Introduction

For more backstory, see here and here

The 438th Harmonious Congress of the People of Mars was perhaps the most anticipated since the early years of the settlement. In a rare action, the Supreme Council of Harmony agreed to broadcast some of the proceedings of the Congress on tele-projector for all the tens of millions of Martians to witness. The occasion was, of course, significant. The Chief Designer was presenting to the Council, and indeed to all the people, a new 100 Year Plan for the Revivification of Mars.

There was a great buzz and anticipation in the air. Rumors flew that some great milestone had been met in the construction of an atmosphere. Already, if you received permission to surface walk outside the airlocks, you could see the fruits of the Bureau of Revivification. In the lowest latitudes, slender pine trees thrust skyward from the red dirt. In more seasonal climes, grass bloomed in great billows of green during spring. Running water could be seen for part of the year anywhere within 30 degrees of the Equator.

People had not been outside for generations stretching back to Old Earth. The first colonists had dug into dormant volcanoes and the cliff faces of vast chasms. Over the centuries, millions of miles of passages and corridors were extended under the surface. No one walked on the surface for centuries, save a few scientists perhaps. But in the past few decades, the air pressure had gotten so high-pressure suits were barely thicker than regular clothes. A rupture was no longer catastrophic.

All Mars waited with anticipation the speech from the Chief Designer. What would she propose? What was the next step for Mars? Was it possible that a Green and Blue Mars, a truly habitable Mars, would soon be a reality?

Question

The Martian air pressure is above 10 kPa. The massive amounts of carbon dioxide available on the surface of the planet have all been vaporized. Nuclear driven oxygen synthesis has greatly sped the conversion of this carbon dioxide to oxygen, and widespread plant life is contributing its part. It will not be long until oxygen levels are 50% that of Earth; equivalent to 5 km altitude on Earth. High enough to be considered habitable and breathable to humans.

The Chief Designer and her team have decided that it is time to raise the atmospheric pressure on Mars. In order to do this, they will need to generate about 40 kPa of air pressure from some inert gas.

Given the energy cost of transporting an inert gas from somewhere else in the solar system, and the energy cost of any chemical reactions needed to put it in the atmosphere, what is the least energy expensive way to add 40 kPa of air pressure to Mars?*

For example, if the best gas is diatomic nitrogen, then the cost of transportation from a source in the outer solar system as well as the cost of turning whatever nitrogen compounds can be found into the diatomic gas must be considered.

Considerations

• The Earth was hit by a large bolide 500 years ago. It is still glowing. Earth's former atmosphere and oceans are not available to be moved to Mars.
• Any other resources in the solar system are available.
• The O$_2$ and CO$_2$ information in the question are presented as facts; they are not relevant to the discussion.
• Technology level is near-future but mostly irrelevant. The correct answer will give an energy cost in Joules (or Calories, I suppose, if you like to be contrarian).
• Energy cost only has to consider the cost of moving the materials; a function of mass and whatever combinations of delta-v's will get it from its current location to Mars. The cost of rockets and fuels and such can be transparent.