Taking into account the reaction stoichiometry, 340.0 moles of methane are produced when 85.1 moles of carbon dioxide gas react with excess hydrogen gas
<h3>Reaction stoichiometry</h3>
In first place, the balanced reaction is:
CO₂ + 4 H₄ → CH₄ + 2 H₂O
By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:
- CO₂: 1 mole
- H₄: 4 moles
- CH₄: 1 mole
- H₂O: 2 moles
<h3>Moles of CH₄ formed</h3>
The following rule of three can be applied: if by reaction stoichiometry 1 mole of CO₂ form 4 moles of CH₄, 85.1 moles of CO₂ form how many moles of CH₄?

<u><em>moles of CH₄= 340.4 moles</em></u>
Then, 340.0 moles of methane are produced when 85.1 moles of carbon dioxide gas react with excess hydrogen gas
Learn more about the reaction stoichiometry:
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Answer: The volume of the sample after the reaction takes place is 29.25 L.
Explanation:
The given reaction equation is as follows.

So, moles of product formed are calculated as follows.
Hence, the given data is as follows.
= 0.17 mol,
= 0.255 mol
= 19.5 L, 
As the temperature and pressure are constant. Hence, formula used to calculate the volume of sample after the reaction is as follows.

Substitute the values into above formula as follows.

Thus, we can conclude that the volume of the sample after the reaction takes place is 29.25 L.
The answer here is letter C. The optimal solution. The optimal solution is the one that affects how certain things changes with sensitivity analysis. The optimal solution is a feasibility solution where the objective function of it is to reach the minimum and maximum value.