Describe dynamic equilibrium and its shifts, and explain acids, bases, pH and neutralization

Learning goal: Describe dynamic equilibrium as two opposing processes occurring at the same rate, predict qualitatively how an equilibrium shifts when temperature, pressure or concentration is changed, identify acids by the formation of hydronium ion in water and bases by the formation of hydroxide ion, calculate pH from hydronium ion concentration and the reverse, and write and interpret neutralization reactions including the idea of a titration.

Reactions that appear to stop. All reactions are reversible to some degree. Many do not run until the reactants are used up; instead the amounts of reactants and products stop changing while some of each remain. The reaction has not stopped. As products build up, the reverse reaction, products turning back into reactants, speeds up, while the forward reaction slows as reactants are used. When the two rates become equal, every product molecule that forms is matched by one that turns back, and the concentrations hold steady. This is dynamic equilibrium: two opposing processes occurring at the same time at the same rate, with no apparent change. Dynamic is the important word. A student who pictures equilibrium as everything sitting still, or as equal amounts of reactants and products, has both ideas wrong: the molecules are reacting continuously in both directions, and the amounts are usually unequal. The diagram shows one reaction approaching equilibrium: the reactant falls from 1.00 to 0.40 and the product rises from 0 to 0.60 over the first six time units and both are flat afterwards, not because reaction has stopped but because the two rates are equal.

Disturbing an equilibrium. If a system at equilibrium is disturbed by a change in conditions, it responds by shifting toward a new equilibrium in the direction that reduces the effect of the change; this is Le Chatelier's principle. Concentration: adding a reactant makes the forward reaction faster for a while, so the system shifts toward products until a new balance is reached; removing a product does the same. Removing a product as it forms therefore forces the system to keep making it, which is how an otherwise unfavorable reaction can be driven to completion. Pressure, for gases only: increasing the pressure by reducing the volume shifts the equilibrium toward the side with fewer moles of gas, because fewer particles exert less pressure; if both sides have the same number of gas moles, pressure has no effect on the position. Temperature: raising the temperature shifts the equilibrium in the endothermic direction, the direction that absorbs the added energy; lowering it favors the exothermic direction. Temperature is the only one of the three that changes the balance point itself (in later courses, the equilibrium constant); concentration and pressure changes shift the mixture to a new composition that satisfies the same balance point. A catalyst speeds both directions equally and does not shift the position; it only shortens the time to reach equilibrium.

A worked model: making ammonia. The synthesis N₂(g) + 3H₂(g) ⇌ 2NH₃(g) is exothermic in the forward direction and reaches equilibrium with much nitrogen and hydrogen unreacted. To maximize ammonia: increase the pressure, since four moles of gas become two, so the forward direction reduces pressure; remove ammonia continuously by cooling it to a liquid, so the system keeps shifting forward; and use a low temperature, which favors the exothermic direction. But a low temperature makes the reaction slow, so in practice a moderate temperature and a catalyst are used, trading some yield for speed. Every prediction follows from asking which direction reduces the disturbance. The mathematics of equilibrium constants is reserved for later study.

Acids and hydronium. Physical Science introduced the properties of acids and bases and the pH scale; this course explains them by structure. An acid is a substance that produces hydronium ions, H₃O⁺, when dissolved in water. This happens when hydrogen is covalently bonded to an electronegative atom, so that the bond is very polar and the hydrogen can leave as a bare proton, H⁺, which immediately bonds to a water molecule's lone pair: HCl + H₂O → H₃O⁺ + Cl⁻. Writing H⁺(aq) is a common shorthand for H₃O⁺. Hydrochloric and nitric acids, and sulfuric acid for its first hydrogen, dissociate essentially completely in water and are called strong; acetic acid in vinegar dissociates only slightly and is weak. A base is a substance that produces hydroxide ions, OH⁻, in water: sodium hydroxide dissociates directly, NaOH → Na⁺ + OH⁻, and ammonia does it by taking a proton from water, NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. The Brønsted-Lowry and Lewis definitions are for later courses.

pH. Even pure water contains a tiny concentration of hydronium, 1.0 × 10⁻⁷ mol/L at 25 °C, balanced by the same concentration of hydroxide; the product of the two concentrations is always 1.0 × 10⁻¹⁴ at that temperature. Because concentrations range over many powers of ten, acidity is reported as pH = −log[H₃O⁺], where the brackets mean concentration in mol/L. A hydronium concentration of 1.0 × 10⁻³ mol/L gives pH 3.00; 1.0 × 10⁻⁷ gives 7.00, neutral; 1.0 × 10⁻¹¹ gives 11.00, basic. Each unit of pH is a factor of ten in concentration, so pH 2 is a hundred times more acidic than pH 4. Going the other way, [H₃O⁺] = 10⁻ᵖᴴ: a solution of pH 5.5 has [H₃O⁺] = 10⁻⁵·⁵ = 3.2 × 10⁻⁶ mol/L. For a strong acid such as 0.010 mol/L hydrochloric acid, which dissociates completely, [H₃O⁺] = 0.010 and pH = 2.00. Indicators are dyes whose color changes over a particular pH range; red cabbage juice runs from red in acid through purple to green and yellow in base, and a pH meter reads the value directly.

