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:
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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