How many moles of hydrogen gas would be needed to react with excess carbon dioxide to produce 99.1 moles of water vapor?

Hello!

The first step is to write and balance the chemical equation. it is

`X*H_2 + Y*CO_2 = Z*CH_4 + W*H_2O.`

To balance it, consider equations for `H,` `C` and `O:`

`H:` `2X = 4Z + 2W` (thus `X = 2Z + W`),

`C:` `Y = Z,`

`O:` `2Y = W.`

The irreducible solution is `Y = Z = 1,` `W = 2Y = 2` and `X = 2Z + W = 4,`

`4H_2 + CO_2 = CH_4 + 2H_2O.`

The second step is to create and solve a simple proportion: `4` moles of hydrogen gas `H_2` are required for each `2` moles of water, and `h` moles of hydrogen is required for `99.1` moles of water.

The proportion is  `4 : 2 = h : 99.1,` thus `h = 99.1*4/2 =198.2` (moles). This is the answer.

Note that this reaction also requires a catalyst and high temperature.