Neutralization and titration. An acid reacts with a hydroxide base to form a salt and water: HCl + NaOH → NaCl + H₂O, or H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, where the hydronium and hydroxide ions combine to make water and the remaining ions form the salt. Antacids work this way: baking soda neutralizes stomach acid, NaHCO₃ + HCl → NaCl + H₂O + CO₂, and magnesium hydroxide does so with Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O, one formula unit neutralizing two acid particles. Neutralization is studied quantitatively by titration: a solution of known concentration, the standard, is added from a burette to a measured volume of the unknown until the indicator changes color (the endpoint), with the indicator chosen so that the endpoint falls at the equivalence point, where the moles of acid and base match the equation. The volume used, the known concentration and the mole ratio then give the unknown concentration. Suppose 25.00 mL of hydrochloric acid needs 18.40 mL of 0.100 mol/L sodium hydroxide. Moles of NaOH: 0.100 × 0.01840 = 0.00184 mol. The ratio is 1 : 1, so moles of HCl = 0.00184 mol in 0.02500 L, a concentration of 0.0736 mol/L. This is why a standardized solution matters: without a known concentration on one side, the volume tells you nothing.

Acid rain and limestone. Lakes on limestone beds suffer less from acid rain than lakes on granite because calcium carbonate reacts with and neutralizes acid, CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂ in simplified form, while granite's silicate minerals neutralize acid only very slowly. The same reaction erodes marble statues. Roofing and building materials can be tested for acid resistance with dilute vinegar and a balance.

Where the rest of the standards is taught. From C.IM.3 this lesson teaches titration; mole ratios, yields, limiting reagents, molarity and dilution are in the stoichiometry lesson. Reaction types and rates from C.IM.1 are in the two earlier reaction lessons.

Investigation: a household pH survey and a neutralization. Materials: red cabbage indicator (chop cabbage, steep in hot water from a kettle handled by an adult, cool and strain), white vinegar, lemon juice, baking soda solution, soapy water, distilled water, clear cups, a dropper, goggles. Do not use bleach, drain cleaner, oven cleaner or any concentrated acid; they are hazardous and must not be mixed. Steps: add a few drops of indicator to each solution and record the color; arrange the cups from most acidic to most basic; then add baking soda solution dropwise to a cup of vinegar plus indicator, swirling, and count drops until the color reaches the neutral purple. Record colors and drop counts and repeat the neutralization twice. A result that supports the claim: vinegar and lemon juice give red-pink, baking soda and soap give green-blue, distilled water stays purple, and a definite number of drops turns the vinegar neutral, more drops for more vinegar. What the model cannot show: the indicator gives a color range, not a pH value, and drops are not calibrated volumes, so this is a titration in method but not in precision; it cannot show the hydronium ions themselves or the dynamic equilibrium of the weak acid.

Worked example 1 — recognize equilibrium from data. A sealed flask contains a colored gas mixture. The color deepens for the first minute and then stays constant for an hour. A student concludes the reaction has stopped. The better conclusion is that the observation is consistent with dynamic equilibrium: the constant color means the concentrations are steady, which is what equal forward and reverse rates would produce. Steady color alone does not prove it, because a reaction that had run to completion or simply stalled would look the same. Evidence for equilibrium comes from disturbing it: warming the flask changes the color to a new steady value and cooling it again brings the first color back, as a reversible equilibrium should; experiments with labelled atoms give the direct evidence that both directions continue.

Worked example 2 — predict shifts. For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), exothermic forward: (a) adding O₂ increases the collision rate of the forward reaction, so the system shifts toward SO₃; (b) compressing the mixture shifts toward the side with fewer gas moles, three on the left against two on the right, so toward SO₃; (c) raising the temperature favors the endothermic direction, which is the reverse, so the amount of SO₃ falls; (d) adding a catalyst shifts nothing but brings the system to equilibrium sooner.

Worked example 3 — pH both ways. (a) A soft drink has [H₃O⁺] = 2.5 × 10⁻⁴ mol/L: pH = −log(2.5 × 10⁻⁴) = 3.60. (b) Blood has pH 7.40: [H₃O⁺] = 10⁻⁷·⁴⁰ = 4.0 × 10⁻⁸ mol/L. (c) 0.0010 mol/L nitric acid, a strong acid, gives [H₃O⁺] = 0.0010 = 1.0 × 10⁻³, pH 3.00. (d) A solution with pH 11.00 has [H₃O⁺] = 1.0 × 10⁻¹¹ and, since the product of the two concentrations is 1.0 × 10⁻¹⁴, [OH⁻] = 1.0 × 10⁻³ mol/L.

Worked example 4 — a titration with a 2 : 1 ratio. 20.00 mL of sulfuric acid requires 30.00 mL of 0.150 mol/L sodium hydroxide. Moles NaOH = 0.150 × 0.03000 = 0.00450 mol. From H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O, one mole of acid needs two of base, so moles of acid = 0.00450 / 2 = 0.00225 mol. Concentration = 0.00225 / 0.02000 = 0.113 mol/L. Skipping the ratio step would double the answer; the equation is part of the calculation.

Representation task: an equilibrium sketch and a pH ladder. Sketch a graph of concentration against time for a reaction reaching equilibrium, label the point where the rates become equal, and beneath it draw arrows showing the shift for each of four disturbances to the ammonia synthesis. Then draw a pH ladder from 0 to 14, mark the hydronium concentration at each whole number in scientific notation, and place vinegar (about 3), pure water (7), blood (7.4) and a baking soda solution (about 8.5) on it.

Independent performance: pH survey and neutralization report. Carry out the cabbage indicator investigation with at least five safe household solutions and the drop-count neutralization in triplicate. Success criteria: a color table and an ordering from most acidic to most basic with reasons; an equation for the neutralization of acetic acid by sodium hydrogen carbonate; an explanation of why an indicator can order solutions but not give a pH; three pH calculations set by your teacher, in both directions, with the logarithm work shown; a titration calculation from data your teacher supplies that uses the mole ratio from the balanced equation; and a paragraph explaining what dynamic equilibrium means and one way the acetic acid in vinegar illustrates it.