Acids and Bases

By the Brønsted–Lowry definition, an acid 酸 is a proton ($\text{H}^+$) donor and a base 碱 is a proton acceptor. When an acid donates a proton it becomes its conjugate base 共轭碱; a base gaining a proton becomes its conjugate acid 共轭酸. Water is amphoteric – it can act as either.

Even pure water conducts a tiny current, because water molecules react with each other in a reaction called autoionization 自偶电离:

One water molecule passes a proton to another, making a hydronium ion 水合氢离子 ($\text{H}_3\text{O}^+$, the ion we loosely write as $\text{H}^+$) and a hydroxide ion. This equilibrium has its own constant, the ion-product constant of water 水的离子积: at 25 °C. Defining $\text{pOH}=-\log[\text{OH}^-]$ and taking $-\log$ of the $K_w$ expression gives the rule the rest of this topic leans on: (again at 25 °C). Know one of pH or pOH and you get the other by subtracting from 14.

In pure water the two ions form in equal numbers, so $[\text{H}_3\text{O}^+]=[\text{OH}^-]$ and $\text{pH}=\text{pOH}=7.0$. This is what neutral 中性 means. Acidic means $[\text{H}_3\text{O}^+]>[\text{OH}^-]$ (pH below 7); basic is the reverse.

Worked example. A solution has $[\text{H}_3\text{O}^+]=2.0\times10^{-3}\ \text{M}$. Find $[\text{OH}^-]$. Because $K_w$ always holds in water,

The hydroxide concentration is far smaller than the hydronium, confirming the solution is acidic.

$K_w$ is temperature dependent: autoionization is endothermic, so heating water shifts it forward and raises $K_w$. At 50 °C, $K_w>1.0\times10^{-14}$, so neutral water has $\text{pH}=\text{pOH}<7.0$. It is still neutral, because the ion concentrations are still equal – neutral means equal ions, not a pH of exactly 7.

The pH pH值 scale measures acidity: $\text{pH}=-\log[\text{H}^+]$, with $\text{pH}+\text{pOH}=14$ at 25 °C. A strong acid 强酸 or strong base 强碱 dissociates completely, so its ion concentration equals its concentration – read pH directly. Lower pH means more acidic.

Worked example. Find the pH of $0.010\ \text{M}$ HCl. Because HCl is a strong acid it is fully dissociated, so $[\text{H}^+]=0.010\ \text{M}$ and

For a strong base like $0.010\ \text{M}$ NaOH, $\text{pOH}=2.0$, so $\text{pH}=14-2.0=12.0$.

A weak acid 弱酸 only partly dissociates, described by an equilibrium constant $K_a$ (larger $K_a$ = stronger weak acid); a weak base has $K_b$. For any conjugate acid–base pair the two are linked through water, $K_a\times K_b = K_w$, so $\text{p}K_a+\text{p}K_b=14$ – a stronger acid always has a weaker conjugate base. Because dissociation is small, find $[\text{H}^+]$ with an ICE table and the $K_a$ expression, often using the small-$x$ approximation.

Worked example. Find the pH of $0.10\ \text{M}$ acetic acid, $K_a=1.8\times10^{-5}$. Let $x=[\text{H}^+]$ at equilibrium; the ICE table gives $K_a=\dfrac{x^2}{0.10-x}\approx\dfrac{x^2}{0.10}$ (small-$x$ approximation), so

The weak acid is far less acidic than a strong acid of the same concentration (which would be pH $1.0$).

A buffer 缓冲溶液 resists pH change. It contains a weak acid and its conjugate base (or a weak base and its conjugate acid) in comparable amounts. Added acid is neutralized by the conjugate base, and added base by the weak acid, so pH barely moves.

A titration curve 滴定曲线 plots pH as base (or acid) is added. Key points: the equivalence point 等当点 (moles of acid = moles of base – a steep jump), and the half-equivalence point, where $\text{pH}=\text{p}K_a$ (half the weak acid is converted, so a buffer is at its center).

An acid-base indicator 酸碱指示剂 is itself a weak acid whose protonated and deprotonated forms have different colours, so its colour responds to pH. You pick an indicator whose colour change happens near the titration's equivalence-point pH, so the colour flips just as the reaction completes.

Strength has structural roots. An acid is stronger when its conjugate base is more stable – for example, more electronegative atoms or resonance spreading the negative charge stabilize it. For oxoacids, more oxygen atoms on the central atom means a stronger acid.

$\text{p}K_a=-\log K_a$: a smaller $\text{p}K_a$ means a stronger acid. Comparing pH to $\text{p}K_a$ tells you the dominant form: below $\text{p}K_a$ the acid form dominates; above it, the conjugate base form dominates.

A buffer works best when the weak acid and conjugate base concentrations are similar (pH near $\text{p}K_a$). Choose a buffer whose $\text{p}K_a$ is close to the target pH. Diluting a buffer barely changes its pH, because the acid-to-base ratio stays the same.

For a buffer, the pH follows from the acid-to-base ratio:

When the concentrations are equal, the log is zero and $\text{pH}=\text{p}K_a$. Use it to design a buffer or find its pH quickly.

Worked example. A buffer holds $0.20\ \text{M}$ acetic acid ($\text{p}K_a=4.74$) and $0.30\ \text{M}$ acetate. Its pH is

A little more conjugate base than acid pushes the pH just above $\text{p}K_a$, as the equation predicts.

Buffer capacity 缓冲容量 is how much acid or base a buffer can absorb before its pH changes sharply. It is greatest when the components are concentrated and in roughly equal amounts. Once one component is used up, the buffer fails.

The solubility of a salt with a basic anion rises in acidic solution: the added $\text{H}^+$ reacts with the anion, removing it from the solubility equilibrium and pulling more solid to dissolve (Le Chatelier applied to $K_{sp}$). So pH can control whether an ionic solid dissolves.

• Neutral means equal ions, not pH 7. In pure water $[\text{H}_3\text{O}^+]=[\text{OH}^-]$; since $K_w$ rises with temperature, neutral pH drifts below 7 above 25 °C. Use $K_w=[\text{H}_3\text{O}^+][\text{OH}^-]=1.0\times10^{-14}$ (25 °C) to convert between $[\text{OH}^-]$ and $[\text{H}_3\text{O}^+]$.
• $\text{pH}=-\log[\text{H}^+]$ is logarithmic — each unit is a ten-fold change in $[\text{H}^+]$.
• A strong acid/base dissociates completely (so $[\text{H}^+]$ = concentration); a weak one only partly, needing $K_a$.
• A buffer contains a weak acid and its conjugate base together; it resists pH change by mopping up added acid or base.
• On a titration curve the equivalence point is the steep jump; the half-equivalence point has $\text{pH}=\text{p}K_a$.
• A smaller $\text{p}K_a$ means a stronger acid.