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Stoichiometry Question

Stoichiometry Question

NASAs long term plans for sending astronauts to Mars involves an ISRU strategy. ISRU is in-situ resource utilization and means that to the extent possible, chemical resources already on Mars will be utilized. The Martian atmosphere contains about 95.3% carbon dioxide. According to one NASA plan, hydrogen will be sent to Mars from Earth before astronaut crews arrive. Fuel for the Mars Ascent Vehicle (MAV) will consist of methane-oxygen combustion: CH4 + 2O2  CO2 + 2H2O. The fuel and oxygen will be made by the following reactions:

CO2 + 4H2CH4 + 2H2O (the Sabatier reaction)
And 2H2O2H2 + O2 (the electrolysis of water)
Energy to run these latter reactions will come perhaps from Plutonium power sources or solar cells. Making use of the above reactions, calculate the minimum mass of hydrogen that will have to be sent from Earth to Mars in order to produce 500 kg of methane and the necessary oxygen to combust it.

Solution Preview

We need to produce 500 Kg of CH4.

Therefore number of moles of CH4 = weight/mol. mass = 500*10^3/16
= 31250 moles

Now, we have the reaction,
CO2 + 4H2 - gt; CH4 + 2H20

It implies,
4 moles of H2 give 1 mole CH4
That is,
to obtain 31250 CH4, we need 4*31250 moles of H2 = 125000 moles of H2

Therefore, mass of H2 = moles * mol mass
= 12500 * 2
= 250000 g
= 250 Kg

But,
2CH4 + 4O2 - 2CO2 + 4H20
That is 2 mole ...

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