Recycling of resources is essential for long-term space missions. For example, w

Question

Recycling of resources is essential for long-term space missions. For example, water is distilled from many sources, including the astronauts' urine. Some of this water from the distillation system is used to produce oxygen and hydrogen gases by electrolysis. Oxygen is returned to the cabin; in current designs, the hydrogen gas is vented from the spacecraft. Another gas that is currently vented from the spacecraft is carbon dioxide. Research is ongoing to recycle both the hydrogen and carbon dioxide gases. One design under development is a Methane Formation System (MFS) (Figure 3.36). With an appropriate catalyst, CO_2 and H_2 react to form water and methane gas (CH_4). the water can then be sent to the electrolysis unit for O_2 recovery. the H_2 gas from the electrolysis unit, rather than being vented, is sent to the MFS as the exclusive source of H_2. the goal is to produce 10.0 mol O_2/hr in the electrolysis unit from water sent directly from the MFS. Assume 20.0 mol/hr of CO_2 is supplied to the MFS and that all water in the electrolysis unit is converted to O_2 and H_2 For this problem, assume that any excess reagent can be vented from the MFS. Write out balanced chemical equations for the electrolysis reaction and the methane formation reaction. Determine the limiting reactant, reaction rate, and molar flow for all constituents for the MFS unit. Determine the limiting reactant, reaction rate, and molar flow for all constituents in the electrolysis unit.

Explanation / Answer

A)electrolysis reaction:H2O=H2 +1/2 O2

Methane formation reaction: CO2+4H2=CH4+2H2O

B) For MFS unit.   

Ffor production of 10moleO2/hr

Mole of H2O required=2×10=20mole

For20 mole H2O, mole of CO2required =20×1/2=10mole

So H2 is limiting reagent

Mole of CO2 required=10 mole

Mole of H2 required =10×4=40mole

Mole of CH4 formed=10×1=10 mole

Mole of H2O formed =10×2=20 mole

Rate of reaction=-d[O2]/dt=10/1=10 mole/hour

C)for electrolysis unit

Mole of H2O decomposed =20 mole

Mole of H2 formed =20 mole

Mole of O2 formed=1/2×20=10mole

Limiting reactant=H2o(sole reactant)

Rate of reaction=-d[H2O]/dt=20mole/1hour= 20mole /hour

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