Question

(a) Would you expect a reaction to take place between \(\operatorname{HCN}(a q)\) and \(\operatorname{AgNO}_{3}(a q)\) $$ \left(K_{\mathrm{sp}} \text { for } \mathrm{AgCN}=5.97 \times 10^{-17}\right) \text { ? } $$ Explain, and if a reaction occurs, write the net ionic equation. (b) If \(\mathrm{NaCN}\) is added to distilled water, would you expect the solution to be acidic, basic, or neutral? Explain using any chemical equations that may be appropriate.

Short answer

A reaction will occur between HCN and AgNO3, forming a precipitate of AgCN as evidenced by the net ionic equation \(\text{Ag}^+ (aq) + \text{CN}^- (aq) \rightarrow \text{AgCN} (s)\). When NaCN is added to water, the solution becomes basic due to the production of OH- ions.

Step-by-step solution

Understanding the reaction between HCN and AgNO3

To determine whether a reaction occurs between hydrocyanic acid (HCN) and silver nitrate (AgNO3), we need to consider the potential formation of silver cyanide (AgCN). When AgNO3 is mixed with a solution containing cyanide ions (CN-), silver cyanide, a very insoluble compound, might precipitate according to the equation: \[\text{Ag}^+ (aq) + \text{CN}^- (aq) \rightarrow \text{AgCN} (s)\] Since HCN is a weak acid, it will partially dissociate into H+ and CN- ions in solution, providing the CN- ions needed for the reaction.

Comparing the product solubility with Ksp

To predict whether a precipitate of AgCN will form, we compare the ion product (Q) of the reaction with the known solubility product constant (Ksp) for AgCN. If Q is greater than Ksp, a precipitate will form. The Ksp given for AgCN is \(5.97 \times 10^{-17}\), which is extremely low, indicating that AgCN is not very soluble. As CN- ions are available in the solution, it's very likely that the ion product will exceed the Ksp, leading to the formation of a precipitate.

Writing the net ionic equation

Assuming that a precipitate forms due to exceeding the Ksp value, the net ionic equation representing the formation of AgCN precipitate is: \[\text{Ag}^+ (aq) + \text{CN}^- (aq) \rightarrow \text{AgCN} (s)\] This is the net ionic equation as Ag+ ions from AgNO3 and CN- ions from HCN react to form AgCN.

Predicting the pH of NaCN solution

When NaCN is dissolved in water, it dissociates into Na+ and CN- ions. The CN- ion is the conjugate base of the weak acid HCN. As a weak base, CN- will react with water to produce OH- ions, increasing the pH of the solution: \[\text{CN}^- (aq) + \text{H}_2\text{O} (l) \leftrightarrow \text{HCN} (aq) + \text{OH}^- (aq)\] Since CN- generates OH- in water, the solution will be basic.

Key concepts

Solubility Product Constant

The solubility product constant, often abbreviated as Ksp, is a value that helps us predict whether a solid will precipitate out of solution. It is specific to a particular insoluble compound and depends on the temperature of the solution. In simple terms, Ksp represents how much of a compound can dissolve in water before it starts to precipitate.

A low Ksp value, such as the given for silver cyanide (AgCN) with a Ksp of 5.97 x 10^-17, means the compound is very insoluble. In the context of the exercise, when HCN reacts with AgNO3, the potential formation of AgCN is considered. To predict whether AgCN will form, we calculate the ion product (Q) - if Q is greater than Ksp, it indicates that the concentration of ions in the solution has reached a point where AgCN will start to precipitate. This is critical in understanding chemical equilibria involving sparingly soluble salts.

Net Ionic Equation

A net ionic equation is a chemical equation that shows only those compounds and ions that are actively involved in the chemical reaction. It excludes spectator ions, which are present in the reaction mixture but don't directly participate in the formation of the product. This makes it easier to visualize the actual chemical change occurring in solution.

In our exercise, the net ionic equation for the reaction between HCN and AgNO3, leading to the formation of AgCN precipitate, is derived by removing the spectator ions and leaving only the participating ions and compounds:
\[\text{Ag}^+ (aq) + \text{CN}^- (aq) \rightarrow \text{AgCN} (s)\] This equation tells us that silver ions (Ag+) from the AgNO3 and cyanide ions (CN-) from the dissociation of HCN are combining to form solid silver cyanide, AgCN. The net ionic equation is a powerful tool for understanding the essentials of a precipitation reaction.

pH of Solutions

The pH of a solution is a measure of its acidity or basicity. On the pH scale, 7 is considered neutral, values less than 7 are acidic, and values greater than 7 are basic (or alkaline). The pH level is determined by the concentration of hydrogen ions (H+) in a solution.

When dealing with a solution like NaCN in water, it's essential to understand how it dissociates and interacts with water. NaCN, which is a salt of a weak acid (HCN) and a strong base (NaOH), will dissociate into Na+ and CN- ions. The CN- ion will act as a weak base by accepting a proton from water, forming HCN and hydroxide ion (OH-), as shown in the chemical equilibrium equation:
\[\text{CN}^- (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{HCN} (aq) + \text{OH}^- (aq)\] This reaction results in an increase in OH- ions, shifting the pH of the solution to a basic range. Therefore, a NaCN solution in water is expected to be basic.