Chapter 8. Chemical Compositions of Atmospheres

8.1 Introduction

The goals of this module. In this module you will use Kepler's third law to identify two of the planets. Once you have identified them, you will compare and contrast the orbits of all the planets, to see how they are related.

Why you are doing it: By understanding how gases interact with the gravity of their planet, you can learn a lot about why different planets have atmospheres with different chemical compositions.

8.2 Background

Three major factors determine whether a gas remains in an atmosphere, rather than drifting into space. These are:

1. The mass of the gas atom or molecule, m
2. The temperature of the air, T
3. The escape velocity from the surface of the planet, v_esc

The masses of the gas particles combine with the planet's surface temperature to determine how rapidly atoms and molecules move in the air. If the average speed of any type of gas particle is less than the planet's escape velocity divided by six, then that gas will typically stay near the surface of the planet for billions of years. Otherwise, it will be gone from around that planet today, four and a half billion years after it formed. The escape velocity, v_esc , is the speed that a particle moving straight up without striking any other particles must have to escape from the gravitational clutches of the body holding it down. The factor six takes into account the fact that gas particles travel in all different directions, as well as that they experience many collisions during their time in the air.

How you will determine whether various gases can remain in the air:
You need to determine whether common atmospheric gases are moving at average speeds, v_avg, that are greater than or less than v_esc/6 . The gases you will examine are: hydrogen, helium, nitrogen, oxygen, carbon dioxide, and water. Note that ammonia and methane, common gases in the solar system, have about the same mass and therefore the same v_esc as water. If water is retained, so are these other two gases and vice versa.

8.3 Getting Started

The average speed of a gas atom or molecule is determined by equating two versions of the kinetic energy equation, E_k , for the gas. First:

Where k = 1.38 · 10^-23 J/K is the Boltzmann constant and T is the temperature in Kelvins.

The other equation is:

Where m is the mass of the gas atom or molecule and v_avg is its average velocity at that temperature. Equating these two equations and solving for v_avg , we find:

You will not need your calculator to do this, as this tutorial has a built-in average velocity calculator.

At the escape velocity, v_esc , the kinetic energy of the gas moving straight upward from the surface is equal to the gravitational potential energy, E_p , it feels straight downward

Where G = 6.67 · 10^-11 Nm²/kg² is the universal constant of gravitation, m is the mass of the gas atom or molecule, and M and R are the mass and radius of the body holding the gas down. Equating E_p = E_k , we find that:

As noted above, if 6v_avg > v_esc , a gas will not remain bound to its planet or moon, and vice versa. This tutorial will calculate 6v_avg when you specify T and m.

8.4 Determining a Planet's Atmosphere

Before you determine what gases can exist in the terrestrial atmospheres and in the atmosphere of some moons, we will work through one world with you. Use Earth as the example, with the mass and the radius given below. Please enter these values into the vesc calculator. It will give you the escape velocity. Earth's radius is 6378 km and its mass is 59.7×10²³kg.

We will consider two gases: water and hydrogen. First, determine the average velocity of water by looking up the mass of a water molecule in the Gas Table and putting that number, along with the surface temperature of Earth (300°K), into the v_avg calculator, or selecting "Earth" and "water" from the presets.

8.5 Atmospheres of Terrestrial Solar System Bodies

Here is the data for a variety of terrestrial worlds in the solar system, along with the masses of some molecules:

Data about several stars:

Data about some chemical compositions:

Use the techniques you just learned to determine whether these gases exist in the atmospheres of the other terrestrial worlds. Guideline for this analysis: If the lightest gas, hydrogen, is held down by a planet or moon, then all available gases are held down by that planet. You can see why this is so by noting from the equations above that (a) the escape velocity is independent of the mass of the gas being held down and, (b) the lighter an element, the higher its v_avg. Since all other gases are moving more slowly, if hydrogen is held down then all other gases are, too.

First determine whether a terrestrial planet or moon retains hydrogen in its atmosphere. If so, it retains all other available gases. For each terrestrial world that doesn't retain hydrogen, try helium, the second lightest gas. If neither of these gases is retained, proceed with the same analysis through increasingly more massive gases. When you are done with each world, press the "Finished with World" button and your results will be compared to the correct answers.

8.6 Atmospheres of Jovian Planets

The kinds of calculations you have just done can be applied to the Jovian planets (Jupiter, Saturn, Uranus, and Neptune), but there is a caveat. Just because a planet can contain certain gases in its atmosphere (This is also true for the terrestrials, e.g., carbon dioxide on the earth.) doesn't mean that it will necessarily have those gases. Some gases that were in the air may have been dissolved deep inside the liquid Jovian worlds or been chemically changed on them into other compounds, while some gases may have always been lacking in the region of the solar system containing these worlds. Therefore, the results from the list above for the Jovian planets yield allowed gases, although not necessarily gases that are found on them. Perform the calculations for the Jovian worlds, listed below.

8.7 Quick Check Quiz

Indepth Activity: Chemical Compositions of Atmospheres