Suppose that on another planet the atmosphere consists of 17% Kr, 38% CH4, and 45% O2. What is the average molar mass at the surface? What is the average molar mass at an altitude at which all the O2 is photodissociated?

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Identify the components of the atmosphere and their respective percentages: Krypton (Kr) 17%, Methane (CH4) 38%, and Oxygen (O2) 45%.

Calculate the molar mass of each component: Kr = 83.80 g/mol, CH4 = 16.04 g/mol, O2 = 32.00 g/mol.

Determine the average molar mass at the surface using the formula: \( M_{avg} = (\text{fraction of Kr} \times M_{Kr}) + (\text{fraction of CH4} \times M_{CH4}) + (\text{fraction of O2} \times M_{O2}) \).

Consider the scenario at altitude where all O2 is photodissociated, meaning O2 is no longer present. Recalculate the average molar mass using only Kr and CH4: \( M_{avg, altitude} = (\text{fraction of Kr} \times M_{Kr}) + (\text{fraction of CH4} \times M_{CH4}) \).

Adjust the fractions of Kr and CH4 to account for the absence of O2, ensuring their sum equals 100% before recalculating the average molar mass.

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Key Concepts

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

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. Understanding molar mass is essential for converting between grams and moles, which is crucial for stoichiometric calculations in chemistry.

Average Molar Mass of a Mixture

The average molar mass of a gas mixture is determined by taking the weighted average of the molar masses of the individual components, based on their mole fractions. This concept is important for calculating properties of gas mixtures, such as density and partial pressures, and is essential for solving problems involving atmospheric compositions.

Photodissociation

Photodissociation is the process by which a chemical compound is broken down into its constituent atoms or simpler molecules through the absorption of light energy. In the context of the question, understanding photodissociation is crucial for determining how the composition of the atmosphere changes with altitude, particularly the removal of O2 and its impact on the average molar mass.

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In the following three instances, which choice is greener in a chemical process? Explain. (a) A reaction that can be run at 350 K for 12 h without a catalyst or one that can be run at 300 K for 1 h with a reusable catalyst.

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