pH and the Strength of Acids and Bases
A swimming pool, a glass of lemonade and the drain cleaner under the kitchen sink have one thing in common: each can be given a single number, its pH, that tells you how acidic or basic it is. Behind that number is a concentration of ions that changes by many powers of ten. How can one small scale handle all of that? Let's find out.
pH and pOH: Measuring Acidity
With a sensor in the lab you might measure $[\mathrm{H_3O^+}] \approx 1\ \mathrm{M}$ in a strong cleaning acid, $10^{-5}\ \mathrm{M}$ in black coffee, $10^{-7}\ \mathrm{M}$ in distilled water and $10^{-13}\ \mathrm{M}$ in bleach. Writing negative exponents that far apart is clumsy and easy to get wrong. A logarithm squeezes all of them into a friendly scale.
Why does it work? Taking $-\log$ of a power of ten just gives you the exponent without the minus sign: $-\log(10^{-5}) = 5$. Because $K_\mathrm{w}$ is a constant, if $[\mathrm{H_3O^+}]$ goes up then $[\mathrm{OH^-}]$ must go down, so pH and pOH always add to 14.
In the chemistry lab there is an aqueous solution of nitric acid, $\mathrm{HNO_3}$, of concentration $0.025\,\mathrm{mol\times L^{-1}}$ at $25\,^\circ\mathrm{C}$. Given…
In the chemistry lab there is an aqueous solution of nitric acid, $\mathrm{HNO_3}$, of concentration $0.025\,\mathrm{mol\times L^{-1}}$ at $25\,^\circ\mathrm{C}$. Given that nitric acid behaves as a strong monoprotic acid that dissociates completely in water and that the ionic product of water is $K_\mathrm{w} = 1.0\times 10^{-14}$ at that temperature, assume ideal behavior where $\mathrm{pH} = -\log[\mathrm{H_3O^+}]$. Calculate: a) The concentration of hydronium ions, $[\mathrm{H_3O^+}]$, and the value of the $\mathrm{pH}$ of the solution. b) The concentration of hydroxide ions, $[\mathrm{OH^-}]$, present in the medium. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.
Strong Acids and Bases: Complete Dissociation
Picture a light bulb wired to two electrodes in $0.10\ \mathrm{M}$ HCl. It glows brightly. Put the same electrodes in $0.10\ \mathrm{M}$ acetic acid (vinegar's acid) and the glow is faint. Same concentration, so why the difference?
An aqueous solution is prepared by dissolving $0.171\,\mathrm{g}$ of barium hydroxide, $\mathrm{Ba(OH)2}$, in distilled water to make an exact volume of…
An aqueous solution is prepared by dissolving $0.171\,\mathrm{g}$ of barium hydroxide, $\mathrm{Ba(OH)_2}$, in distilled water to make an exact volume of $500\,\mathrm{mL}$ at $25\,^\circ\mathrm{C}$. This compound is assumed to be a strong base that dissociates completely according to the process $\mathrm{Ba(OH)_2(s) \rightarrow Ba^{2+}(aq) + 2\,OH^-(aq)}$. Molar mass of $\mathrm{Ba(OH)_2}$: $171.3\,\mathrm{g\times mol^{-1}}$; $K_\mathrm{w} = 1.0\times 10^{-14}$. Under the ideal approximation, determine: a) The molar concentration of $\mathrm{OH^-}$ ions in the resulting solution. b) The $\mathrm{pOH}$ and the $\mathrm{pH}$ of the final solution. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.
Mixing a Strong Acid and a Strong Base
What happens to the pH when you pour an acid and a base together? They neutralize each other, so the answer depends on which one has more moles.
A laboratory reactor is filled with a mixture of $250\,\mathrm{mL}$ of an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, of concentration…
A laboratory reactor is filled with a mixture of $250\,\mathrm{mL}$ of an aqueous solution of hydrochloric acid, $\mathrm{HCl}$, of concentration $0.060\,\mathrm{mol\times L^{-1}}$ and $150\,\mathrm{mL}$ of an aqueous solution of barium hydroxide, $\mathrm{Ba(OH)_2}$, of concentration $0.040\,\mathrm{mol\times L^{-1}}$ at $25\,^\circ\mathrm{C}$. Assume that the volumes are additive (final volume $400\,\mathrm{mL}$), that both substances behave as strong electrolytes that are fully dissociated, and that $K_\mathrm{w} = 1.0\times 10^{-14}$ at that temperature in an ideal solution. a) Write the net ionic neutralization reaction and determine, with justification, which reagent is in excess, quantifying the moles remaining. b) Calculate the molar concentration of all the ionic species present in the resulting mixture ($\mathrm{H_3O^+}$, $\mathrm{OH^-}$, $\mathrm{Ba^{2+}}$ and $\mathrm{Cl^-}$) and determine the $\mathrm{pH}$ of the final solution. Use the ideal model and neglect the autoprotolysis of water where that approximation is valid.
Extension: Weak Acids, Ka and Degree of Dissociation
Weak acids and bases dissociate only partly, so an equilibrium forms between the molecules and their ions.
Back to the start: Lemon juice has $\mathrm{pH} \approx 2$, pool water is kept near $7.4$, and drain cleaner is near $13$. That is about eleven powers of ten in $[\mathrm{H_3O^+}]$, and the log scale squeezes them into one easy range.