celsius or Kelvin, K since the difference in temperature in Celsius and Kelvin is the same)
**Calculation:**
1. Calculate the change in temperature (ΔT):
\[ \Delta T = T₂ - T₁ = 10.0°C - 0°C = 10.0 K \]
2. Substitute the values into the formula:
\[ Q = 0.513 \, \text{g} \times 0.139 \, \text{J·g}^{-1} \text{·K}^{-1} \times 10.0 \, \text{K} \]
\[ Q = 0.513 \times 0.139 \times 10.0 \]
\[ Q = 0.71307 \text{ J} \]
**Result:**
\[ Q = 0.713 \
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