Strong vs weak acids - bases; degree of dissociation α: Foundations

This page assumes you have seen nothing. Before you can read the parent note Strong vs Weak Acids/Bases, you must own every symbol it uses. We build each one from a picture, in an order where each rests on the one before.

1. A molecule and what "dissolving" means

When we drop a substance into water, we imagine two boxes: the "whole molecule" box and the "broken-into-ions" box. Every unit of the substance sits in one box or the other. Look at the figure — the left box holds intact molecules, the right box holds the charged pieces they split into.

Figure — Strong vs weak acids - bases; degree of dissociation α

The whole story of this chapter is: how full is each box?

2. The acid molecule: HA

Why one letter for "everything else"? Because the chapter's logic is identical whether $A$ is $Cl$ (making $HCl$ ) or $CH_{3} COO$ (making acetic acid). Using $A$ lets us reason once and apply everywhere.

The little raised symbols are charges:

$H^{+}$ ::: a hydrogen that has lost its electron, so it is positively charged — this is "acidity" itself.
$A^{-}$ ::: the leftover part that kept the electron, so it is negatively charged.

Charges always balance: one $+$ and one $-$ come from one neutral $HA$ .

3. The splitting arrow — and why there are TWO kinds

The parent note uses two different arrows. They mean completely different things, so we learn them by picture.

Look at the two panels in the figure. The one-way arrow (left) drains the molecule box; the double harpoon (right) reaches a steady split where the two boxes stop changing even though molecules are still shuttling back and forth. That steady, unchanging split is what the word equilibrium means.

4. Concentration — the symbol $c$ and the brackets $[]$

The unit is molar, written $M$ , meaning "moles per litre." A mole is just a fixed counting number of particles (like "dozen" but huge); you do not need its exact value here, only that $c$ counts crowding.

So $c$ is what you poured in; the bracket quantities are what you find floating after the split settles. They are different numbers unless dissociation is total.

5. The star of the show: degree of dissociation $α$

Now we can define the symbol the whole topic is named after.

Because it is a fraction, $α$ always lives between $0$ and $1$ :

$α = 0$ ::: nothing split — everything stayed as $HA$ .
$α = 1$ ::: everything split — the whole-molecule box is empty (this is a strong acid).
$α = 0.0134$ ::: only $1.34%$ split (a typical weak acid).

The figure is a single bar coloured to show the split at three values of $α$ . Read the red portion as "broke apart" and the black portion as "stayed whole." That red fraction is $α$ .

6. The ICE ledger — counting the boxes

Before we can talk about the constant $K_{a}$ , we need one bookkeeping picture the parent leans on heavily: the ICE table.

Read the figure column by column: each column is one species ( $HA$ , $H^{+}$ , $A^{-}$ ), each row is a moment in time. Follow the red Change row — every $- c α$ that leaves $HA$ shows up as a $+ c α$ under each ion, because splitting one molecule makes exactly one of each ion.

The bottom (Equilibrium) row is what you plug into every formula from here on.

7. The equilibrium constant $K_{a}$ — WHY that ratio is fixed

The parent uses $K_{a}$ to predict $α$ before you measure anything. But the parent just states the ratio — here we see why nature forces it to be constant.

That is why this exact ratio always lands on the same value no matter how much you poured in — it is the acid's fingerprint. A big $K_{a}$ (top-heavy) means the pieces are favoured → strong acid. A tiny $K_{a}$ means the whole molecule is favoured → weak acid. The subscript $a$ just labels it as an acid constant (there is a matching $K_{b}$ for bases). You will see this ratio derived and used fully in Acid-base equilibria and Ka, Kb.

molecule and ion → the acid $HA$ → splitting arrows (one-way vs equilibrium).
the acid $HA$ → concentration $c$ and brackets.
splitting arrows + concentration → degree of dissociation $α$ .
$α$ → ICE ledger → $K_{a}$ (from equal forward/backward rates); concentration also feeds $K_{a}$ .
$α$ → $[H^{+}]$ crowding → pH (base-10 log) → then $OH^{-}$ /pOH for bases, and the water self-ionization floor.
$K_{a}$ , pH, pOH, the water floor, and $α$ all feed the parent topic strong vs weak and $α$ .

Equipment checklist

Test yourself: cover the right side and answer before revealing.

What does

HA

stand for, and what are its two pieces?

A general acid;

H^{+}

(the leaving hydrogen ion) and

A^{-}

(the leftover part that keeps the electron).

What is the difference between

\to

and

⇌

\to

means the reaction runs to completion (box empties);

⇌

means equilibrium, both boxes stay partly full because breaking and re-joining happen at equal speed.

In plain words, what is

α

, and what range can it take?

The fraction of poured-in molecules that dissociated; it lies between

0

(none split) and

1

(all split).

How do you get

[H^{+}]

from

c_{0}

and

α

[H^{+}] = c_{0} α

, since each split molecule gives one

H^{+}

What does the Change row of the ICE table say for

HA

H^{+}

A^{-}

- c α

for

HA

, and

+ c α

for each of

H^{+}

and

A^{-}

Why is the ratio

\frac{[ H ^{+} ] [ A ^{-} ]}{[ HA ]}

a fixed number?

At equilibrium the forward rate (

\propto [HA]

) equals the backward rate (

\propto [H^{+}] [A^{-}]

), so the ratio equals the fixed dial ratio

k_{f} / k_{b} = K_{a}

What base does

lo g

use here, and what is pH?

Base 10 (

lo g_{10}

);

pH = - lo g_{10} [H^{+}]

, low pH meaning crowded with

H^{+}

Define

OH^{-}

and pOH.

OH^{-}

is the hydroxide ion a base releases;

pOH = - lo g_{10} [OH^{-}]

, low pOH meaning strongly basic.

Why can't an acid's

[H^{+}]

ever fall below about

1 0^{- 7} M

Water self-ionizes (

H_{2} O ⇌ H^{+} + OH^{-}

), supplying a

1 0^{- 7} M

background of

H^{+}

that no dilute acid can go beneath.

Foundations — Strong vs weak acids - bases; degree of dissociation α

1. A molecule and what "dissolving" means

2. The acid molecule: HA

3. The splitting arrow — and why there are TWO kinds

4. Concentration — the symbol $c$ and the brackets $[]$

5. The star of the show: degree of dissociation $α$

6. The ICE ledger — counting the boxes

7. The equilibrium constant $K_{a}$ — WHY that ratio is fixed

8. The measuring stick for acidity: pH and the base-10 $lo g$

9. The mirror for bases: $OH^{-}$ and pOH

10. The always-present background: water self-ionizes

Prerequisite map

Equipment checklist