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

Expert Answers

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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.

Approved by eNotes Editorial Team
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