Question

Write balanced equations and \(K_{b}\) expressions for these Bronsted-Lowry bases in water: (a) Guanidine, \(\left(\mathrm{H}_{2} \mathrm{~N}\right)_{2} \mathrm{C}=\mathrm{NH}\) (the double-bonded \(\mathrm{N}\) is more basic) (b) Acetylide ion, \(\mathrm{HC} \equiv \mathrm{C}^{-}\)

Short answer

Guanidine: \( \text{(H}_2 \text{N})_2 \text{C}=\text{NH} + \text{H}_2\text{O} \rightleftharpoons \text{(H}_2 \text{N})_2 \text{C}=\text{NH}_2^+ + \text{OH}^- \ \(K_b = \frac{{[\text{(H}_2 \text{N})_2 \text{C}=\text{NH}_2^+][\text{OH}^-]}}{{[\text{(H}_2 \text{N})_2 \text{C}=\text{NH}]}} \Acetylide ion: \( \text{HC} \text{C}^- + \text{H}_2\text{O} \rightleftharpoons \text{HC} \text{CH} + \text{OH}^- \ \(K_b = \frac{{[\text{HC} \text{CH}][\text{OH}^-]}}{{[\text{HC} \text{C}^-]}} \)

Step-by-step solution

- Identify each Base and its Reaction with Water

Identify the Bronsted-Lowry base and write its equation of reaction with water. Bronsted-Lowry bases accept protons.

- Write the Balanced Equation for Guanidine

Guanidine, \(\text{(H}_2 \text{N})_2 \text{C}=\text{NH}\), reacts with water. The double-bonded nitrogen (N) will accept a proton from water. The balanced equation is: \[ \text{(H}_2 \text{N})_2 \text{C}=\text{NH} + \text{H}_2\text{O} \rightleftharpoons \text{(H}_2 \text{N})_2 \text{C}=\text{NH}_2^+ + \text{OH}^- \]

- Write the \(K_b\) Expression for Guanidine

Write the expression for the base dissociation constant \(K_b\) for the guanidine equilibrium: \[ K_b = \frac{{[\text{(H}_2 \text{N})_2 \text{C}=\text{NH}_2^+][\text{OH}^-]}}{{[\text{(H}_2 \text{N})_2 \text{C}=\text{NH}]}} \]

- Write the Balanced Equation for Acetylide Ion

Acetylide ion, \(\text{HC} \text{C}^-\), reacts with water. The \(\text{C}^-\text{C}\) will accept a proton from water. The balanced equation is: \[ \text{HC} \text{C}^- + \text{H}_2\text{O} \rightleftharpoons \text{HC} \text{CH} + \text{OH}^- \]

- Write the \(K_b\) Expression for Acetylide Ion

Write the expression for the base dissociation constant \(K_b\) for the acetylide ion equilibrium: \[ K_b = \frac{{[\text{HC} \text{CH}][\text{OH}^-]}}{{[\text{HC} \text{C}^-]}} \]

Key concepts

base dissociation constant

The base dissociation constant, represented as \(K_b\), measures the strength of a base in water. It quantifies how well a base accepts protons from water, forming its conjugate acid and hydroxide ions \(OH^-\). For example, let's consider the Bronsted-Lowry base guanidine \((H_2N)_2C=NH\). When guanidine reacts with water, it accepts a proton from the water molecule and forms \(\text{(H}_2 \text{N})_2 \text{C}=\text{NH}_2 ^+ \) and \( \text{OH}^- \):
\[ (H_2N)_2C=NH + H_2O \rightleftharpoons (H_2N)_2C=NH_2^+ + OH^- \]
The expression for its base dissociation constant \(K_b\) can be written as:
\[ K_b = \frac{{[(H_2N)_2C=NH_2^+][OH^-]}}{{[(H_2N)_2C=NH]}} \]
The larger the value of \(K_b\), the stronger the base, meaning it more readily accepts protons from water.

balanced chemical equations

Balanced chemical equations are essential in representing chemical reactions accurately, showing the relationship between reactants and products. A balanced equation has the same number of atoms of each element on both sides of the reaction. For the guanidine example:
\[ (H_2N)_2C=NH + H_2O \rightleftharpoons (H_2N)_2C=NH_2^+ + OH^- \]
This equation is balanced as it has the following atoms on both sides:

• 2 Nitrogen (N) atoms
• 6 Hydrogen (H) atoms
• 1 Oxygen (O) atom

Similarly, for the acetylide ion (HCC^-), the balanced chemical reaction with water is:
\[ HC \equiv C^- + H_2O \rightleftharpoons HC \equiv CH + OH^- \]
In this reaction, we must ensure the following atoms are balanced on both sides:

• 2 Carbon (C) atoms
• 2 Hydrogen (H) atoms
• 1 Oxygen (O) atom

chemical equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products over time. In the context of Bronsted-Lowry bases, the reaction between the base and water establishes an equilibrium. For instance, with guanidine:
\[ (H_2N)_2C=NH + H_2O \rightleftharpoons (H_2N)_2C=NH_2^+ + OH^- \]
At equilibrium, the concentrations of guanidine, water, \( (H_2N)_2C=NH_2^+ \), and \(OH^- \) remain constant. The equilibrium constant \(K_b\) for this reaction quantifies the ratio of product concentrations to reactant concentrations, giving insights into the extent of the reaction.
For the acetylide ion:
\[ HC \equiv C^- + H_2O \rightleftharpoons HC \equiv CH + OH^- \]
At equilibrium, the reaction balances the forward conversion of \( HC \equiv C^- \) to \( HC \equiv CH \) and \(OH^- \) with the reverse reaction. Understanding equilibrium helps predict how changing conditions, like concentration or temperature, affect the reaction's position.