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:**
If you combine 290.0 mL of water at 25.00 °C and 110.0 mL of water at 95.00 °C, what is the final temperature of the mixture? Use 1.00 g/mL as the density of water.
\[ T_{\text{final}} = \] \[ \_\_\_\_ \] °C
---
**Explanation:**
To find the final temperature of the mixture, use the formula for the conservation of energy which considers the masses and specific heat capacities of the water samples:
\[ m_1 \cdot c \cdot (T_{\text{final}} - T_1) + m_2 \cdot c \cdot (T_{\text{final}} - T_2) = 0 \]
where:
- \( m_1 \) is the mass of the first water sample,
- \( m_2 \) is the mass of the second water sample,
- \( c \) is the specific heat capacity of water (approximately 4.18 J/g°C),
- \( T_1 \) and \( T_2 \) are the initial temperatures of the first and second water samples, respectively.
Since the density of water is 1.00 g/mL, the mass in grams is numerically equivalent to the volume in mL for each sample.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa13eef44-f673-4796-be37-c768f494742c%2F0f5fee12-b6f6-45da-b1c7-72b058eea3b7%2Fx52sb97_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If you combine 290.0 mL of water at 25.00 °C and 110.0 mL of water at 95.00 °C, what is the final temperature of the mixture? Use 1.00 g/mL as the density of water.
\[ T_{\text{final}} = \] \[ \_\_\_\_ \] °C
---
**Explanation:**
To find the final temperature of the mixture, use the formula for the conservation of energy which considers the masses and specific heat capacities of the water samples:
\[ m_1 \cdot c \cdot (T_{\text{final}} - T_1) + m_2 \cdot c \cdot (T_{\text{final}} - T_2) = 0 \]
where:
- \( m_1 \) is the mass of the first water sample,
- \( m_2 \) is the mass of the second water sample,
- \( c \) is the specific heat capacity of water (approximately 4.18 J/g°C),
- \( T_1 \) and \( T_2 \) are the initial temperatures of the first and second water samples, respectively.
Since the density of water is 1.00 g/mL, the mass in grams is numerically equivalent to the volume in mL for each sample.
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