Question

When NaCN dissolves in water, the resulting solution is basic. Account for this observation given that \(\mathrm{p} K_{\mathrm{a}}\) for \(\mathrm{HCN}\) is 9.31.

Short answer

NaCN solution is basic because CN⁻ hydrolyzes to form OH⁻ and HCN, indicating a basic environment due to high \\text{p}K_b.

Step-by-step solution

Understanding the Dissolution

When sodium cyanide (NaCN) dissolves in water, it dissociates into sodium ions (Na⁺) and cyanide ions (CN⁻). The sodium ions are spectators and do not affect the pH of the solution.

Identify the Relevant Ion

The cyanide ion (CN⁻) is crucial for determining the solution's pH. It is capable of interacting with water in a hydrolysis reaction to produce hydroxide ions (OH⁻) and hydrogen cyanide (HCN). The equation for this process is: \ \[ \text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^- \] \ The formation of OH⁻ makes the solution basic.

Calculating the Basic Nature Using pKa

The \text{p}K_a of HCN is 9.31, meaning it is a weak acid. Using the relationship \text{p}K_w = \text{p}K_a + \text{p}K_b, where \text{p}K_w is 14, we can calculate \text{p}K_b for CN⁻: \ \[ \text{p}K_b = 14 - 9.31 = 4.69 \] \ This \text{p}K_b value indicates that CN⁻ is a relatively strong base, confirming the solution's basic property.

Conclusion

The dissolution of NaCN in water results in a basic solution because CN⁻ acts as a base. It hydrolyzes to form HCN and OH⁻, increasing the solution's pH.

Key concepts

Sodium Cyanide in Solution

When sodium cyanide (NaCN) is added to water, it dissolves and breaks apart into its constituent ions. These ions are sodium ions (Na⁺) and cyanide ions (CN⁻). While sodium ions typically act as 'spectators' during the reaction, meaning they do not engage in chemical reactions that change the pH, the cyanide ions play a crucial role in influencing the solution's properties. Understanding how these ions behave when in the solution is essential to grasping why the resulting mixture is basic. Essentially, it is the action of CN⁻, rather than Na⁺, that alters the pH and leads to a basic environment.

Understanding Hydrolysis Reactions

The cyanide ion (CN⁻) engages in a hydrolysis reaction when in water. Hydrolysis involves a chemical reaction between an ion and water that produces an acid, a base, or both. In the case of cyanide ions, they react with water to form hydrogen cyanide (HCN) and hydroxide ions (OH⁻).The balanced chemical equation for this hydrolysis reaction is: \[ \text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^- \] The generation of OH⁻ ions increases the basicity of the solution. This transformation is a classic example of how hydrolysis can influence the pH of a mixture by shifting it towards a basic environment.

pKa and pKb in pH Calculations

The relationship between the acid dissociation constant (pKa) and the base dissociation constant (pKb) is key in understanding the chemical behavior of a solution. For any conjugate acid-base pair, the sum of their pKa and pKb is always equal to 14, derived from the product constant of water (pKw).In the case of hydrogen cyanide (HCN) and cyanide ion (CN⁻), the pKa of HCN is 9.31. Thus, the pKb of CN⁻ can be calculated as:\[ \text{p}K_b = 14 - \text{p}K_a = 14 - 9.31 = 4.69 \]This relatively low pKb hints at the cyanide ion's strong basic nature, reinforcing why the solution of NaCN becomes distinctly basic upon dissolution in water.

Properties of Basic Solutions

A basic solution is one that exhibits a pH greater than 7. This occurs when the concentration of hydroxide ions (OH⁻) is greater than that of hydronium ions (H⁺) in the solution. In the case of sodium cyanide in water, the hydrolysis reaction produces OH⁻, which increases the pH and creates a basic environment. Basic solutions are often characterized by a soapy feel and a bitter taste. Understanding the formation of such solutions is important for practical applications in chemistry and industry, where controlling pH is often crucial.

Weak Acids and Bases

Weak acids and bases do not completely dissociate in water. Instead, an equilibrium is established between the undissociated molecules and the ions formed. Like HCN, which is a weak acid with a pKa of 9.31, weak acids only partially release their hydrogen ions. Similarly, weak bases, such as the cyanide ion (CN⁻), partially interact with water to produce hydroxide ions. The equilibrium established contributes to only a moderate increase in pH, characteristic of a basic but not excessively alkaline solution. Comprehending weak acids and bases is essential in recognizing how small changes can significantly affect a solution's pH, crucial for both academic studies and industrial applications.