After a 120.0-mL sample of a solution that is 2.8 * 10^-3 M in AgNO3 is mixed with a 225.0-mL sample of a solution that is 0.10 M in NaCN and the solution reaches equilibrium, what concentration of Ag+(aq) remains?

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

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Determine the initial moles of AgNO3 by using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \). Convert the volume from mL to L before calculation.

Determine the initial moles of NaCN using the same formula: \( \text{moles} = \text{concentration} \times \text{volume} \). Again, convert the volume from mL to L.

Write the balanced chemical equation for the reaction between AgNO3 and NaCN. The reaction is: \( \text{Ag}^+ + 2\text{CN}^- \rightleftharpoons [\text{Ag(CN)}_2]^- \).

Calculate the limiting reactant by comparing the mole ratio from the balanced equation with the initial moles of reactants.

Use the stoichiometry of the reaction to determine the change in moles of \( \text{Ag}^+ \) at equilibrium, and then calculate the concentration of \( \text{Ag}^+ \) by dividing the remaining moles by the total volume of the solution in liters.

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Molarity and Dilution

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. When two solutions are mixed, the total volume changes, affecting the concentration of each solute. To find the new concentration after mixing, one must calculate the total moles of solute and divide by the total volume of the mixed solution.

Equilibrium and Le Chatelier's Principle

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. Le Chatelier's Principle states that if a system at equilibrium is disturbed, it will shift in a direction that counteracts the disturbance. This principle is crucial for predicting how the concentrations of Ag+ and other species will change when NaCN is added.

Complex Ion Formation

In this scenario, Ag+ ions can react with CN- ions to form a complex ion, [Ag(CN)2]-. This reaction significantly affects the concentration of free Ag+ ions in solution. Understanding the formation of complex ions is essential for calculating the remaining concentration of Ag+ after equilibrium is established, as it directly influences the distribution of ions in the solution.