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Ch.7 - Thermochemistry
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.7 - ThermochemistryProblem 52
Chapter 7, Problem 52

An unknown mass of each substance, initially at 23.0 °C, absorbs 1.95 × 103 J of heat. The final temperature is recorded. Find the mass of each substance.
a. Pyrex glass (Tf = 55.4°C)
b. sand (Tf = 62.1°C)
c. ethanol (Tf = 44.2°C)
d. water (Tf = 32.4°C)

Verified step by step guidance
1
Identify the specific heat capacity of Pyrex glass, which is typically around 0.75 J/g°C.
Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat absorbed, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
Calculate the change in temperature \( \Delta T \) using the initial and final temperatures: \( \Delta T = T_f - T_i = 55.4 \text{ °C} - 23.0 \text{ °C} \).
Rearrange the formula to solve for mass \( m \): \( m = \frac{q}{c \cdot \Delta T} \).
Substitute the known values into the rearranged formula: \( q = 1.95 \times 10^3 \text{ J} \), \( c = 0.75 \text{ J/g°C} \), and \( \Delta T \) calculated in the previous step, to find the mass \( m \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It varies for different materials and is crucial for calculating temperature changes when heat is absorbed or released. In this problem, knowing the specific heat capacity of Pyrex glass allows us to relate the heat absorbed to the change in temperature and ultimately find the mass.
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Heat Transfer Equation

The heat transfer equation, often expressed as Q = mcΔT, relates the heat absorbed or released (Q) to the mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental in thermodynamics and is used to solve for unknown variables, such as mass, when heat transfer is involved. In this case, it will help determine the mass of the Pyrex glass based on the heat absorbed and the temperature change.
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Temperature Change

Temperature change (ΔT) is the difference between the final temperature (Tf) and the initial temperature (Ti) of a substance. It is a critical factor in thermodynamic calculations, as it directly influences the amount of heat absorbed or released. In this scenario, the temperature change of the Pyrex glass from 23.0 °C to 55.4 °C is essential for applying the heat transfer equation to find the mass of the substance.
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