Chemistry | Proton transfer reactions

Welcome to Reactivity 3.1: Proton Transfer Reactions!

Hello future chemists! This chapter dives deep into the world of acids and bases—the chemical opposites that govern everything from the taste of lemons to the pH of your blood. This is a foundational topic for understanding chemical mechanisms, as the transfer of a tiny particle—the proton—is responsible for some of the most common and vital reactions in chemistry.

Don't worry if you found earlier topics challenging. We will break down the concepts of proton donors and acceptors using clear analogies and step-by-step logic. Get ready to understand exactly what makes a reaction an acid-base reaction!

Section 1: The Brønsted-Lowry Model – The Mechanism of Proton Transfer

What is a Proton in Chemistry?

In the context of proton transfer reactions, the term proton refers specifically to the hydrogen ion, \(H^+\).

• A hydrogen atom (\(H\)) has one proton, one electron, and typically no neutrons.
• When it loses its single electron to become an ion (\(H^+\)), all that is left is the single proton.

Because this bare proton is extremely reactive, it never exists alone in aqueous solution. It immediately binds to a water molecule to form the hydronium ion, \(H_3O^+\).
(In most calculations, we use \([H^+]\) and \([H_3O^+]\) interchangeably to represent acidity.)

The Brønsted-Lowry Definitions (CORE CONCEPT)

The most useful definition for understanding the mechanism of acid-base reactions involves the movement of the proton. This is the Brønsted-Lowry Theory:

• Brønsted-Lowry Acid: A species that donates a proton (\(H^+\)).
  Think of the 'D' in Acid (Donor).
• Brønsted-Lowry Base: A species that accepts a proton (\(H^+\)).
  Bases typically have a lone pair of electrons available to form a bond with the incoming proton.

Analogy: The Proton Handoff

Imagine an acid and a base meeting. The proton (\(H^+\)) is a valuable package.
An Acid (the donor) is carrying the package and is ready to give it away.
A Base (the acceptor) has open arms (a lone pair) ready to receive the package.
The reaction is simply the transfer (the "handoff") of the \(H^+\) from the acid to the base.

Key Takeaway: All Brønsted-Lowry reactions involve the mechanism of proton transfer.

Section 2: Conjugate Acid-Base Pairs

When an acid donates its proton, it doesn't just disappear—it turns into something new. Similarly, when a base accepts a proton, it is transformed. This leads us to the concept of conjugate pairs.

Defining Conjugate Pairs

An acid-base reaction is always an equilibrium (even if the equilibrium strongly favors the products).

\[Acid_1 + Base_2 \rightleftharpoons Base_1 + Acid_2\]

• When Acid\(_1\) loses its proton, it forms Base\(_1\). Base\(_1\) is called the conjugate base of Acid\(_1\).
• When Base\(_2\) gains a proton, it forms Acid\(_2\). Acid\(_2\) is called the conjugate acid of Base\(_2\).

How to Identify Conjugate Pairs (Step-by-Step)

A conjugate acid-base pair differs by exactly one proton (\(H^+\)).

Example: Ammonia dissolving in water.

\[NH_3 (aq) + H_2O (l) \rightleftharpoons NH_4^+ (aq) + OH^- (aq)\]

1. Look at \(H_2O\): It lost a proton to become \(OH^-\). Therefore, \(H_2O\) is the acid, and \(OH^-\) is its conjugate base. (Pair 1)
2. Look at \(NH_3\): It gained a proton to become \(NH_4^+\). Therefore, \(NH_3\) is the base, and \(NH_4^+\) is its conjugate acid. (Pair 2)

Memory Aid: Charges

Adding \(H^+\) increases the charge by +1 (forming the conjugate acid).
Removing \(H^+\) decreases the charge by -1 (forming the conjugate base).

Example: The conjugate base of \(HSO_4^-\) is \(SO_4^{2-}\). (Removed \(H^+\), charge went from -1 to -2).

Did You Know? Amphiprotic Substances

Some substances, like water (\(H_2O\)), can act as both an acid and a base. These are called amphiprotic (or amphoteric) species.

• Water as an Acid: Donates \(H^+\) to a strong base like ammonia (\(NH_3\)).
• Water as a Base: Accepts \(H^+\) from a strong acid like hydrochloric acid (\(HCl\)).

Key Takeaway: Conjugate pairs are partners in a reaction that differ only by the presence or absence of one \(H^+\).

Section 3: Strength of Acids and Bases (SL & HL)

In chemistry, when we talk about strength, we are talking about the *extent* of the proton transfer—how willing an acid is to donate its proton, or how willing a base is to accept one. Do not confuse strength with concentration!

Strong Acids and Bases

A strong acid (or base) is one that ionizes or dissociates completely (100%) in solution. The reaction goes entirely to completion.

• Strong Acids: Examples include \(HCl\), \(HNO_3\), and \(H_2SO_4\).
  For \(HCl\): \[HCl (aq) \rightarrow H^+ (aq) + Cl^- (aq)\] Note the single arrow, indicating full dissociation.
• Strong Bases: Usually Group 1 metal hydroxides, like \(NaOH\) and \(KOH\).

