Atoms, bonding, gases, balanced equations, moles, solutions, pH, buffers, equilibrium and an organic and biochemistry preview, with short fill-in-the-blank Python calculators.

Chemistry Fundamentals

## Why this matters

pH is one of the most measured numbers in science and industry. Blood must stay between about 7.35 and 7.45; drinking-water plants control pH to protect pipes; enzymes in a biotech process stop working outside a narrow range; concrete is strongly basic, which protects the steel inside it. Knowing what pH means, and how to calculate it, lets you read a lab result or a process sheet with confidence.

## What acids and bases are

The most useful working definition for this course is **Brønsted–Lowry**:

- An **acid** donates a hydrogen ion (H⁺, a proton).
- A **base** accepts a hydrogen ion.

```text
HCl + H2O  ->  H3O+ + Cl-        HCl is the acid (donates H+)
NH3 + H2O  <=> NH4+ + OH-        NH3 is the base (accepts H+)
```

In water, H⁺ is actually attached to a water molecule as H₃O⁺ (hydronium); chemists write [H⁺] and [H₃O⁺] interchangeably. Square brackets mean "concentration in mol/L".

### Strong vs weak

- **Strong acids** ionise completely in water: HCl, HNO₃, HBr, HI, HClO₄ and H₂SO₄ (first proton). For a strong acid, [H⁺] equals the acid concentration.
- **Weak acids** ionise only partly: acetic acid (vinegar), citric acid, carbonic acid. Most molecules stay intact, so [H⁺] is much lower than the acid concentration.
- **Strong bases** such as NaOH and KOH release OH⁻ completely. Ammonia is a **weak base**.

"Strong" is about how completely it ionises, not how concentrated it is. A dilute strong acid can have a higher pH than a concentrated weak one.

## The pH scale

```text
pH  = −log10[H+]
[H+] = 10^(−pH)
```

Because it is a logarithm, each pH unit is a **factor of 10**. pH 3 has ten times more H⁺ than pH 4, and a thousand times more than pH 6.

Water itself ionises a tiny amount: H₂O ⇌ H⁺ + OH⁻. At 25 °C,

```text
Kw = [H+][OH−] = 1.0 × 10^−14
pH + pOH = 14.00
```

In pure water [H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, so pH = 7: **neutral**. Below 7 is acidic, above 7 is basic. (Kw changes with temperature, so "neutral = 7" is exact only at 25 °C.)

| substance | approximate pH |
|---|---|
| stomach acid | 1–3 |
| lemon juice | about 2 |
| black coffee | about 5 |
| pure water (25 °C) | 7 |
| blood | 7.35–7.45 |
| baking soda in water | about 8–9 |
| household ammonia | about 11–12 |

## Worked examples

**1. A strong acid.** 0.010 M HCl ionises completely, so [H⁺] = 0.010 = 1.0 × 10⁻² M.

```text
pH = −log10(0.010) = 2.00
```

**2. A non-round concentration.** [H⁺] = 2.5 × 10⁻⁴ M.

```text
pH = −log10(2.5 × 10^−4) ≈ 3.60
```

Sanity check: 2.5 × 10⁻⁴ sits between 10⁻⁴ (pH 4) and 10⁻³ (pH 3), so 3.60 is sensible.

**3. A strong base.** 0.0010 M NaOH gives [OH⁻] = 1.0 × 10⁻³ M.

```text
pOH = −log10(0.0010) = 3.00
pH  = 14.00 − 3.00  = 11.00
```

**4. Going backwards.** A sample reads pH 5.0. Then [H⁺] = 10⁻⁵ M = 0.00001 M.

**5. Dilution and pH.** Diluting 0.010 M HCl ten times gives 0.0010 M, so the pH rises from 2 to 3. Diluting only ever moves pH toward 7; no amount of water makes an acid basic.

## Neutralisation

An acid and a base react to form water and a salt:

```text
HCl + NaOH -> NaCl + H2O
```

This is the basis of a **titration**, where a base of known concentration is added to an acid until an indicator changes colour, so you can calculate the acid's concentration. You will meet titrations in lab courses.

