A tank of syngas produced by coal gasification contains 60.0% carbon monoxide, 30.0% hydrogen, and 10.0% carbon dioxide. What is the mass of hydrogen (in g) in 1.00 cubic meter of this syngas mixture at 1.00 atm and 25.0 °C? (1 m³ = 1000 L)

Answers

Answer 1

Considering the ideal gas law, the mass of hydrogen is 24.552 grams.

An ideal gas is a theoretical gas that is considered to be composed of randomly moving point particles that do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.

An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:

P× V = n× R× T

In this case, you know:

P= 1 atmV= 1 m³= 1000 Ln= ?R= 0.082[tex]\frac{atmL}{molK}[/tex]T= 25 °C= 298 °K

Replacing in the ideal gas law:

1 atm× 1000 L = n× 0.082[tex]\frac{atmL}{molK}[/tex]× 298 K

Solving:

[tex]n=\frac{1 atmx1000 L}{0.082 \frac{atmL}{molK}x298 K}[/tex]

n= 40.92 mol

The mol of syngas mixture is 40.92 mol.

Syngas mixture contains 30.0% hydrogen. So, there is a mol fraction of [tex]x_{hydrogen} =[/tex]0.3 . Thus, the mols of hydrogen in syngas mixture is calculated as:

40.92 moles of syngas mixture× 0.3= 12.276 moles of hydrogen

Finally, being the molar mass of hydrogen H₂ 2 [tex]\frac{g}{mole}[/tex], then the mass is:

[tex]12.276 molesx\frac{2 grams}{1 mole}[/tex]= 24.552 grams

In summary, the mass of hydrogen is 24.552 grams.

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Answer:

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___________________

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___________________

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Answers

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