Grade 11 Chemistry Knowledge Summary 2: Electrolyte Fundamentals | Brief Solutions

$\mathrm{H_2O\rightleftharpoons H^++OH^-}$; $\Delta H>0$; an endothermic process.

Heating or removing $\mathrm{H^+}$ or $\mathrm{OH^-}$ promotes ionization; cooling or adding either ion suppresses it.

$\mathrm{pH}=-\lg[\mathrm{H^+}]$; $\mathrm{pOH}=-\lg[\mathrm{OH^-}]$; $[\mathrm{H^+}]=10^{-\mathrm{pH}}$; $[\mathrm{OH^-}]=10^{-\mathrm{pOH}}$, with concentrations in $\mathrm{mol\,L^{-1}}$.

$K_w=[\mathrm{H^+}][\mathrm{OH^-}]$. At 25 degrees Celsius, $K_w=10^{-14}$ and $\mathrm{pH+pOH}=14$; generally, $\mathrm{pH+pOH}=\mathrm pK_w$.

Neutral: $[\mathrm{H^+}]=[\mathrm{OH^-}]$, $\mathrm{pH=pOH}$. Acidic: $[\mathrm{H^+}]>[\mathrm{OH^-}]$, $\mathrm{pH<pOH}$. Alkaline: $[\mathrm{H^+}]<[\mathrm{OH^-}]$, $\mathrm{pH>pOH}$.

$[\mathrm{H^+}]_w=[\mathrm{OH^-}]_w$. In the acid, total concentrations are $10^{-a}$ and $10^{a-14}$, and both water-derived concentrations are $10^{a-14}$. In the alkali, totals are $10^{-b}$ and $10^{b-14}$, and both water-derived concentrations are $10^{-b}$. These expressions concern acidity or alkalinity supplied by an acid or base, not by salt hydrolysis.

Excess acid: acidic. Excess base: alkaline. Equal amounts of acid-derived $\mathrm{H^+}$ and base-derived $\mathrm{OH^-}$: neutral.

Strong electrolytes ionize completely; weak electrolytes ionize partially. Polyprotic weak acids ionize stepwise; weak polybasic bases are usually written as one overall ionization step.

$\mathrm{HCl\rightarrow H^++Cl^-}$;$\mathrm{Ca(OH)_2\rightarrow Ca^{2+}+2OH^-}$;$\mathrm{HCOOH\rightleftharpoons H^++HCOO^-}$.

$\mathrm{H_2SO_3\rightleftharpoons H^++HSO_3^-}$ and $\mathrm{HSO_3^-\rightleftharpoons H^++SO_3^{2-}}$; $\mathrm{NaHSO_3\rightarrow Na^++HSO_3^-}$, followed by partial ionization of $\mathrm{HSO_3^-}$; $\mathrm{Fe(OH)_3\rightleftharpoons Fe^{3+}+3OH^-}$.

Methyl orange: pH 3.1–4.4, red to orange to yellow. Methyl red: 4.4–6.2, red to orange to yellow. Litmus: 5.0–8.0, red to purple to blue. Phenolphthalein: 8.2–10.0, colorless to pink to red.

Universal paper: usually whole pH units. Narrow-range paper: commonly about 0.1–0.5 pH unit, depending on its scale. A pH meter commonly reads to 0.01, depending on the instrument.

Ions formed by ionization coexist with unionized molecules; $\alpha=\dfrac{n_{\mathrm{ionized}}}{n_{\mathrm{initial}}}\times100\%$.

$\mathrm{CH_3COOH\rightleftharpoons H^++CH_3COO^-}$; under the usual textbook treatment, $\Delta H>0$; $K_a=\dfrac{[\mathrm{H^+}][\mathrm{CH_3COO^-}]}{[\mathrm{CH_3COOH}]}$.

$\mathrm{NH_3\cdot H_2O\rightleftharpoons NH_4^++OH^-}$; under the usual textbook treatment, $\Delta H>0$; $K_b=\dfrac{[\mathrm{NH_4^+}][\mathrm{OH^-}]}{[\mathrm{NH_3\cdot H_2O}]}$.

A larger $K_a$ means stronger release of $\mathrm{H^+}$ and weaker proton binding by the conjugate anion. A larger $K_b$ means stronger release of $\mathrm{OH^-}$ and weaker hydroxide binding by the conjugate cation.

Under the textbook endothermic-ionization model, heating, removing product ions or dilution promotes ionization; cooling or adding common product ions suppresses it.

$\dfrac{[\mathrm{CH_3COO^-}]}{[\mathrm{CH_3COOH}]}=\dfrac{K_a}{[\mathrm{H^+}]}$;$\dfrac{[\mathrm{CH_3COO^-}]}{K_a}=\dfrac{[\mathrm{CH_3COOH}]}{[\mathrm{H^+}]}$;$\dfrac{[\mathrm{CH_3COO^-}]}{[\mathrm{CH_3COOH}][\mathrm{OH^-}]}=\dfrac{K_a}{K_w}$.

Neglecting water ionization, $K_a=\dfrac{[\mathrm{H^+}]^2}{c-[\mathrm{H^+}]}$; for small ionization, this is approximately $[\mathrm{H^+}]^2/c$.

Total positive charge equals total negative charge: $[\mathrm{NH_4^+}]+[\mathrm{H^+}]=[\mathrm{Cl^-}]+[\mathrm{OH^-}]$.

Conservation of each element: $[\mathrm{NH_4^+}]+[\mathrm{NH_3\cdot H_2O}]=[\mathrm{Cl^-}]$.

$[\mathrm{H^+}]=[\mathrm{OH^-}]+[\mathrm{NH_3\cdot H_2O}]$.

