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Chapter 18: Problem 62

Suppose that on another planet the atmosphere consists of $10 \% \mathrm{Kr}, 40 \% \mathrm{CH}_{4},\( and \)50 \% \mathrm{O}_{2} .$ What is the average molar mass at the surface? What is the average molar mass at an altitude at which all the \(\mathrm{O}_{2}\) is photodissociated?

Short Answer

Expert verified
The average molar mass at the surface of the planet is \(30.796 g/mol\), and the average molar mass at the altitude where all the \(O_{2}\) is photodissociated is \(14.796 g/mol\).

Step by step solution

01

Calculate the surface average molar mass

To calculate the average molar mass at the surface, first find the molar mass of each gas Kr, CH₄, and O₂. Then, multiply these values by their respective volume percentages and sum the results to obtain the average molar mass. Molar mass of Kr = 83.8 g/mol Molar mass of CH₄ = 16.04 g/mol Molar mass of O₂ = 32.00 g/mol Surface average molar mass = (0.10)(83.8 g/mol) + (0.40)(16.04 g/mol) + (0.50)(32.00 g/mol) = 8.38 g/mol + 6.416 g/mol + 16.00 g/mol
02

Add the individual contributions to find the average molar mass at the surface

Sum the contributions from each gas at the surface to find the final average molar mass: Surface average molar mass = 8.38 g/mol + 6.416 g/mol + 16.00 g/mol = 30.796 g/mol
03

Calculate the average molar mass at the altitude where O₂ is photodissociated

Since all O₂ is photodissociated, we only need to consider the contributions from Kr and CH₄. Using the same method as above, calculate the average molar mass without O₂: No O₂ average molar mass = (0.1)(83.8 g/mol) + (0.4)(16.04 g/mol) = 8.38 g/mol + 6.416 g/mol
04

Add the individual contributions to find the average molar mass at the altitude without O₂

Sum the contributions from Kr and CH₄ to find the final average molar mass: No O₂ average molar mass = 8.38 g/mol + 6.416 g/mol = 14.796 g/mol The average molar mass at the surface of the planet is 30.796 g/mol, and the average molar mass at the altitude where all the O₂ is photodissociated is 14.796 g/mol.

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Most popular questions from this chapter

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