## How pH is measured

- **Indicator paper** gives a rough colour reading.
- A **pH meter** with a glass electrode gives two decimal places, but only if it is calibrated against standard buffers first. Calibration is a routine lab task done under the lab's procedures.

## Safety note

Strong acids and bases cause serious burns, and some household products react dangerously with each other (for example, mixing bleach with acids or with ammonia releases toxic gases). Never mix cleaning products. Working with acids and bases is learned in a lab under supervision with proper eye and skin protection; employer or institution training is required. See OSHA's [laboratory safety guidance](https://www.osha.gov/laboratories). Checked on 2026-10-23.

## Common mistakes

- **Forgetting the minus sign.** log10(0.010) = −2, so pH = −(−2) = 2.
- **Treating the scale as linear.** pH 2 is 100 times more acidic than pH 4, not twice.
- **Using pH directly for a base.** Find pOH from [OH⁻] first, then pH = 14 − pOH.
- **Using the acid concentration for a weak acid.** That only works for strong acids.

## Quick recap

- Acids donate H⁺; bases accept it. Strong means fully ionised.
- pH = −log10[H⁺]; each unit is a factor of 10.
- At 25 °C, pH + pOH = 14 and neutral is 7.

## Try it

Open the **Do** tab: you will write the pH formula in a small Python calculator, then take the quiz.


Tell strong and weak acids and bases apart and compute pH and pOH from a hydrogen- or hydroxide-ion concentration.

Acids, bases, and pH

pH and pOH: Crash Course Chemistry #30

Acids and Bases, pH and pOH

## Why this matters

Your blood stays near pH 7.4 even after you eat, exercise or hold your breath. Cell cultures, enzyme assays and DNA work all happen in buffered solutions, and many clinical tests depend on buffered reagents. A buffer is the reason a small spill of acid into a reaction mix does not wreck it. Biotech, clinical and chemistry jobs all involve preparing and choosing buffers, so it pays to understand why they work.

## The core idea

A **buffer** is a solution that resists changes in pH when a small amount of acid or base is added. It contains two partners in similar amounts:

- a **weak acid**, HA, which can neutralise added base, and
- its **conjugate base**, A⁻, which can neutralise added acid.

The classic example is acetic acid (CH₃COOH) with sodium acetate (CH₃COONa), which supplies the acetate ion CH₃COO⁻.

### What happens when you add acid

Added H⁺ is grabbed by the conjugate base:

```text
CH3COO−  +  H+   ->  CH3COOH
```

The strong acid is turned into a weak acid, which barely ionises, so [H⁺] hardly changes.

### What happens when you add base

Added OH⁻ is neutralised by the weak acid:

```text
CH3COOH  +  OH−  ->  CH3COO−  +  H2O
```

The strong base becomes water and more conjugate base, so again pH changes very little.

Pure water has no such partners. Add 1 mL of 1 M HCl to a litre of pure water and the pH drops from 7 to about 3. Add the same acid to a litre of buffer containing 0.10 M acetic acid and 0.10 M acetate and the pH moves by only about 0.01.

## The Henderson–Hasselbalch equation

For a buffer, the pH depends on the acid's strength (its **pKa**) and the ratio of base to acid:

```text
pH = pKa + log10( [A−] / [HA] )
```

pKa is −log10 of the acid dissociation constant Ka. A lower pKa means a stronger acid. Acetic acid has pKa ≈ 4.76.

### Worked example 1: equal amounts

0.10 M acetic acid and 0.10 M sodium acetate:

```text
pH = 4.76 + log10(0.10 / 0.10) = 4.76 + log10(1) = 4.76 + 0 = 4.76
```

When acid and conjugate base are equal, **pH = pKa**. This is where the buffer works best.

### Worked example 2: more base than acid

0.10 M acetate and 0.050 M acetic acid:

```text
pH = 4.76 + log10(0.10 / 0.050) = 4.76 + log10(2) ≈ 4.76 + 0.30 = 5.06
```

### Worked example 3: a tenfold ratio

If [A⁻] / [HA] = 10, pH = pKa + 1 = 5.76. If the ratio is 1/10, pH = pKa − 1 = 3.76.

