Acid-base equilibria explain how acids and bases partially or completely ionize in water and how their concentrations are related at equilibrium. This cheat sheet helps students organize the key constants, formulas, and calculation steps used in Grade 11-12 chemistry. It is especially useful for solving pH, pOH, weak acid, weak base, and conjugate acid-base problems.
The goal is to connect equilibrium ideas with fast, accurate calculations.
The most important relationships are for weak acids, for weak bases, and for water. At , , so . Strong acids and bases are treated as fully dissociated, while weak acids and bases require equilibrium expressions.
Conjugate pairs are linked by , which helps compare acid and base strength.
Key Facts
- For water at , .
- The pH of a solution is calculated with , where is measured in .
- The pOH of a solution is calculated with , where is measured in .
- At , pH and pOH are related by .
- For a weak acid , the acid dissociation constant is .
- For a weak base , the base dissociation constant is .
- For a conjugate acid-base pair at , .
- A small or means the acid or base ionizes only slightly, while a larger value means stronger ionization.
Vocabulary
- Acid
- An acid is a substance that donates or increases in water.
- Base
- A base is a substance that accepts or increases in water.
- Conjugate acid-base pair
- A conjugate acid-base pair consists of two species that differ by exactly one .
- Dissociation constant
- A dissociation constant such as or measures the extent to which an acid or base ionizes at equilibrium.
- pH
- pH is a logarithmic measure of acidity defined by .
- Equilibrium expression
- An equilibrium expression relates product and reactant concentrations at equilibrium using coefficients as exponents.
Common Mistakes to Avoid
- Using initial concentrations directly in or expressions for weak acids or bases is wrong because the expression must use equilibrium concentrations.
- Forgetting that strong acids and strong bases fully dissociate leads to unnecessary ICE tables and incorrect pH values.
- Mixing up pH and pOH gives the wrong acidity because and measure different ions.
- Applying at temperatures other than without checking is wrong because changes with temperature.
- Assuming a larger means a stronger base is wrong because a larger means a stronger acid and a weaker conjugate base.
Practice Questions
- 1 Calculate the pH of a solution with .
- 2 Calculate and pH for a solution with at .
- 3 A weak acid has . Find for its conjugate base at .
- 4 Explain why a weak acid can have a low pH even though it does not fully dissociate.
Understanding Acid-Base Equilibria, Ka Kb Kw, pH Calculations
Equilibrium is dynamic, not frozen. In a weak acid solution, acid particles keep transferring protons to water while the reverse reaction rebuilds acid particles. The forward and reverse changes happen at the same rate once equilibrium is reached.
That is why the concentrations stay steady even though particles are still reacting. A larger Ka means the products are favored at equilibrium, so more hydronium ions form. This gives a lower pH at the same starting concentration.
Strength and concentration are different ideas. A dilute strong acid can have a higher pH than a concentrated weak acid.
The same reasoning applies to bases. A weak base takes a proton from water, producing hydroxide ions and its conjugate acid. When comparing two bases with equal concentrations, the one with the larger Kb usually produces more hydroxide and has the higher pH.
Conjugate partners have opposite strengths. If an acid gives up protons readily, its conjugate base has little tendency to take a proton back. If an acid is weak, its conjugate base is relatively stronger.
This pattern helps students predict which direction an acid-base reaction will favor. Proton transfer tends to move from the stronger acid toward the weaker acid.
Many calculation errors come from mixing up starting amounts and equilibrium amounts. An ICE table keeps these separate. ICE means initial, change, and equilibrium.
First write a balanced reaction in water. Next enter the known initial concentration. Use a variable for the amount that reacts.
For a weak acid, hydronium and conjugate base each increase by that amount, while the acid decreases by that amount. Put the equilibrium values into the Ka expression, then solve for the variable. The common shortcut of ignoring the change in the denominator is only valid when the change is very small compared with the initial concentration.
Check this afterward using the five percent rule. If the change is more than five percent, solve the full quadratic equation instead.
Logarithms make the pH scale compact, but they require careful handling. The number before the decimal point in pH comes from the exponent of the hydronium concentration. The decimal digits of pH are linked to the significant figures in that concentration.
For example, a hydronium concentration of one point zero times ten to the minus three gives a pH of three point zero zero. A change of one pH unit means a factor of ten change in hydronium concentration. Students meet this in soil testing, swimming pool care, food preservation, antacid products, blood chemistry, and water treatment.
Temperature matters because the ionization of water changes as temperature changes. The familiar neutral value of seven applies specifically near twenty five degrees Celsius. Neutral always means equal hydronium and hydroxide concentrations, even when the numerical pH is not exactly seven.