Weak Acids and Bases

A weak acid (or base) is one that ionizes partially (usually less than 5%) in solution. An equilibrium is established.

• Weak Acids: Examples include ethanoic acid (\(CH_3COOH\)) and carbonic acid (\(H_2CO_3\)).
  For ethanoic acid: \[CH_3COOH (aq) \rightleftharpoons H^+ (aq) + CH_3COO^- (aq)\] Note the double arrow, indicating equilibrium.
• Weak Bases: Ammonia (\(NH_3\)) and most organic amines.

The Inverse Relationship of Conjugate Strength

There is a critical relationship between the strength of an acid and its conjugate base (and vice versa):

• If an acid is strong (great proton donor), its conjugate base must be weak (poor proton acceptor). Example: \(Cl^-\) is the conjugate base of \(HCl\). Since \(HCl\) gives up its proton easily, \(Cl^-\) has no desire to take it back.
• If an acid is weak (poor proton donor), its conjugate base must be strong (good proton acceptor). Example: The ethanoate ion (\(CH_3COO^-\)) is a relatively strong base because its parent acid, \(CH_3COOH\), held onto the proton tightly.

Common Mistake Alert!

Do not confuse Strength (how much ionizes, determined by chemical structure) with Concentration (the total amount of acid or base dissolved per volume). You can have a concentrated solution of a weak acid (like vinegar) or a dilute solution of a strong acid.

Key Takeaway: Strength refers to the extent of the proton transfer reaction. Strong means full transfer; weak means partial transfer (equilibrium).

Section 4: Quantifying Proton Transfer: \(K_a\), \(K_b\), and \(pH\) (SL & HL)

To compare the strengths of weak acids and bases, we use equilibrium constants that specifically measure the tendency of the proton transfer mechanism.

The Ion Product Constant of Water (\(K_w\))

Water itself is amphiprotic and undergoes a self-ionization reaction (or auto-ionization):
\[H_2O (l) + H_2O (l) \rightleftharpoons H_3O^+ (aq) + OH^- (aq)\]

The equilibrium constant for this reaction is \(K_w\), the ion product constant of water:
\[K_w = [H_3O^+][OH^-] \quad \text{or simply} \quad K_w = [H^+][OH^-]\]

• At \(25^{\circ}C\), \(K_w\) is always \(1.00 \times 10^{-14}\).
• In pure water, \([H^+] = [OH^-] = \sqrt{1.00 \times 10^{-14}} = 1.00 \times 10^{-7} \text{ mol } dm^{-3}\).

The pH Scale

The pH scale is a convenient way to express the concentration of hydrogen ions (the transferred protons) in a solution. It is a logarithmic scale (base 10).

• Definition of pH: \(pH = -\log_{10}[H^+]\)
• Definition of pOH: \(pOH = -\log_{10}[OH^-]\)

Since \(K_w = 1.00 \times 10^{-14}\), we can take the negative log of the whole expression:
\[p\text{K}_w = pH + pOH = 14.00 \quad \text{(at } 25^{\circ}C\text{)}\]

• Acidic: \(pH < 7\) (\([H^+] > [OH^-]\))
• Neutral: \(pH = 7\) (\([H^+] = [OH^-]\))
• Basic (Alkaline): \(pH > 7\) (\([H^+] < [OH^-]\))

HL: Acid and Base Dissociation Constants (\(K_a\) and \(K_b\))

For weak acids and bases, the extent of proton transfer is measured by specific equilibrium constants. A larger constant means a stronger acid/base.

1. Acid Dissociation Constant (\(K_a\)):
   For a weak acid (\(HA\)): \[HA (aq) + H_2O (l) \rightleftharpoons H_3O^+ (aq) + A^- (aq)\] \[K_a = \frac{[H_3O^+][A^-]}{[HA]}\]
2. Base Dissociation Constant (\(K_b\)):
   For a weak base (\(B\)): \[B (aq) + H_2O (l) \rightleftharpoons BH^+ (aq) + OH^- (aq)\] \[K_b = \frac{[BH^+][OH^-]}{[B]}\]

The pKa and pKb Scale

Just like pH, we use the negative logarithm of \(K_a\) and \(K_b\) for convenience:

• \(p\text{K}_a = -\log_{10}K_a\)
• \(p\text{K}_b = -\log_{10}K_b\)

Crucial Relationship (HL): A smaller \(p\text{K}_a\) value means a larger \(K_a\), which means a stronger acid.

Relating \(K_a\) and \(K_b\) for Conjugate Pairs (HL)

If you multiply the \(K_a\) of a weak acid by the \(K_b\) of its conjugate base, you get \(K_w\):
\[K_a \times K_b = K_w = 1.00 \times 10^{-14}\]
Taking the negative log of this gives the simpler relationship:
\[p\text{K}_a + p\text{K}_b = p\text{K}_w = 14.00\]

This mathematical relationship proves the inverse strength relationship we discussed earlier. If \(K_a\) is large (strong acid), \(K_b\) must be small (weak conjugate base) to maintain the product \(K_w\).