Chapter 6: Problem 45
Write the \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) reactions of \(\mathrm{NaHCO}_{3}\).
Short Answer
Expert verified
Ka: \(\text{HCO}_3^-\) dissociates to \(\text{CO}_3^{2-}\); Kb: \(\text{HCO}_3^-\) to \(\text{H}_2\text{CO}_3\).
Step by step solution
01
Identify the Components of NaHCO3
The compound NaHCO3 is made up of the sodium cation (Na+) and bicarbonate anion (HCO3-). Since Na+ is a spectator ion, we focus on the HCO3- for acid and base dissociation.
02
Determine the Acid Reaction
The bicarbonate ion (HCO3-) can donate a proton (H+) to become the carbonate ion (CO3^2-). This gives:\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{CO}_3^{2-} + \text{H}_3\text{O}^+\]This is the acid dissociation reaction, and its equilibrium constant is denoted as \(K_a\).
03
Determine the Base Reaction
The bicarbonate ion (HCO3-) can also accept a proton to become carbonic acid (H2CO3). This gives:\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 + \text{OH}^-\]This is the base dissociation reaction, and its equilibrium constant is denoted as \(K_b\).
04
Write the Formulas for Ka and Kb
For the acid reaction \(K_a\), the equilibrium constant expression is:\[K_a = \frac{[\text{CO}_3^{2-}][\text{H}_3\text{O}^+]}{[\text{HCO}_3^-]}\]For the base reaction \(K_b\), the equilibrium constant expression is:\[K_b = \frac{[\text{H}_2\text{CO}_3][\text{OH}^-]}{[\text{HCO}_3^-]}\]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Bicarbonate Ion
The bicarbonate ion, represented as \( \text{HCO}_3^- \), plays a crucial role in maintaining the acid-base balance in various systems, particularly in biological organisms and natural waters. It serves both as an acid and as a base, which can seem slightly confusing at first.
The bicarbonate ion originates from carbonic acid (\(\text{H}_2\text{CO}_3 \)), a weak acid that partially dissociates in water. This dual nature allows \( \text{HCO}_3^- \) to either donate or accept protons (\( \text{H}^+ \)).
The bicarbonate ion originates from carbonic acid (\(\text{H}_2\text{CO}_3 \)), a weak acid that partially dissociates in water. This dual nature allows \( \text{HCO}_3^- \) to either donate or accept protons (\( \text{H}^+ \)).
- As an acid: It donates a hydrogen ion to become \( \text{CO}_3^{2-} \) (carbonate ion).
- As a base: It accepts a hydrogen ion to become \(\text{H}_2\text{CO}_3 \) (carbonic acid).
Equilibrium Constants
Equilibrium constants are important because they quantify the extent to which a reaction proceeds to completion. There are different types of equilibrium constants, but in acid-base chemistry, \( K_a \) and \( K_b \) are the most relevant.
For the reactions involving \( \text{HCO}_3^- \):
For the reactions involving \( \text{HCO}_3^- \):
- \( K_a \) represents the equilibrium constant for the acid dissociation reaction, and it indicates how well \( \text{HCO}_3^- \) donates protons to form \( \text{CO}_3^{2-} \) and \( \text{H}_3\text{O}^+ \).
- \( K_b \) represents the equilibrium constant for the base dissociation reaction, showing how efficiently \( \text{HCO}_3^- \) accepts protons to form \( \text{H}_2\text{CO}_3 \) and \( \text{OH}^- \).
Acid Dissociation
Acid dissociation describes the process where an acid donates a proton to another molecule, usually water, resulting in the formation of a conjugate base. For \( \text{HCO}_3^- \), its acid dissociation reaction can be described as follows:
\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{CO}_3^{2-} + \text{H}_3\text{O}^+\]
This reaction shows \( \text{HCO}_3^- \) donating a proton to water to create \( \text{CO}_3^{2-} \) and \( \text{H}_3\text{O}^+ \). The equilibrium constant of this reaction, \( K_a \), measures the tendency of the bicarbonate ion to dissociate into its ionic components.
Understanding \( K_a \) helps in predicting how \( \text{HCO}_3^- \) behaves in different environments, influencing reactions' pH levels and the system's overall acidity. The larger \( K_a \), the more \( \text{HCO}_3^- \) dissociates, indicating a stronger acid nature.
\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{CO}_3^{2-} + \text{H}_3\text{O}^+\]
This reaction shows \( \text{HCO}_3^- \) donating a proton to water to create \( \text{CO}_3^{2-} \) and \( \text{H}_3\text{O}^+ \). The equilibrium constant of this reaction, \( K_a \), measures the tendency of the bicarbonate ion to dissociate into its ionic components.
Understanding \( K_a \) helps in predicting how \( \text{HCO}_3^- \) behaves in different environments, influencing reactions' pH levels and the system's overall acidity. The larger \( K_a \), the more \( \text{HCO}_3^- \) dissociates, indicating a stronger acid nature.
Base Dissociation
Base dissociation refers to the process where a base accepts a proton, forming its conjugate acid. In the case of the bicarbonate ion, its base dissociation can be expressed as:
\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 + \text{OH}^-\]
Here, \( \text{HCO}_3^- \) accepts a proton from water, producing carbonic acid (\(\text{H}_2\text{CO}_3\)) and hydroxide ions (\(\text{OH}^-\)). The equilibrium constant for this reaction, \( K_b \), helps indicate the basic strength of \( \text{HCO}_3^- \).
A higher \( K_b \) value suggests that \( \text{HCO}_3^- \) is more efficient at acting as a base. This dissociation is vital for understanding buffering in solutions where bicarbonate ions play a role, maintaining an optimal and stable pH by balancing acidic and basic shifts.
\[\text{HCO}_3^- + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 + \text{OH}^-\]
Here, \( \text{HCO}_3^- \) accepts a proton from water, producing carbonic acid (\(\text{H}_2\text{CO}_3\)) and hydroxide ions (\(\text{OH}^-\)). The equilibrium constant for this reaction, \( K_b \), helps indicate the basic strength of \( \text{HCO}_3^- \).
A higher \( K_b \) value suggests that \( \text{HCO}_3^- \) is more efficient at acting as a base. This dissociation is vital for understanding buffering in solutions where bicarbonate ions play a role, maintaining an optimal and stable pH by balancing acidic and basic shifts.