Answer:
a) 0.06 mol K₂(CO₃) and 0.07 mol Al(NO₃)₃
b) The limiting reactant is K₂CO₃
c) 0.03 moles of Al₂(CO₃)₃
Explanation:
The balanced reaction between K₂CO₃ and Al(NO₃)₃ is the following:
3 K₂CO₃ + 2 Al(NO₃)₃ → Al₂(CO₃)₃ + 6 KNO₃
(a) We can calculate the moles for each reactant as the product of the molarity (M) and the volume (V) in liters.
K₂(CO₃): M = 2.4 mol/L , V = 25 mL x 1 L/1000 mL = 0.025 L
⇒ moles K₂(CO₃) = M x V = 2.4 mol/L x 0.025 L = 0.06 mol K₂(CO₃)
Al(NO₃)₃: M = 2.0 mol/L , V = 35 mL x 1 L/1000 mL = 0.035 L
⇒ moles Al(NO₃)₃ = M x V = 2.0 mol/L x 0.035 L = 0.07 mol Al(NO₃)₃
(b) According to the balanced equation, the stoichiometric ratio is 3 moles K₂CO₃/2 moles Al(NO₃)₃. We have 0.07 moles of Al(NO₃)₃, so we multiply the moles of Al(NO₃)₃ by the stiochiometric ratio to calculate how many moles of K₂CO₃ are needed:
0.07 mol Al(NO₃)₃ x 3 mol K₂CO₃/2 mol Al(NO₃)₃ = 0.105 moles of K₂CO₃
We need 0.105 moles of K₂CO₃ but we have only 0.06 moles of K₂CO₃. Therefore, the limiting reactant is K₂CO₃.
(c) We use the limiting reactant to calculate how many moles of product (Al₂(CO₃)₃) are formed. According to the equation, 2 moles of K₂CO₃ produce 1 mol of Al₂(CO₃)₃, thus the stoichiometric ratio is 1 mol Al₂(CO₃)₃/2 moles K₂CO₃. We have 0.06 moles of K₂CO₃, so the number of moles of Al₂(CO₃)₃ will be:
0.06 moles K₂CO₃ x 1 mol Al₂(CO₃)₃/2 moles K₂CO₃ = 0.03 moles of Al₂(CO₃)₃
