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Ch 18: A Macroscopic Description of Matter
Chapter 18, Problem 18

In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). p₂=300 cm^3/ 100 cm^3 ×1×2 atm

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Identify the variables and constants in the equation: Here, p₂ represents the final pressure, the initial volume is 100 cm³, the final volume is 300 cm³, and the initial pressure is 2 atm.
Understand the relationship: The equation suggests an inverse relationship between pressure and volume, consistent with Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional.
Formulate a scenario: Imagine a scenario where a gas is initially confined in a 100 cm³ container at a pressure of 2 atm and is then allowed to expand to a 300 cm³ container. The temperature remains constant throughout the process.
Apply Boyle's Law: Use Boyle's Law, P₁V₁ = P₂V₂, to find the new pressure after expansion. Here, P₁ = 2 atm, V₁ = 100 cm³, V₂ = 300 cm³. Solve for P₂.
Write the problem statement: 'A gas is initially at a pressure of 2 atm in a 100 cm³ container. If the gas expands to fill a 300 cm³ container while maintaining a constant temperature, what is the new pressure of the gas?'

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Key Concepts

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

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The ideal gas law, for example, relates these variables through the equation PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Understanding these relationships is crucial for solving problems involving gas behavior.
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Pressure and Volume Relationship

The relationship between pressure and volume of a gas is often described by Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if the volume decreases, the pressure increases, and vice versa. This concept is essential for understanding how changes in one variable affect the other in gas-related problems.
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Units of Measurement

In physics, using consistent units is vital for accurate calculations and problem-solving. In the given equation, volumes are expressed in cubic centimeters (cm³) and pressure in atmospheres (atm). Understanding how to convert between different units and apply them correctly in equations is crucial for formulating realistic problems and interpreting results.
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