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Chapter 4: Problem 71

A \(10.0 \mathrm{~g}\) sample of mercury absorbs 110 cal as it is heated from \(25^{\circ} \mathrm{C}\) to its boiling point at \(356^{\circ} \mathrm{C}\). It then requires an additional 697 cal to vaporize. How much energy is released as the mercury vapor cools from \(356^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The energy released is 807 cal.

Step by step solution

01

Understanding the Problem

The problem requires us to find out how much energy is released when mercury vapor cools from its boiling point, 356掳C, back down to room temperature, 25掳C. Since we know the energy the mercury absorbed, we can use that information to determine the energy released.
02

Recognize the Given Information

The mercury initially absorbs 110 cal to heat from 25掳C to 356掳C and an additional 697 cal to vaporize. Therefore, the total energy absorbed is the sum of these two quantities.
03

Calculating Total Energy Absorbed

Firstly, calculate the total energy absorbed by adding the energy required to heat the mercury and the energy required to vaporize it. \[\text{Total Energy Absorbed} = 110 \text{ cal} + 697 \text{ cal} = 807 \text{ cal}\]
04

Apply the Law of Conservation of Energy

According to the law of conservation of energy, the energy absorbed by the system when heated is equal to the energy released when returning to its initial temperature (assuming no other losses or gains in the process). Thus, the energy released when the mercury vapor cools down must equal the total energy previously absorbed.
05

Solution

The energy released as mercury cools from 356掳C to 25掳C is the total energy it absorbed: The answer is 807 cal.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Law of Conservation of Energy
The Law of Conservation of Energy is a fundamental concept that states energy cannot be created or destroyed. Instead, it can only be transformed from one form to another. This principle is pivotal in thermochemistry. When you heat a substance, it absorbs energy (often in the form of heat). Conversely, when it cools down, it releases the same amount of energy.
  • This implies that any energy that was absorbed by mercury, for instance, when heated, will be released when it cools down to its original temperature.
  • The law helps us understand and predict how much energy will be released or absorbed in chemical reactions and physical processes like phase changes.
  • In our exercise, when mercury vapor cools from 356掳C to 25掳C, it releases the same 807 cal it initially absorbed.
By applying this law, scientists can predict energy changes in reactions, helping in designing efficient energy systems and understanding natural phenomena.
Calorimetry
Calorimetry is a technique used to measure the amount of heat absorbed or released during a chemical reaction or physical process. It is essential for understanding how substances interact thermally and is a fundamental part of thermochemistry studies.

To measure heat changes, a calorimeter is employed. This device captures and measures the energy change through temperature variations in its insulated container.
  • In the context of our exercise, understanding the calorimetry principle allows us to comprehend that measuring the energy mercury absorbs or releases helps determine these reactions' feasibility and efficiency.
  • The energy change is often expressed in calories or joules, which are units of heat energy.
  • A precise calorimetric measurement can differentiate between energy required for temperature change and energy involved in phase changes, such as from liquid to vapor.
Calorimetry is thus an invaluable tool not just in laboratory settings but also in real-world applications like assessing energy efficiency in fuels or engines.
Phase Changes
Phase changes refer to the transformation of a substance from one state of matter (solid, liquid, gas) to another. These changes involve energy exchanges, even though the temperature might remain constant during the process.

Let's break down the process:
  • An example is boiling, where a liquid substance, like mercury, absorbs heat until it reaches its boiling point and then transitions to a gaseous state without a temperature rise during the phase change itself.
  • Similarly, when mercury vaporizes, it absorbs additional energy, which is part of the phase change process.
  • Conversely, when mercury vapor cools and condenses back to a liquid, it releases energy, consistent with the previously absorbed one.
Understanding phase changes is crucial for explaining phenomena such as condensation and evaporation, which are integral to many environmental and industrial processes. The energy balance involved in phase changes also highlights the intricate relationship between thermal dynamics and physical transformations of matter.

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Most popular questions from this chapter

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