Foundations — Common ion effect

#chemistry/equilibrium #solubility #foundations

This page assumes you know nothing. Before you can read the parent note, every letter, arrow, and squiggle it uses must mean something concrete to you. We build them one at a time, each on top of the last. Nothing is used before it is drawn.

Symbol 0 — the substances: "salt", "sparingly soluble", "(s)" and "(aq)"

The picture. Look at the left half of the figure: a solid block of ions. On the right half: those same ions torn loose and drifting in water, each hugged by little water molecules.

Why the topic needs it. The whole story is about a solid (s) turning into free ions (aq) and back. If you can't tell those two states apart, the arrows later mean nothing.

Symbol 1 — square brackets $[]$ : concentration

The picture. Imagine a fixed 1-litre box. Concentration = how many red dots you can count inside that box. More dots crammed in = larger $[\text{X}]$.

Symbol 2 — the superscripts ${\text{Ag}}^{+}$, ${\text{Cl}}^{-}$, ${\text{Pb}}^{2+}$ : charge

The picture. A $+$ atom and a $-$ atom pull toward each other (opposite charges attract) — that pull is what glued them into the solid grid, and what re-forms solid when they meet again in water.

Why the topic needs it. A "common ion" is defined by charge and identity. ${\text{Cl}}^{-}$ from salt A is the same particle as ${\text{Cl}}^{-}$ from salt B — water cannot tell them apart. That "sameness" is the whole trick.

Symbol 3 — the double arrow $\rightleftharpoons$ : equilibrium

The picture. Two doors between a "solid room" and a "dissolved room". People walk out the top door and back in the bottom door. When equally many go each way per second, the crowd in each room looks frozen — even though everyone is still moving.

$\text{AgCl(s)}\rightleftharpoons {\text{Ag}}^{+}\text{(aq)}+{\text{Cl}}^{-}\text{(aq)}$

Read this now as a sentence: "Solid silver chloride is, at the same rate, breaking into free ${\text{Ag}}^{+}$ and free ${\text{Cl}}^{-}$, and re-forming from them."

Symbol 4 — solubility $s$

The picture. The size of the "dissolved room" crowd once the doors balance. A big $s$ = lots dissolved; a tiny $s$ (sparingly soluble) = almost empty dissolved room.

Link to Symbol 1. For $\text{AgCl}$, every solid unit that dissolves releases exactly one ${\text{Ag}}^{+}$ and one ${\text{Cl}}^{-}$. So if $s$ mol/L dissolved: $[{\text{Ag}}^{+}]=s[{\text{Cl}}^{-}]=s$ Solubility ($s$, a property of the solid) and concentration ($[]$, a property of an ion in the water) are linked by the recipe of the formula.

Symbol 5 — stoichiometric numbers (the "2" in $2{\text{Cl}}^{-}$)

The picture. Break one ${\text{PbCl}}_2$ brick and two chloride marbles roll out, one lead marble. So if $s$ bricks dissolve: $[{\text{Pb}}^{2+}]=s[{\text{Cl}}^{-}]=2s$

Symbol 6 — the equilibrium constant $K_{sp}$

Why "product" and why those powers? This is the equilibrium-constant rule from Solubility Product (Ksp): multiply the ion crowdedness values, and each ion appears as many times as it is produced — two chlorides means $[{\text{Cl}}^{-}]$ times itself, i.e. $[{\text{Cl}}^{-}{]}^2$.

Where did the solid go? The solid $\text{AgCl(s)}$ has a constant "purity" (activity $=1$), so it contributes a factor of 1 and never appears in $K_{sp}$. Only the dissolved ions do.

Symbol 7 — the square root  ​ and the primed $s^{\prime }$

Symbol 8 — the "much-less-than" sign $\ll$ and $\approx$

How these feed together

Every arrow is a "you need this before that". Trace any path top to bottom and you have earned the right to read the parent derivation.

Equipment checklist

Cover the right side and answer aloud; reveal to check.

Connections

• Le Chatelier's Principle: the "why" behind the backward shift.
• Solubility Product (Ksp): where the $K_{sp}$ product rule comes from.
• Ionic Equilibrium: the broader world of simultaneous ion balances.
• Buffer Solutions and Qualitative Analysis: places this foundation gets used.
• Hinglish version →