13.2 Solutions, Acids, and Bases

13.2 Solutions, Acids, and Bases

Within CEM NMAT Chemistry (30 items, ~30 minutes), solutions, acids/bases, and equilibrium form a tightly linked cluster: concentration math feeds pH calculations, and weak-acid/base behavior is equilibrium applied to protons. Depth stays introductory college premed — expect clean strong-acid pH items, dilution algebra, and conceptual buffers/Le Chatelier rather than multi-step polyprotic ICE tables.

Quick frame: Molarity turns mass into “how many moles per liter.” pH is a log scale of [H₃O⁺]. Equilibrium is a two-way street; stress moves the position, not the meaning of the equilibrium constant’s temperature dependence.

Concentration units

Molarity (M):

[ M = \frac{n_{\mathrm{solute}}}{V_{\mathrm{solution}}(\mathrm{L})} ]

Use liters of solution, not liters of pure solvent (unless dilute approximation is justified). Common related ideas: molality (mol solute / kg solvent) appears in colligative formulas; mass percent and volume percent are everyday lab labels.

Percent by mass (w/w):

[ %,\mathrm{w/w} = \frac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}} \times 100% ]

Worked example — molarity. Dissolve 5.85 g NaCl ((M = 58.5,\mathrm{g/mol})) in water to make 0.500 L solution.

• (n = 5.85/58.5 = 0.100,\mathrm{mol})
• (M = 0.100/0.500 = 0.200,\mathrm{M})

Worked example — mass percent. 10.0 g sugar in 90.0 g water → solution mass 100.0 g → % w/w = 10.0%.

Dilution: (M_1 V_1 = M_2 V_2)

Adding solvent keeps moles of solute constant: (n = M_1 V_1 = M_2 V_2). Volumes must use the same unit throughout (mL with mL is fine if consistent).

Worked example — dilution. How much 12.0 M HCl is needed to prepare 250 mL of 0.500 M HCl?

• (V_1 = M_2 V_2 / M_1 = (0.500)(250)/12.0 = 10.4,\mathrm{mL}) of concentrated stock, then dilute to 250 mL total.

Worked example — after dilution. 25.0 mL of 2.00 M NaOH diluted to 100.0 mL:

• (M_2 = M_1 V_1 / V_2 = (2.00)(25.0)/100.0 = 0.500,\mathrm{M}).

Safety note (conceptual): add acid to water carefully in the lab; NMAT cares more about the mole balance than glassware choreography, but “dilution reduces concentration proportionally to volume increase” is the tested idea.

Colligative properties (conceptual)

Colligative properties depend on the number of solute particles per amount of solvent, not chemical identity (ideal dilute limit):

1. Vapor-pressure lowering (Raoult’s law idea): nonvolatile solute lowers solvent vapor pressure.
2. Boiling-point elevation: solution boils higher than pure solvent ((\Delta T_b = i K_b m)).
3. Freezing-point depression: solution freezes lower ((\Delta T_f = i K_f m)) — antifreeze and road salt themes.
4. Osmotic pressure: (\Pi = i MRT) conceptually — water flows toward higher solute concentration across a semipermeable membrane; critical for cells and IV fluid tonicity.

The van ’t Hoff factor (i) counts particles: glucose (i \approx 1); NaCl (i \approx 2); (\mathrm{CaCl_2}) (i \approx 3) (ideal complete dissociation). Real solutions show ion pairing; NMAT usually uses ideal integers.

Acids and bases: Arrhenius and Brønsted

Arrhenius (aqueous): acid increases [H⁺]/[H₃O⁺]; base increases [OH⁻].

Brønsted–Lowry: acid is a proton donor; base is a proton acceptor. Conjugate pairs differ by one H⁺ (e.g., (\mathrm{HCl/Cl^-}), (\mathrm{NH_4^+/NH_3}), (\mathrm{H_2O/OH^-}), (\mathrm{H_3O^+/H_2O})). Water is amphoteric (can act as acid or base).

