Gas Laws
Boyle's Law (constant T, n)
P₁V₁ = P₂V₂
Pressure and volume are inversely related.
Charles's Law (constant P, n)
V₁/T₁ = V₂/T₂
Volume and temperature (in Kelvin!) are directly related.
Gay-Lussac's Law (constant V, n)
P₁/T₁ = P₂/T₂
Pressure and temperature are directly related.
Combined Gas Law
P₁V₁/T₁ = P₂V₂/T₂
Use when P, V, and T all change and n is constant.
Ideal Gas Law
PV = nRT
R = 0.08206 L·atm/(mol·K), or 8.314 J/(mol·K)
Avogadro's Law (constant T, P)
V₁/n₁ = V₂/n₂
Volume and moles are directly related.
Dalton's Law of Partial Pressures
Ptotal = P₁ + P₂ + P₃ + …
Each gas contributes pressure independently.
Graham's Law of Effusion
rate₁/rate₂ = √(M₂/M₁)
Lighter gases (smaller molar mass M) effuse faster.
Types of Reactions
pH, pOH & Acid-Base Formulas
pH
pH = −log[H⁺]
pOH
pOH = −log[OH⁻]
pH + pOH
pH + pOH = 14 (at 25°C)
Because Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹&sup4;
pKa
pKa = −log(Ka)
Smaller pKa → stronger acid.
Henderson–Hasselbalch (buffers)
pH = pKa + log([A⁻]/[HA])
[A⁻] = conjugate base, [HA] = weak acid.
Concentration from pH
[H⁺] = 10−pH
Solubility Rules
| Ion / rule | Solubility |
|---|---|
| Group 1 (Li⁺, Na⁺, K⁺…), NH₄⁺ | All salts soluble — no exceptions |
| NO₃⁻, ClO₄⁻, ClO₃⁻ | Always soluble |
| C₂H₃O₂⁻ (acetate) | Soluble, except with Ag⁺ (limited) |
| Cl⁻, Br⁻, I⁻ | Soluble, except with Ag⁺, Pb²⁺ |
| SO₄²⁻ | Soluble, except with Ba²⁺, Pb²⁺ (Ca²⁺, Ag⁺ only slightly) |
| OH⁻ | Insoluble, except Group 1 and Ba²⁺ (Ca²⁺ only slightly) |
| CO₃²⁻, PO₄³⁻ | Insoluble, except with Group 1 or NH₄⁺ |
| S²⁻ | Insoluble, except with Group 1, Group 2, or NH₄⁺ |
"Slightly soluble" salts (marked as exceptions with parentheses above) can go either way depending
on the concentration — check with your instructor's specific rule sheet if a problem hinges on one.
Common Polyatomic Ions
| Formula | Name |
|---|