The planet Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 K and 700 K and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

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Step 1: Understand the ideal gas law. The ideal gas law is a good approximation for many gases under many conditions, but it becomes less accurate at very high pressures and very low temperatures. This is because the ideal gas law assumes that gas molecules do not interact with each other and occupy no volume, which is less true under these extreme conditions.

Step 2: Compare the conditions on Jupiter and Mercury. Jupiter has a very low temperature (140 K) and a high mass (318 times that of Earth), which suggests high pressure. Mercury has a higher temperature (between 600 K and 700 K) and a lower mass (0.05 times that of Earth), which suggests lower pressure.

Step 3: Consider the implications of these conditions. The ideal gas law is more likely to be accurate under conditions of higher temperature and lower pressure, because these conditions make the assumptions of the ideal gas law more valid. Therefore, the atmosphere of Mercury is more likely to obey the ideal gas law than the atmosphere of Jupiter.

Step 4: Remember that this is a simplification. In reality, the behavior of a gas depends on many factors, including its specific properties and the exact conditions. This question is asking for a general comparison based on the ideal gas law, not a precise prediction.

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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 is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law assumes that gas particles do not interact and occupy no volume, which is more applicable under certain conditions of low pressure and high temperature.

Temperature and Gas Behavior

Temperature significantly affects gas behavior, influencing the kinetic energy of gas molecules. Higher temperatures generally increase molecular motion, leading to more ideal behavior as gas particles are less likely to condense or interact. In contrast, lower temperatures can result in deviations from ideal behavior, especially if the gas is near its condensation point or if intermolecular forces become significant.

Atmospheric Composition and Pressure

The composition and pressure of a planet's atmosphere play crucial roles in determining whether it behaves like an ideal gas. A dense atmosphere with high pressure can lead to interactions between gas molecules, causing deviations from ideal behavior. Conversely, a thinner atmosphere with lower pressure, like that of Jupiter, may allow gases to behave more ideally, especially at higher temperatures, where molecular interactions are minimized.

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Textbook Question

Arsenic(III) sulfide sublimes readily, even below its melting point of 320 °C. The molecules of the vapor phase are found to effuse through a tiny hole at 0.52 times the rate of effusion of Xe atoms under the same conditions of temperature and pressure. What is the molecular formula of arsenic(III) sulfide in the gas phase?

Textbook Question

A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required 105 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 s for 1.0 L of O2 gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; in other words, rate is the amount that diffuses over the time it takes to diffuse.)

Textbook Question

(b) List two reasons why the gases deviate from ideal behavior.

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.

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.)

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.