The Earth's atmosphere has a mass of approximately 5.15 * 1015 kg. If the average molar mass of air is 28.8 g/mol, how many moles of gas make up the atmosphere? What is the volume of the atmosphere in liters under conditions of STP? (Note: The average molar mass of air is the weighted average of the molar mass of nitrogen and oxygen. 0.20132.0 g>mol2 + 0.80128.0 g>mol2 = 28.8 g>mol.)

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Convert the mass of the Earth's atmosphere from kilograms to grams by multiplying by 1000, since 1 kg = 1000 g.

Calculate the number of moles of gas in the atmosphere using the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \). Use the given molar mass of air, 28.8 g/mol.

Recall that at Standard Temperature and Pressure (STP), 1 mole of an ideal gas occupies 22.4 liters.

Calculate the volume of the atmosphere in liters by multiplying the number of moles by 22.4 L/mol.

Ensure all units are consistent and check calculations for any potential errors.

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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 atoms in a molecule. In this question, the average molar mass of air is given as 28.8 g/mol, which is essential for converting the total mass of the atmosphere into moles.

Moles and Avogadro's Number

A mole is a unit in chemistry that represents 6.022 x 10²³ entities, such as atoms or molecules. To find the number of moles in a given mass, the formula used is: moles = mass (g) / molar mass (g/mol). This concept is crucial for determining how many moles of gas are present in the Earth's atmosphere based on its total mass and the average molar mass of air.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) refers to a set of conditions commonly used in gas calculations, defined as 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure. Under STP, one mole of an ideal gas occupies 22.4 liters. This concept is necessary for calculating the volume of the atmosphere in liters once the number of moles has been determined.