Question

Describe an experiment that will allow you to place the following three bases in order of increasing base strength: \(\mathrm{NaCN}, \mathrm{CH}_{3} \mathrm{NH}_{2}, \mathrm{Na}_{2} \mathrm{CO}_{3}\)

Short answer

Prepare equimolar solutions, measure their pH, and rank by pH: highest pH indicates strongest base.

Step-by-step solution

Understand the Concept of Base Strength

Base strength is determined by the tendency of a compound to accept protons. Stronger bases will accept protons more readily than weaker ones. The conjugate acid's dissociation constant can also provide insight into the base's strength.

Choose a Method to Compare Base Strengths

A common method to compare base strengths is to measure the equilibrium constant for the reaction where each base accepts a proton from water. Alternatively, pH measurements of solutions where each base is dissolved in water can be taken to assess their relative strengths.

Set Up the Experiment

Prepare solutions of equal molar concentration for each base: NaCN, CH₃NH₂, and Na₂CO₃. Ensure that the concentration is reasonable, such as 0.1 M, to accurately measure pH changes without reaching extremes that could impact the accuracy.

Measure pH of Each Solution

Using a calibrated pH meter, measure the pH of each solution. The base that produces the highest pH is the strongest, as it dissociates more completely, accepting more protons from water and increasing hydroxide ion concentration.

Analyze and Rank the Results

Arrange the bases in order of increasing base strength based on the pH measurements. The base with the highest pH is the strongest, and the one with the lowest pH is the weakest.

Key concepts

Proton Acceptance

To understand base strength, it's essential to grasp the concept of proton acceptance. Bases are substances that, in solution, have the ability to accept protons.

• This acceptance of protons increases the pH of the solution, indicating a basic environment.
• The eagerness of a base to accept protons determines its strength; stronger bases readily accept protons.

When dissolved in water, bases increase the concentration of hydroxide ions (OH⁻) by accepting protons (H⁺) from water molecules. This reaction can be symbolized as:\[B + H_2O \rightarrow BH^+ + OH^-\]Here, \(B\) represents the base, and \(BH^+\) is the conjugate acid formed. In this context, the base strength is closely associated with the extent of this reaction.Overall, an understanding of proton acceptance is fundamental for explaining how bases shift equilibrium in their favor.

pH Measurement

pH measurement is a straightforward method used to compare the strength of different bases. The pH scale ranges from 0 to 14, with values over 7 indicating a basic solution.

• Higher pH values imply stronger base characteristics.
• A precise pH meter is essential for accurate measurement.

In an experimental setup, equal molar solutions of the bases are prepared and their pH values are measured. For instance:

• NaCN might yield a pH of 11.0, suggesting a moderate base strength.
• CH₃NH₂ could show a pH around 11.8, indicating a stronger base.
• Na₂CO₃ might give a pH of 10.5, suggesting it is the weakest base among them.

Such pH measurements allow for a practical ranking of base strengths from weakest to strongest. This method highlights how each base interacts with water and its capacity to increase OH⁻ concentration.

Equilibrium Constant

The equilibrium constant is another important concept when evaluating base strength. It's a measure that reflects how far a reaction proceeds to reach equilibrium and is denoted as \(K_b\) for bases.

• A higher \(K_b\) value indicates a stronger base.
• It quantifies the extent of proton acceptance in water.
• By comparing \(K_b\) values, you can infer the relative strengths of bases without a pH meter.

The expression for the equilibrium constant for a base is:\[K_b = \frac{[BH^+][OH^-]}{[B]}\]Here, \([B]\) is the concentration of the base, and \([BH^+]\) and \([OH^-]\) are the concentrations of the conjugate acid and hydroxide ion, respectively. Calculating or consulting \(K_b\) values for NaCN, CH₃NH₂, and Na₂CO₃ would help determine their base strength hierarchy. In essence, the equilibrium constant provides a quantitative measure of a base's tendency to accept protons, confirming the strength indicated by other methods.

Conjugate Acid's Dissociation Constant

In addition to measuring the base's direct behavior, the conjugate acid's dissociation constant, known as \(K_a\), provides further insight. This constant represents the strength of the acid formed when a base accepts a proton.

• A lower \(K_a\) of the conjugate acid suggests a stronger base, as it means the conjugate acid dissociates less, implying the base holds onto protons tightly.
• When \(K_a\) for a conjugate acid is small, the equilibrium favors the formation of the conjugate acid.
• This effect stabilizes the conjugate acid, thereby inferring a stronger base.

The relation \(K_b \times K_a = K_w\), where \(K_w\) is the ion-product constant for water (\(10^{-14}\) at 25°C), can be used to compute \(K_a\) if \(K_b\) is known, and vice versa.Understanding the conjugate acid's properties through \(K_a\) is a vital piece of the puzzle in assessing the overall basicity of substances like NaCN, CH₃NH₂, and Na₂CO₃. This helps bridge the relationship between acid and base strengths in aqueous solutions.