Phases and Equilibrium

Solids and pure liquids do not appear in the equilibrium expression. This is because the moles of a pure solid or liquid per liter of that solid or liquid is really equivalent to the density, which is constant.

For example, in the chemical reaction:

CCl₄ (g) C (s) + 2 Cl₂ (g)

The equilibrium expression would be:

Where does this come from?

Start with the usual products over reactants:

However, [C] is the concentration of carbon (in moles per liter) in solid carbon, which is just the density (a constant) divided by the molar mass (also a constant). A constant divided by a constant is just another constant, which we’ll call “K_carbon”. This means:

Now, applying the “a constant divided by a constant is just another constant” idea again, we simply adjust K_eq so that the new K_eq is the old K_eq divided by K_carbon. Therefore, the equilibrium becomes:

Net Ionic Equations

net ionic equation: a shorthand version of a chemical equation that shows only the ions that are changed by the reaction.

For example, in the reaction:

2 AgNO₃ (aq) + Na₂SO₄ (aq) à Ag₂SO₄ (s) + 2 NaNO₃ (aq)

The AgNO₃ starts out dissolved into Ag⁺ and NO₃⁻ ions, and the Na₂SO₄ is dissolved into Na⁺ and SO₄²⁻ ions. The Ag⁺ and SO₄²⁻ ions combine to form the precipitate Ag₂SO₄. The Na⁺ and NO₃⁻ ions remain in solution.

The net ionic equation is therefore:

2 Ag⁺ (aq) + SO₄²⁻ (aq) à Ag₂SO₄ (s)

Spectator ions: ions that are not directly involved in the reaction. In the above equation, Na⁺ and NO₃⁻ are spectator ions.

Solubility Product Constant (K_sp)

When we learned solubility rules, we defined “insoluble” to mean that less than 3 g of solute is able dissolve in 100 g of H₂O. (Some sources say less than 0.1 mole of solute per liter of solution.)

Actually, some amount of every ionic compound can dissolve in water, though this can be a miniscule amount. For these “insoluble” compounds, when the compound is placed in water, the precipitate is in equilibrium with the solute.

The solubility product constant (K_sp) is an equilibrium constant for the process of the ionic solid dissociating (splitting up) and dissolving in water at 25°C.

For example, the chemical equation for the dissolving of Ag₂SO₄ is:

Ag₂SO₄ (s)2 Ag⁺ (aq) + SO₄²⁻ (aq)

As we saw earlier, solids do not appear in equilibrium constants, so the denominator is omitted. This gives the following equation:

K_sp = [Ag⁺]² [SO₄²⁻]

For Ag₂SO₄, K_sp = 1.2 × 10⁻⁵ = [Ag⁺]² [SO₄²⁻]

We can solve the above equation, because we know that one Ag₂SO₄ molecule dissolves into 2 Ag⁺ + 1 SO₄²⁻. If we let [SO₄²⁻] = x, then [Ag⁺] = 2x, and:

K_sp = [Ag⁺]² [SO₄²⁻] = (2x)² (x) = 4x³

Therefore:

In other words, a 0.0144 M solution of Ag₂SO₄ would be saturated (at 25°C).