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Taking into account the reaction stoichiometry and definition of limiting reactant, AgNO₃ will be the limiting reagent.
In first place, the balanced reaction is:
Cu + 2 AgNO₃ → 2 Ag + Cu(NO₃)₂
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 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 1 mole of Cu reacts with 2 moles of AgNO₃, 1.8 moles of Cu reacts with how many moles of AgNO₃?
[tex]amount of moles of AgNO_{3} =\frac{1.8 moles of Cux2 moles of AgNO_{3} }{1 mole of Cu}[/tex]
amount of moles of AgNO₃= 3.6 moles
But 3.6 moles of AgNO₃ are not available, 2 moles are available. Since you have less moles than you need to react with 1.8 moles of Cu, AgNO₃ will be the limiting reagent.
In summary, AgNO₃ will be the limiting reagent.
Learn more about the reaction stoichiometry:
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