With $C_T=[\mathrm{H_2CO_3}]+[\mathrm{HCO_3^-}]+[\mathrm{CO_3^{2-}}]$, the fractions are respectively $[\mathrm{H_2CO_3}]/C_T$, $[\mathrm{HCO_3^-}]/C_T$ and $[\mathrm{CO_3^{2-}}]/C_T$; their sum is 1.

Equal fractions mean equal concentrations. The first crossing gives $[\mathrm{H^+}]=K_{a1}$ and $\mathrm{pH=p}K_{a1}$, about 6 in the sketch. The second gives $[\mathrm{H^+}]=K_{a2}$ and $\mathrm{pH=p}K_{a2}$, about 10 in the sketch.

Salt ions react with water-derived $\mathrm{H^+}$ or $\mathrm{OH^-}$ to form weak acids or bases, shifting water ionization to the right and promoting it.

The weaker the conjugate acid or base and the smaller its $K_a$ or $K_b$, the stronger hydrolysis and, at equal concentrations, the greater alkalinity or acidity.

$\mathrm{CO_3^{2-}+H_2O\rightleftharpoons HCO_3^-+OH^-}$;$\mathrm{HCO_3^-+H_2O\rightleftharpoons H_2CO_3+OH^-}$.$\mathrm{S^{2-}+H_2O\rightleftharpoons HS^-+OH^-}$;$\mathrm{HS^-+H_2O\rightleftharpoons H_2S+OH^-}$.

$\mathrm{Fe^{3+}+3H_2O\rightleftharpoons Fe(OH)_3+3H^+}$;$\mathrm{Mg^{2+}+2H_2O\rightleftharpoons Mg(OH)_2+2H^+}$.

Hydrolysis is the reverse of neutralization and is usually treated as endothermic. Heating, dilution or removing products promotes it; cooling or adding products suppresses it.

Strong acid/strong base: no hydrolysis, neutral. Strong acid/weak base: cation hydrolysis, acidic. Weak acid/strong base: anion hydrolysis, alkaline. Weak acid/weak base: both ions hydrolyze; relative strengths determine pH.

$K_h(\mathrm{CO_3^{2-}})=K_w/K_{a2}(\mathrm{H_2CO_3})$;$K_h(\mathrm{HCO_3^-})=K_w/K_{a1}(\mathrm{H_2CO_3})$;$K_h(\mathrm{NH_4^+})=K_w/K_b(\mathrm{NH_3\cdot H_2O})$;$K_h(\mathrm{S^{2-}})=K_w/K_{a2}(\mathrm{H_2S})$.

Add a few drops of saturated iron(III) chloride solution to boiling water and stop heating when reddish brown: $\mathrm{FeCl_3+3H_2O\xrightarrow{\Delta}Fe(OH)_3+3HCl}$, with iron(III) hydroxide in colloidal form.

Add a small amount of iron powder. Concentrate under HCl protection until a crystal film or a few crystals appear; stop heating, hot-filter to remove iron and cool to crystallize.

Dissolve in a small amount of concentrated hydrochloric acid, then dilute. To prepare the anhydrous salt, heat $\mathrm{FeCl_3\cdot6H_2O}$ in dry HCl gas.

$\mathrm{CO_3^{2-}+H_2O\rightleftharpoons HCO_3^-+OH^-}$ and $\mathrm{SiO_2+2OH^-\rightarrow SiO_3^{2-}+H_2O}$. The alkaline solution attacks ground glass; silicate can make a glass stopper stick.

$\mathrm{Al^{3+}+3HCO_3^-\rightarrow Al(OH)_3\downarrow+3CO_2\uparrow}$; $\mathrm{2NH_4^++CO_3^{2-}+H_2O\rightleftharpoons2NH_3\cdot H_2O+H_2CO_3}$, with decomposition possible as $\mathrm{(NH_4)_2CO_3\rightarrow2NH_3\uparrow+CO_2\uparrow+H_2O}$.

Oxides, hydroxides and carbonates (or basic carbonates).

Calculate $K_h$ from $K_a$ or $K_b$, compare ionization and hydrolysis, then apply charge, material and proton balances together with acidity or alkalinity.

Less than $0.01\,\mathrm g$ dissolves in $100\,\mathrm g$ of water near room temperature.

A dynamic equilibrium in which dissolution and precipitation rates are equal.

$K_{sp}$. For a given compound and solvent it depends on temperature, not ion concentrations. It characterizes dissolution and precipitation tendency; direct comparison is valid for salts of the same stoichiometric type, otherwise calculate solubility.

$Q<K_{sp}$: undersaturated; any solid present can dissolve. $Q=K_{sp}$: saturated, with equilibrium if solid is present. $Q>K_{sp}$: supersaturated; precipitation occurs.

Both rankings are $\mathrm{AgCl>AgBr>AgI}$.

Using the usual approximation neglecting water self-ionization, $s=(2.2\times10^{-20}/4)^{1/3}=1.77\times10^{-7}\,\mathrm{mol\,L^{-1}}$, so $[\mathrm{Cu^{2+}}]=s$; mass solubility is about $1.73\times10^{-6}\,\mathrm g$ per $100\,\mathrm g$ of water.

Using the usual approximation neglecting sulfide hydrolysis, $s=(6.3\times10^{-50}/4)^{1/3}=2.51\times10^{-17}\,\mathrm{mol\,L^{-1}}$; $[\mathrm{Ag^+}]=2s=5.01\times10^{-17}\,\mathrm{mol\,L^{-1}}$; mass solubility is about $6.22\times10^{-16}\,\mathrm g$ per $100\,\mathrm g$ of water.

Residual ion concentration is typically $\leq1.0\times10^{-5}\,\mathrm{mol\,L^{-1}}$.

React with an acid, undergo a redox reaction or form a coordination complex. Removing dissolved ions shifts the equilibrium toward dissolution.