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Taking into account the reaction stoichiometry and the ideal gas law, 22.84 L of hydrogen gas at 27°c and 680 torr is produced in the reaction of 15 g Al metal with excess hydrochloric acid to produce AlCl₃ and H₂.
In first place, the balanced reaction is:
2 Al + 6 HCl → 2 AlCl₃ + 3 H₂
By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:
The molar mass of the compounds is:
Then, by reaction stoichiometry, the following mass quantities of each compound participate in the reaction:
The following rule of three can be applied: If by stoichiometry of the reaction 54 grams of Al produces 3 moles of H₂, 15 grams of Al produces how many moles of H₂?
[tex]moles of H_{2} =\frac{15 grams of Alx3 moles of H_{2} }{54 grams of Al}[/tex]
moles of H₂= 0.83 moles
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 gases:
P×V = n×R×T
In this case, you know:
Replacing in the ideal gas:
680 torr×V = 0.83 moles×62.364 [tex]\frac{torr L}{mol K}[/tex]×300 K
Solving:
V= (0.83 moles×62.364 [tex]\frac{torr L}{mol K}[/tex]×300 K)÷ 680 torr
V= 22.84 L
Finally, 22.84 L of hydrogen gas at 27°c and 680 torr is produced in the reaction of 15 g Al metal with excess hydrochloric acid to produce AlCl₃ and H₂.
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