What volume of a $0.100 M \text{AgNO}_3$ solution is required to completely react with the $\text{CaCl}_2$ in 3.00 L of a $0.100 M \text{CaCl}_2$ solution? The balanced chemical equation is:
$2 \text{AgNO}_3 + \text{CaCl}_2 \rightarrow 2 \text{AgCl} + \text{Ca(NO}_3)_2$
Answer (2)
Calculate the moles of C a C l 2 : moles = 0.100 M × 3.00 L = 0.300 moles .
Use the stoichiometric ratio from the balanced equation (2:1) to find moles of A g N O 3 : moles of A g N O 3 = 2 × 0.300 moles = 0.600 moles .
Calculate the volume of A g N O 3 solution: Volume = 0.100 M 0.600 moles = 6.00 L .
The required volume of A g N O 3 solution is 6.00 L .
Explanation
Problem Analysis We are given the balanced chemical equation: 2 A g N O 3 + C a C l 2 → 2 A g Cl + C a ( N O 3 ) 2 We are also given the molarity and volume of the C a C l 2 solution, which are 0.100 M and 3.00 L, respectively. We need to find the volume of a 0.100 M A g N O 3 solution required to completely react with the C a C l 2 solution.
Calculate moles of Calcium Chloride First, calculate the number of moles of C a C l 2 using the formula: moles = Molarity × Volume moles of C a C l 2 = 0.100 M × 3.00 L = 0.300 moles .
Determine Stoichiometric Ratio From the balanced chemical equation, the stoichiometric ratio between A g N O 3 and C a C l 2 is 2:1. This means that 2 moles of A g N O 3 are required to react with 1 mole of C a C l 2 .
Calculate moles of Silver Nitrate Now, calculate the number of moles of A g N O 3 required to react completely with 0.300 moles of C a C l 2 :
moles of A g N O 3 = 2 × moles of C a C l 2 = 2 × 0.300 moles = 0.600 moles .
Calculate Volume of Silver Nitrate Solution Finally, calculate the volume of 0.100 M A g N O 3 solution required using the formula: Volume = Molarity moles Volume of A g N O 3 = 0.100 M 0.600 moles = 6.00 L .
Final Answer Therefore, the volume of a 0.100 M A g N O 3 solution required to completely react with the C a C l 2 in 3.00 L of a 0.100 M C a C l 2 solution is 6.00 L.
Examples
In chemical titrations, determining the exact volume of a reactant needed to fully react with another is crucial. For instance, in water treatment, we might need to determine how much silver nitrate solution is needed to precipitate all the chloride ions from a contaminated water sample as silver chloride. This calculation ensures that the water is safe for consumption, preventing potential health hazards. The stoichiometry and molarity calculations, as demonstrated in this problem, are fundamental in ensuring accurate and effective chemical treatments.
To react completely with the CaCl 2 in 3.00 L of a 0.100 M solution, you need 6.00 L of a 0.100 M AgNO 3 solution. The stoichiometric calculations showed that 0.300 moles of CaCl 2 require 0.600 moles of AgNO 3 . Finally, using the molarity equation, we found the volume required.
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