## Choosing a buffer

Rule of thumb: a buffer works well within about **±1 pH unit of its pKa**. Pick the acid whose pKa is closest to the pH you need.

| buffer pair | pKa (approx., 25 °C) | useful range | typical use |
|---|---|---|---|
| acetic acid / acetate | 4.76 | about 3.8–5.8 | food chemistry, some assays |
| H₂PO₄⁻ / HPO₄²⁻ (phosphate) | 7.21 | about 6.2–8.2 | biology (phosphate-buffered saline) |
| Tris | about 8.1 | about 7.1–9.1 | molecular biology |
| carbonic acid / bicarbonate | about 6.1 (in blood) | the body's main blood buffer | physiology, clinical chemistry |

## Buffer capacity

**Capacity** is how much acid or base a buffer can absorb before its pH changes a lot. It grows with the total concentration of the pair: 0.5 M acetate buffer resists more than 0.05 M at the same ratio. Once nearly all of one partner is used up, the buffer is **exhausted** and the pH swings quickly.

## The blood example

In blood, carbonic acid (from dissolved CO₂) and bicarbonate form a buffer:

```text
CO2 + H2O  <=>  H2CO3  <=>  H+ + HCO3−
```

The lungs adjust CO₂ and the kidneys adjust bicarbonate, so the body can tune the ratio. Clinical labs measure blood gases and bicarbonate to see whether this system is coping; interpreting those results is part of clinical laboratory training.

## Common mistakes

- **Thinking a buffer keeps pH constant forever.** It resists change only until its capacity runs out.
- **Using a strong acid as the buffer acid.** HCl and its conjugate base Cl⁻ do not buffer; the acid must be weak.
- **Inverting the ratio.** It is base over acid: [A⁻]/[HA]. More base means a pH above the pKa.
- **Choosing a buffer far from its pKa.** A phosphate buffer at pH 4 does very little.

## Quick recap

- A buffer is a weak acid plus its conjugate base in similar amounts.
- The base partner absorbs added H⁺; the acid partner absorbs added OH⁻.
- pH = pKa + log10([A⁻]/[HA]); equal amounts give pH = pKa.
- Choose a pKa within 1 unit of the target pH; more concentrated means more capacity.

## Try it

Open the **Do** tab and take the quiz: you will explain how a buffer reacts to added acid and base and estimate buffer pH.


Explain how a weak acid and its conjugate base absorb added acid or base, and estimate a buffer's pH with the Henderson–Hasselbalch equation.

Buffers

Buffers, the Acid Rain Slayer: Crash Course Chemistry #31

Acid-Base Equilibria and Buffer Solutions

## Why this matters

Two separate questions decide whether a reaction is useful: **how fast** does it go, and **how far** does it go? Food spoils faster on the counter than in the fridge (rate). An ammonia plant runs at high pressure to push more nitrogen and hydrogen into product (equilibrium). Engineers, chemists and lab staff deal with both every day, whether they are speeding up a production step or keeping a reagent stable on the shelf.

## Part 1: reaction rate (kinetics)

The **rate** of a reaction is how quickly reactants are used up or products form, for example in mol/L per second.

### Collision theory

Particles react only when they **collide**, with **enough energy** (at least the **activation energy**, Eₐ) and in the **right orientation**. Anything that makes useful collisions more frequent or more energetic speeds the reaction up.

### Four factors that change the rate

| factor | effect | why |
|---|---|---|
| concentration (or gas pressure) | higher -> faster | more particles in the same space, more collisions |
| temperature | higher -> faster | particles move faster and more collisions exceed Eₐ |
| surface area | more surface -> faster | more particles of a solid are exposed |
| catalyst | faster | provides a lower-energy pathway (lower Eₐ) and is not used up |

Examples:

- Sugar dissolves and reacts faster as powder than as a cube (surface area). Fine powders can even be explosion hazards in industry for this reason.
- Refrigeration slows the reactions that spoil food (temperature). A common rough rule is that many reactions near room temperature go about **twice as fast for every 10 °C** rise; it is a rule of thumb, not a law.
- Enzymes are biological catalysts: catalase speeds the breakdown of hydrogen peroxide, 2 H₂O₂ → 2 H₂O + O₂, enormously.
- A car's catalytic converter speeds the conversion of carbon monoxide and unburned fuel to CO₂ and water.

