### Sample Problem: Thermal Equilibrium#### Problem Statement:A sample of a metal block at 75.5°C was placed in 250.0 g water with a temperature of 22.5°C. When the two substances reached thermal equilibrium, the final temperature was 24.3°C. Find the mass of the metal block. The specific heat capacity of the metal is 0.385 J/g°C and the specific heat capacity of water is 4.184 J/g°C.##### Choices:- [ ] 150 g- [ ] 74 g- [ ] 120 g- [ ] 96 g#### Explanation:This problem involves the concept of thermal equilibrium, where two substances at different temperatures come into contact and exchange heat until they reach the same temperature.#### Diagram or Graph (Not Provided in the Image):If there were a diagram, it would likely depict:1. **Initial Conditions:** - Metal Block: 75.5°C - Water: 22.5°C2. **Final Condition:** - Both Metal Block and Water: 24.3°CThe heat lost by the metal equals the heat gained by the water, which can be expressed as:\[ m_{metal} \cdot c_{metal} \cdot \Delta T_{metal} = m_{water} \cdot c_{water} \cdot \Delta T_{water} \]Where:- \( m \) is mass- \( c \) is specific heat capacity- \( \Delta T \) is the change in temperature (\(T_{initial} - T_{final}\))#### Calculation Example:- For the metal: \[ (m_{metal} \cdot 0.385 \, \text{J/g°C}) \cdot (75.5°C - 24.3°C) \]- For the water: \[ (250.0 \, \text{g} \cdot 4.184 \, \text{J/g°C}) \cdot (24.3°C - 22.5°C) \]Set the heat lost by the metal equal to the heat gained by the water and solve for \( m_{metal} \).#### Solution:To solve the problem step-by-step, please apply the heat exchange formula and solve for the mass of the metal block. The answer will be one

Answered: Image /qna-images/answer/5fe53813-88e0-48cd-b32e-eb7a6f04610d.jpg

7.3) A sample of metal block at 75.5 °C was placed in 250.0 g water with the temperature of 22.5 °C. When the two substances reached thermal equilibrium, the final temperature was 24.3 °C. Find the mass of the metal block. The specific heat capacity of the metal is 0.385 J/g.°C and the specific heat capacity of water is 4.184 J/g. °C. 150 g O 74 g O 120 g O 968

7.3) A sample of metal block at 75.5 °C was placed in 250.0 g water with the temperature of 22.5 °C. When the two substances reached thermal equilibrium, the final temperature was 24.3 °C. Find the mass of the metal block. The specific heat capacity of the metal is 0.385 J/g.°C and the specific heat capacity of water is 4.184 J/g. °C. 150 g O 74 g O 120 g O 968

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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