Strong acids (common list): HCl, HBr, HI, HNO₃, H₂SO₄ (first proton), HClO₄ — essentially complete dissociation in water. Strong bases: group 1 hydroxides (NaOH, KOH) and heavier group 2 hydroxides (Ba(OH)₂, etc.) — complete dissociation for soluble cases.

Weak acids/bases only partially dissociate; equilibrium constants (K_a), (K_b) quantify strength (larger (K_a) → stronger weak acid). Do not confuse concentration with strength: 0.1 M HCl is strong and fully dissociated; 0.1 M acetic acid is weak and mostly undissociated.

pH, pOH, and strong acid/base calculations

At 25°C for pure water and dilute aqueous solutions:

[ K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14} ]

[ \mathrm{pH} = -\log[\mathrm{H_3O^+}], \quad \mathrm{pOH} = -\log[\mathrm{OH^-}], \quad \mathrm{pH} + \mathrm{pOH} = 14 ]

Neutral: pH 7; acidic: pH < 7; basic: pH > 7 (at 25°C).

Strong monoprotic acid: [H₃O⁺] ≈ molarity of acid (if not extremely dilute). Strong monobasic base: [OH⁻] ≈ molarity of base; then pOH → pH = 14 − pOH.

Worked example — strong acid pH. What is pH of 0.010 M HCl?

• [H₃O⁺] = 0.010 = 1.0 × 10⁻² → pH = 2.00.

Worked example — strong base pH. What is pH of 0.010 M NaOH?

• [OH⁻] = 0.010 → pOH = 2.00 → pH = 12.00.

Worked example — dilution then pH. 10.0 mL of 0.100 M HCl diluted to 100.0 mL:

• (M_2 = (0.100)(10.0)/100.0 = 0.0100,\mathrm{M}) → pH = 2.00.

Log scale reminder: each 1 unit pH change is a 10-fold change in [H₃O⁺]. pH 3 has 10× the [H₃O⁺] of pH 4.

Buffers (conceptual)

A buffer resists pH change when small amounts of strong acid or base are added. Classic composition: weak acid + its conjugate base (e.g., acetic acid + acetate) or weak base + conjugate acid (e.g., NH₃ + NH₄⁺). Mechanism: added H₃O⁺ is consumed by the conjugate base; added OH⁻ is consumed by the weak acid. Capacity fails if one component is exhausted or if huge amounts of strong acid/base are dumped.

Henderson–Hasselbalch (awareness level): (\mathrm{pH} = \mathrm{p}K_a + \log([\mathrm{A^-}]/[\mathrm{HA}])) — pH near p(K_a) when ratio ≈ 1. Blood bicarbonate buffer is a medical-context example, not a calculation requirement for most NMAT items.

Equilibrium intro and Le Chatelier

At chemical equilibrium, forward and reverse rates are equal; concentrations are constant (not necessarily equal). The equilibrium constant (K) (large → products favored) depends on temperature.

Le Chatelier’s principle: if a stress is applied, the system shifts to partially counteract the stress.

Worked conceptual: For (\mathrm{N_2 + 3,H_2 \rightleftharpoons 2,NH_3}) (exothermic forward), high pressure favors ammonia (fewer gas moles); high temperature favors reverse (Le Chatelier on heat as a product of the exothermic forward path).

Common traps

1. Using mL as liters in (M = n/V) (forget ×10⁻³).
2. Diluting by “halving concentration” without checking volumes.
3. Computing pH of NaOH as −log of molarity of NaOH (that gives pOH, not pH).
4. Calling a concentrated weak acid “strong.”
5. Thinking a catalyst changes equilibrium yield.
6. Confusing % w/w with molarity without density/molar mass.

Exam tactics

• Always track moles of solute through dilutions.
• For strong acid/base, write [H₃O⁺] or [OH⁻] first, then log.
• Label conjugate pairs when Brønsted definitions are tested.
• For Le Chatelier, identify heat as reactant or product from endo/exo wording.

Solutions and acid–base equilibrium are the bridge into analytical chemistry: titrations, indicators, and Beer's law all assume you can handle concentration and equivalence ideas cleanly.