### Energy diagram, in words

Picture a hill between reactants and products. The height of the hill is the activation energy. A catalyst digs a lower pass through the hill; it does **not** change where the reactants start or where the products end up, so it does not change the overall energy released.

## Part 2: chemical equilibrium

Many reactions are **reversible**: products can turn back into reactants.

```text
N2(g) + 3 H2(g)  <=>  2 NH3(g)
```

At first the forward reaction dominates. As products build up, the reverse reaction speeds up, until both run at the **same rate**. From then on the concentrations stay constant. This is **dynamic equilibrium**: the reactions have not stopped, they are balanced.

### The equilibrium constant

For `aA + bB <=> cC + dD`:

```text
K = [C]^c [D]^d / ( [A]^a [B]^b )
```

For the ammonia reaction, K = [NH₃]² / ([N₂][H₂]³).

- **K much greater than 1**: products are favoured at equilibrium.
- **K much less than 1**: reactants are favoured.

K changes only with temperature. Concentrations can change, but at a given temperature the system always settles back to the same K.

## Le Chatelier's principle

If you disturb a system at equilibrium, it **shifts to partly undo the disturbance**.

Using the Haber process, which is **exothermic** (it releases heat, ΔH ≈ −92 kJ per mole of N₂ reacting):

| change | shift | reason |
|---|---|---|
| add N₂ or H₂ | right, more NH₃ | uses up the added reactant |
| remove NH₃ as it forms | right | replaces the removed product |
| increase pressure (smaller volume) | right | 4 moles of gas -> 2: fewer gas particles lowers pressure |
| increase temperature | left, less NH₃ | the reverse reaction absorbs heat |
| add a catalyst | no shift | speeds both directions equally; equilibrium is reached sooner |

This creates a real engineering trade-off. Low temperature gives more ammonia at equilibrium but makes the reaction slow. Plants therefore run at a compromise temperature (roughly 400–450 °C), high pressure (around 150–300 atm) and an iron catalyst, and they remove ammonia continuously. Rate and equilibrium are designed together.

### Everyday equilibrium

- A sealed bottle of fizzy drink holds CO₂ in equilibrium with dissolved CO₂. Opening it lowers the pressure, so the equilibrium shifts and gas comes out of solution.
- Haemoglobin picks up oxygen in the lungs (high O₂) and releases it in tissues (low O₂), a shift driven by concentration.

## Common mistakes

- **Thinking equilibrium means equal amounts.** It means equal forward and reverse *rates*; amounts can be very unequal.
- **Saying a catalyst increases yield.** It only gets you to equilibrium faster.
- **Changing K by adding reactant.** Concentrations shift, but K changes only with temperature.
- **Confusing fast with favourable.** A reaction can have a huge K and still be extremely slow (diamond turning to graphite).

## Quick recap

- Rate rises with concentration, temperature, surface area and a catalyst.
- Catalysts lower the activation energy and are not consumed.
- Equilibrium is dynamic: forward and reverse rates are equal; K describes the balance.
- Le Chatelier: the system shifts to counteract a change; temperature is the only thing that changes K.

## Try it

Open the **Do** tab and take the quiz: you will predict rate changes and equilibrium shifts for real situations.


Explain how concentration, temperature, surface area and catalysts change reaction rate, and use Le Chatelier's principle to predict how an equilibrium shifts.

Rates and equilibrium

Kinetics: Chemistry's Demolition Derby - Crash Course Chemistry #32

Equilibrium: Crash Course Chemistry #28

Acids, bases and pH, how buffers resist pH change, and what controls reaction rate and equilibrium.