when equal volumes of .2 M AgNO3 and 1 M KCN solutions were mixed then at equilibrium , concentration of

When equal volumes of 0.2 M AgNO3 and 1 M KCN solutions are mixed, a complex equilibrium is established due to the formation of silver cyanide (AgCN), which is a sparingly soluble salt. To understand the concentrations at equilibrium, we need to analyze the reaction that occurs when these two solutions are combined.

The Reaction Process

When silver nitrate (AgNO3) and potassium cyanide (KCN) are mixed, the following reaction takes place:

• AgNO3 (aq) + KCN (aq) → AgCN (s) + KNO3 (aq)

In this reaction, silver ions (Ag⁺) from AgNO3 react with cyanide ions (CN^-) from KCN to form solid silver cyanide (AgCN), which precipitates out of the solution. The potassium nitrate (KNO3) remains dissolved in the aqueous solution.

Initial Concentrations

Before mixing, we have:

• Volume of AgNO3 = V (let's assume 1 L for simplicity)
• Concentration of AgNO3 = 0.2 M
• Volume of KCN = V (1 L)
• Concentration of KCN = 1 M

When mixed, the total volume becomes 2V (2 L), and the concentrations of the reactants change:

• Concentration of Ag⁺ after mixing = (0.2 M * 1 L) / 2 L = 0.1 M
• Concentration of CN^- after mixing = (1 M * 1 L) / 2 L = 0.5 M

Reaction Stoichiometry

From the stoichiometry of the reaction, one mole of Ag⁺ reacts with one mole of CN^- to form one mole of AgCN. Therefore, the limiting reactant will determine how much of each reactant is consumed:

• Initially, we have 0.1 moles of Ag⁺ (from 0.1 M in 2 L) and 1 mole of CN^- (from 0.5 M in 2 L).

Since Ag⁺ is the limiting reactant, it will completely react with an equivalent amount of CN^-:

• 0.1 moles of Ag⁺ will react with 0.1 moles of CN^-.

Equilibrium Concentrations

After the reaction, the remaining concentrations will be:

• Remaining Ag⁺ = 0 M (since it is completely consumed)
• Remaining CN^- = 0.5 moles - 0.1 moles = 0.4 moles in 2 L = 0.2 M

At equilibrium, the concentration of AgCN will be determined by the solubility product (Ksp) of AgCN, which is very low, indicating that most of the Ag⁺ will precipitate as AgCN. However, since we are not given the Ksp value here, we can conclude that the concentration of AgCN in solution will be negligible, effectively making it 0 M.

Final Summary

In summary, when equal volumes of 0.2 M AgNO3 and 1 M KCN are mixed, the equilibrium concentrations are:

• Ag⁺: 0 M
• CN^-: 0.2 M
• AgCN: Approximately 0 M (due to precipitation)

This illustrates the importance of stoichiometry and solubility in predicting the outcomes of chemical reactions in solution. If you have any further questions or need clarification on any point, feel free to ask!