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Ch.10 - Gases
Chapter 10, Problem 98

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

Calculate the pressure that CCl4 will exert at 80 °C if 1.00 mol occupies 33.3 L, assuming that (a) CCl4 obeys the ideal-gas equation (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.)

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Textbook Question

Table 10.3 shows that the van der Waals b parameter has units of L/mol. This means that we can calculate the sizes of atoms or molecules from the b parameter. Refer back to the discussion in Section 7.3. Is the van der Waals radius we calculate from the b parameter of Table 10.3 more closely associated with the bonding or nonbonding atomic radius discussed there? Explain.

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Textbook Question

Carbon dioxide, which is recognized as the major contributor to global warming as a 'greenhouse gas,' is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6×106 tons of CO2 per year. (a) Assuming ideal-gas behavior, 101.3 kPa, and 27 °C, calculate the volume of CO2 produced by this power plant.

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Textbook Question

Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6⨉106 tons of CO2 per year. (b) If the CO2 is stored underground as a liquid at 10 C and 12.16 MPa and a density of 1.2 g/cm3, what volume does it possess?