/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 94 The planet Jupiter has a surface... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 94

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

Short Answer

Expert verified
Based on the analysis, the atmosphere of Mercury is more likely to obey the ideal gas law compared to Jupiter. Mercury's higher temperature (between 600 K and 700 K) and lower mass (0.05 times Earth's mass) relative to Jupiter (whose temperature is 140 K and has a mass 318 times Earth's mass) make it more likely to meet the conditions necessary for the ideal gas law to be a valid approximation.

Step by step solution

01

1. Jupiter's characteristics

Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth.
02

2. Mercury's characteristics

Mercury has a surface temperature between 600 K and 700 K, and a mass 0.05 times that of Earth.
03

3. Comparing temperatures

Jupiter has a lower temperature (140 K) when compared to Mercury's temperature range (600 K - 700 K).
04

4. Comparing masses

Jupiter has a much larger mass (318 times Earth's mass) compared to Mercury's mass (0.05 times Earth's mass).
05

5. Analyzing ideal gas law conditions

As stated earlier, the ideal gas law tends to work well when the gas particles have high temperatures and low densities. Since Mercury's temperature is higher than Jupiter's, it indicates that the gas particles on Mercury will have more energetic motion, reducing the significance of any intermolecular attractive forces. Additionally, Jupiter's larger mass implies that it likely has a more dense atmosphere than Mercury, which would lead to more deviations from the ideal gas law due to increased particle interactions.
06

6. Conclusion:

Based on the analysis, the atmosphere of Mercury is more likely to obey the ideal gas law compared to Jupiter. Mercury's higher temperature and lower mass relative to Jupiter make it more likely to meet the conditions necessary for the ideal gas law to be a valid approximation.

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Most popular questions from this chapter

A mixture containing \(0.765 \mathrm{~mol} \mathrm{He}(g), 0.330 \mathrm{~mol} \mathrm{Ne}(g),\) and \(0.110 \mathrm{~mol} \mathrm{Ar}(g)\) is confined in a \(10.00-\mathrm{L}\) vessel at \(25^{\circ} \mathrm{C}\). Calculate the partial pressure of each of the gases in the mixture. (b) Calculate the total pressure of the mixture.

At constant pressure, the mean free path \((\lambda)\) of a gas molecule is directly proportional to temperature. At constant temperature, \(\lambda\) is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, \(\lambda\) is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it \(R_{\mathrm{mfp}}\), like the ideal-gas constant) and define units for \(R_{\mathrm{mfp}}\).

(a) Calculate the number of molecules in a deep breath of air whose volume is \(2.25 \mathrm{~L}\) at body temperature, \(37{ }^{\circ} \mathrm{C},\) and a pressure of 735 torr. (b) The adult blue whale has a lung capacity of \(5.0 \times 10^{3} \mathrm{~L} .\) Calculate the mass of air (assume an average molar mass \(28.98 \mathrm{~g} / \mathrm{mol}\) ) contained in an adult blue whale's lungs at \(0.0{ }^{\circ} \mathrm{C}\) and 1.00 atm, assuming the air behaves ideally.

Assume that an exhaled breath of air consists of \(74.8 \% \mathrm{~N}_{2}\), \(15.3 \% \mathrm{O}_{2}, 3.7 \% \mathrm{CO}_{2},\) and \(6.2 \%\) water vapor. (a) If the total pressure of the gases is 0.985 atm, calculate the partial pressure of each component of the mixture. (b) If the volume of the exhaled gas is \(455 \mathrm{~mL}\) and its temperature is \(37^{\circ} \mathrm{C},\) calculate the number of moles of \(\mathrm{CO}_{2}\) exhaled. (c) How many grams of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) would need to be metabolized to produce this quantity of \(\mathrm{CO}_{2}\) ? (The chemical reaction is the same as that for combustion of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} .\) See Section 3.2 and Problem \(\left.10.59 .\right)\)

How does a gas compare with a liquid for each of the following properties: (a) density, (b) compressibility, (c) ability to mix with other substances of the same phase to form homogeneous mixtures, \((\mathrm{d})\) ability to conform to the shape of its container?
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