Answer:
mass of SiO₂ = 59.70 g
Explanation:
2Cr₂O₃(s) + 3Si(s) — 4Cr(s) + 3SiO₂(s)
Let us determine the limiting reactant because it determines the amount of product. The limiting reactant is totally consumed when the chemical reaction is completed.
Cr2O3
mass of Cr₂O₃ = 100 g
molar mass of Cr₂O₃ = 152 g/mol
moles = 100/152
moles = 0.6578947368 moles
moles = 0.658 moles
from the reaction
2 moles of Cr₂O₃ produces 3 moles of SiO₂
0.658 moles will give (3 × 0.658)/2 = 1.974/2 = 0.987 moles
Si
mass of Si = 30 g
molar mass of Si = 28 g/mol
moles = 30/28
moles = 1.07142 moles
3 moles of Si gives 3 moles of SiO₂
1.07142 moles of Si will give 1.07142 moles of SiO₂
The limiting reactant is Cr₂O₃ since it produce the smallest quantity of product .
The mass of SiO₂ can now be calculated as follows :
molar mass of SiO₂ = 60.08
2(152) g of Cr₂O₃ produces 3 (60.08) g of SiO₂
100 g of Cr₂O₃ will produce ?
cross multiply
mass of SiO₂ = (180.24 × 100 )/304
mass of SiO₂ = 18024/304
mass of SiO₂ = 59.289473684
mass of SiO₂ = 59.70 g
Considering the definition of reaction stoichiometry and limiting reagent, the mass of SiO₂ that could be formed is 59.02 grams.
The balanced reaction is:
2 Cr₂O₃ + 3 Si → 4 Cr + 3 SiO₂
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 limiting reagent is one that is consumed first in its entirety, determining the amount of product in the reaction. When the limiting reagent is finished, the chemical reaction will stop.
To determine the limiting reagent, it is possible to use a simple rule of three as follows: if by stoichiometry 84 grams of Si reacts with 304 grams of Cr₂O₃, 30 grams of Si reacts with how much mass of Cr₂O₃?
[tex]mass of Cr_{2} O_{3} =\frac{30 grams of Six304 grams of Cr_{2} O_{3}}{84 grams of Si}[/tex]
mass of Cr₂O₃= 108.57 grams
But 108.57 grams of Cr₂O₃ are not available, 100 grams are available. Since you have less mass than you need to react with 30 grams of Si, Cr₂O₃ will be the limiting reagent.
Then, it is possible to determine the mass of SiO₂ produced by another rule of three, using the limiting reagent: if by stoichiometry 304 grams of Cr₂O₃ produce 180 grams of SiO₂, 100 grams of Cr₂O₃ how much mass of SiO₂ will be formed?
[tex]mass of SiO_{2} =\frac{180 grams of SiO_{2}x100 grams of Cr_{2} O_{3}}{304 grams of Cr_{2} O_{3}}[/tex]
mass of SiO₂= 59.02 grams
In summary, the mass of SiO₂ that could be formed is 59.02 grams.
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