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Ch.10 - Gases
Chapter 10, Problem 95

A gas bubble with a volume of 1.0 mm3 originates at the bottom of a lake where the pressure is 3.0 atm. Calculate its volume when the bubble reaches the surface of the lake where the pressure is 730 torr, assuming that the temperature does not change.

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Step 1: Convert the given pressures into the same units. Since 1 atm = 760 torr, the pressure at the bottom of the lake is 3.0 atm * 760 torr/atm = 2280 torr.
Step 2: Use the ideal gas law in the form P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. This equation is valid because the temperature and the amount of gas are constant.
Step 3: Substitute the given values into the equation. P1 = 2280 torr, V1 = 1.0 mm^3, and P2 = 730 torr. Solve for V2.
Step 4: Rearrange the equation to solve for V2: V2 = (P1V1) / P2.
Step 5: Substitute the values into the equation to find the volume of the gas bubble when it reaches the surface of the lake.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this scenario, while the temperature remains constant, the law helps us understand how changes in pressure affect the volume of a gas bubble as it rises.
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Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant (P1V1 = P2V2). This principle is crucial for solving the problem, as it allows us to calculate the new volume of the gas bubble at a different pressure.
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Unit Conversion

Unit conversion is essential in this problem because the initial pressure is given in atmospheres (atm) and the final pressure in torr. Understanding how to convert between these units (1 atm = 760 torr) ensures accurate calculations when applying gas laws.
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Related Practice
Textbook Question

Which statement concerning the van der Waals constants a and b is true? (a) The magnitude of a relates to molecular volume, whereas b relates to attractions between molecules. (b) The magnitude of a relates to attractions between molecules, whereas b relates to molecular volume. (c) The magnitudes of a and b depend on pressure. (d) The magnitudes of a and b depend on temperature.

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