Question

Write balanced equations and \(K_{b}\) expressions for these Bronsted-Lowry bases in water: (a) Pyridine, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}\) (b) \(\mathrm{CO}_{3}^{2-}\)

Short answer

Pyridine: \[ \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{NH}^+ + \mathrm{OH}^- \] \[ K_b = \frac{[\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{NH}^+][\mathrm{OH}^-]}{[\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}]} \] Carbonate: \[ \mathrm{CO}_{3}^{2-} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{HCO}_{3}^- + \mathrm{OH}^- \] \[ K_b = \frac{[\mathrm{HCO}_{3}^-][\mathrm{OH}^-]}{[\mathrm{CO}_{3}^{2-}]} \]

Step-by-step solution

- Understand the Bronsted-Lowry Base Concept

Bronsted-Lowry bases are substances that can accept a proton (H⁺). In the context of this problem, we need to write the balanced chemical equation for each base reacting with water and then derive the expression for the equilibrium constant, \(K_b\).

- Write the Balanced Equation for Pyridine (\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N})

Pyridine (\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}) acts as a Bronsted-Lowry base and accepts a proton from water: \[ \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{NH}^+ + \mathrm{OH}^- \] Now we have the balanced equation for pyridine in water.

- Write the \(K_b\) Expression for Pyridine

The equilibrium constant expression for the Bronsted-Lowry base reaction is given by the ratio of the concentration of the products to the reactants (excluding water): \[ K_b = \[ \frac{[\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{NH}^+][\mathrm{OH}^-]}{[\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}]} \] \]

- Write the Balanced Equation for \mathrm{CO}_{3}^{2-}

For carbonate ion (\mathrm{CO}_{3}^{2-}), it reacts with water and accepts a proton: \[ \mathrm{CO}_{3}^{2-} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{HCO}_{3}^- + \mathrm{OH}^- \] This is the balanced equation for the carbonate ion in water.

- Write the \(K_b\) Expression for \mathrm{CO}_{3}^{2-}

The equilibrium constant expression for the carbonate ion reaction is: \[ K_b = \[ \frac{[\mathrm{HCO}_{3}^-][\mathrm{OH}^-]}{[\mathrm{CO}_{3}^{2-}]} \] \]

Key concepts

equilibrium constant

The equilibrium constant, represented as \(K_b\), is a fundamental concept in chemistry, particularly for Bronsted-Lowry base reactions. It helps us understand the extent to which a base reacts with water to form its conjugate acid and hydroxide ions. When a base reacts with water, it partially dissociates to form these products. The equilibrium constant for this reaction is mathematically expressed by the ratio of the concentration of the products to the concentration of the reactants.
For instance, if we consider the reaction of pyridine (\(\mathrm{C_3 H_5 N}\)) with water, the balance looks like this:
\[\mathrm{C_3 H_5 N} + \mathrm{H_2 O} \rightleftharpoons \mathrm{C_3 H_5 NH^+} + \mathrm{OH^-}\] Here, the equilibrium constant expression, \(K_b\), for this reaction is:
\[ K_b = \frac{[\mathrm{C_3 H_5 NH^+}][\mathrm{OH^-}]}{[\mathrm{C_3 H_5 N}]} \]
This formula shows us that if we know the concentrations of the reactants and products at equilibrium, we can calculate the value of \(K_b\), indicating how strongly the base reacts with water. A large \(K_b\) value indicates a stronger base, while a smaller value suggests a weaker base. In this way, \(K_b\) serves as a vital tool for chemists to predict and quantify chemical behavior in aqueous solutions.

pyridine base reaction

Pyridine is an example of a Bronsted-Lowry base, recognized by its ability to accept a proton (H⁺). When pyridine (\(\mathrm{C_3 H_5 N}\)) is added to water, it engages in a chemical reaction where it accepts a proton from water, forming its conjugate acid, pyridinium (\(\mathrm{C_3 H_5 NH^+}\)), and hydroxide ions (OH⁻).
Here's the balanced equation for pyridine in water:
\[\mathrm{C_3 H_5 N} + \mathrm{H_2 O} \rightleftharpoons \mathrm{C_3 H_5 NH^+} + \mathrm{OH^-}\]
This reaction demonstrates how pyridine acts as a base by taking a proton from water, a typical Bronsted-Lowry behavior. When we look at the equilibrium constant (\(K_b\)) for this reaction, it reflects the extent to which this proton transfer occurs. The expression for the equilibrium constant, \(K_b\), for the pyridine reaction is:

\[K_b = \frac{[\mathrm{C_3 H_5 NH^+}][\mathrm{OH^-}]}{[\mathrm{C_3 H_5 N}]}\]
This equation tells us that the \(K_b\) value is dependent on the concentrations of pyridinium ions and hydroxide ions in ratio to the concentration of pyridine at equilibrium. If you know the concentrations, you can calculate \(K_b\), and thus understand how likely this reaction is to proceed.

carbonate ion reaction

Carbonate ion (\(\mathrm{CO_{3}^{2-}}\)) is another Bronsted-Lowry base, meaning it can accept a proton when reacting with water. In this reaction, the carbonate ion reacts with water to form hydrogen carbonate (\