# Representations from particles to formulas

Physics I · Chemistry · https://tryals.app/learn/physics-i/representations-from-particles-to-formulas

## The Three Scales of Chemistry

Chemistry operates simultaneously at three connected levels:

| Level | Focus | Example |
| --- | --- | --- |
| **Particulate** | Atoms, ions | $Na^+$ and $Cl^-$ |
| **Symbolic** | Formulas, equations | $NaCl(aq)$ |
| **Macroscopic** | Mass, volume, colour | White solid, 58.44 g/mol |

Moving fluidly across this **representation triangle** separates genuine understanding from mere formula plugging.

**Ionic equilibrium** governs sparingly soluble salts $A_b B_a$:

$$K_{sp} = [A^{m+}]^{b}[B^{n-}]^{a}$$

If the **ion product** $Q > K_{sp}$, a **precipitate** forms.

**Ionic strength** is calculated as:

$$I = \frac{1}{2}\sum c_i z_i^{2}$$

At high ionic strength, activities deviate from concentrations, requiring **activity coefficients** $\gamma_i$ where $a_i = \gamma_i [C_i]$.

## Titrations & Pitfalls

Titration curves reveal reaction properties through specific features:

| Feature | Meaning |
| --- | --- |
| **Curve shape** | Depends on strong vs. weak acid/base strength |
| **Buffer regions** | Resist pH change; appear before equivalence |
| **Inflection point** | Marks the exact equivalence point |

**Common-ion effect:** $K_{sp}$ is fixed at a given temperature, but adding a common ion shifts the equilibrium and reduces solubility.

**Common pitfall:** Molecular formulas record composition, not identity. Isomers like ethanol and dimethyl ether share $C_2H_6O$ but differ completely in properties.

## Practice questions

6 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. The empirical formula of a compound always matches its molecular formula.

**Answer:** False

**Why:** False. The empirical formula gives the simplest whole-number ratio; the molecular formula gives the actual count. Glucose $C_6H_{12}O_6$ and formaldehyde $CH_2O$ share the empirical formula $CH_2O$ and are entirely different substances, which is why combustion analysis alone cannot identify a compound.

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/the-empirical-formula-of-a-compound-always-matches-its-molecular

### 2. Complete the statement with the correct term.

**Answer:** The empirical formula of benzene ($C_{6} H_{6}$) is **CH**.

**Why:** Dividing the subscripts by 6: C$_{6}$H$_{6}$ $\to$ CH. The empirical formula gives the simplest integer ratio of atoms.

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/complete-the-statement-with-the-correct-term

### 3. A chemical equation, a particle diagram and a molar calculation describe the same reaction. Why is the particle diagram the one that catches balancing errors?

A. Because moles cannot be represented at the particle level
B. Because the diagram shows the reaction mechanism as well as the stoichiometry
C. Because particle diagrams are drawn to scale and formulas are not
D. Because it shows individual atoms being created or destroyed

**Answer:** D. Because it shows individual atoms being created or destroyed

**Why:** Balancing is conservation of atoms, and only one representation shows atoms. This is why particle diagrams are used to teach it before the symbolic shorthand takes over.

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/a-chemical-equation-a-particle-diagram-and-a-molar-calculation

### 4. Order the levels of chemical representation from smallest (sub-atomic) to largest (macroscopic).

**Answer:**

1. Sub-atomic: electrons, protons, and neutrons
2. Atomic/ionic: individual atoms or ions (e.g., Na⁺, Cl⁻)
3. Molecular/formula: chemical formulas and equations ($H_{2}$O, NaCl)
4. Macroscopic: observable quantities in grams, moles, litres

**Why:** Moving between representation levels requires Avogadro's number (particle ↔ mole) and molar mass (mole ↔ gram).

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/order-the-levels-of-chemical-representation-from-smallest

### 5. One substance, four lenses. Match each representation of ethanol to what it best reveals.

**Answer:**

- Molecular formula C₂H₆O → Atom counts only, composition
- Structural formula CH₃–CH₂–OH → Which atoms bond to which
- Ball-and-stick model → 3D geometry and bond angles
- C₂H₆O vs. its isomer CH₃–O–CH₃ → Same formula, different connectivity

**Why:** Chemical representations trade detail for clarity: formulas count, structures connect, models shape. Isomers prove the stakes, identical formulas, different connectivity, wildly different substances.

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/one-substance-four-lenses-match-each-representation-of-ethanol-to

### 6. One mole of water is 18 g, a small sip. Estimate the order of magnitude: how many **molecules** in that sip? Set the slider to the exponent $n$ in $10^{n}$.

**Answer:** 23.8 (within ±1)

**Why:** ≈ $6\times10^{23}$ molecules, an exponent near 23.8. For scale: that is millions of times more molecules in a sip than there are stars in the observable universe. The mole is the bridge between gram-scale lab work and molecule-scale reality.

Page: https://tryals.app/practice/physics-i/representations-from-particles-to-formulas/one-mole-of-water-is-18-g-a-small-sip-estimate-the-order-of