How many moles of hydrogen gas would be needed to react with excess carbon dioxide to produce 65.1 moles of water vapor?

The relevant chemical reaction can be written as:

In this reaction, carbon dioxide reacts with hydrogen to form methane and water. This reaction is known as the Sabatier reaction and is very commonly used to generate methane for fuel.

Using stoichiometry, along with the balanced chemical reaction (written above), 4 moles of hydrogen gas are used to produce 2 moles of water. 

or, 2 moles of hydrogen will produce 1 mole of water.

Thus, to produce 88.1 moles of water, 2 x 88.1 = 176.2 moles of hydrogen gas would be needed in the presence of excess carbon dioxide. Knowing this data, we can also calculate the mass of hydrogen gas needed. The molar mass of hydrogen gas (H_2) is 2 g/mole and hence a total of 352.4 grams of hydrogen gas are needed. 

Hope this helps! :3