CHEM1011 · Fundamentals Of Chemistry 1a
Solutions and Periodic Trends
This chapter pairs the solution-prep maths you reach for in every wet-lab problem with the periodic trends that explain why elements behave the way they do. You will learn to count moles in a beaker with c = n/V, dilute a stock with c₁V₁ = c₂V₂, and then predict atomic radius, ionisation energy and electronegativity from one idea — effective nuclear charge. It is a guaranteed source of marks: numeric short-answer items test the concentration triangle, while high-frequency MCQs test whether you can read a trend off the periodic table and justify it.
What this chapter covers
- 011. Solute, solvent, solution: aqueous (aq) and homogeneous mixtures
- 022. Molarity c = n/V (mol L⁻¹) and the rearrangement n = cV
- 033. The mole triangle: chaining n = cV with n = m/M
- 044. Dilution: c₁V₁ = c₂V₂ (moles of solute conserved)
- 055. Effective nuclear charge Z_eff = Z − S (nuclear pull minus shielding)
- 066. Atomic radius: smaller across a period, bigger down a group
- 077. Ionisation energy and electronegativity as the mirror of radius
- 088. The ΔEN bond-type cut (covalent vs ionic) and ionic radius (cation < atom < anion)
Mass of solid needed for a target molarity
- +1Convert the volume to litres: 250 mL = 0.250 L. (Leaving V in mL is the single most common error.)
- +1Find moles of solute with n = cV: n = 0.0800 × 0.250 = 0.0200 mol.
- +1Convert moles to mass with m = nM: m = 0.0200 × 105.99 = 2.1198 g ≈ 2.12 g (3 s.f.).
- +1State the method: weigh 2.12 g, dissolve in a little water in a 250 mL volumetric flask, then make up to the mark — the volume is the solution volume, not the water added.
Key terms
- Molarity (c)
- Concentration measured as moles of solute per litre of solution, c = n/V, with units mol L⁻¹ (written M). V must be in litres before substituting.
- Dilution (c₁V₁ = c₂V₂)
- Adding solvent changes volume and concentration but not the moles of solute, so the product cV is conserved: subscript 1 is the concentrated stock, 2 is the dilute result.
- Effective nuclear charge (Z_eff)
- The net positive pull a valence electron actually feels, Z_eff = Z − S, where Z is the proton count and S is the shielding by inner core electrons.
- Ionisation energy
- The energy required to remove an electron from a gaseous atom, X(g) → X⁺(g) + e⁻; it increases across a period and decreases down a group.
- Electronegativity (EN)
- The ability of a bonded atom to attract the shared bonding electrons; it scales with Z_eff/r², increases across a period, decreases down a group, and is highest for fluorine.
- Ionic radius
- The size of an ion: a cation is smaller than its parent atom (electrons lost, stronger net pull) and an anion is larger (added repulsion and shielding); for an isoelectronic series, more protons means a smaller ion.
Solutions and Periodic Trends FAQ
How do I find the mass of solid to make a solution of a given molarity?
Convert the target volume to litres, find moles with n = cV, then convert to mass with m = nM. In one line, m = c × V × M. Read the molar mass off the periodic table provided and report to 3 significant figures with the unit (g).
When do I use c₁V₁ = c₂V₂ instead of c = n/V?
Use the dilution relation whenever you take a concentrated stock and add solvent to reach a target concentration — the moles of solute do not change, only the volume and concentration. Use c = n/V (or n = cV) when you are converting between moles, volume and concentration for a single solution, or preparing one from a solid.
Why does atomic radius decrease across a period but increase down a group?
Across a period, protons are added to the same shell faster than shielding grows, so effective nuclear charge rises and the shell is pulled in tighter — the atom shrinks. Down a group, each new row adds a whole electron shell, so the valence electrons sit further out and the atom grows. Ionisation energy and electronegativity are the mirror image of radius.
How do I decide if a bond is ionic or covalent from electronegativity?
Take the difference in electronegativity, ΔEN, between the two bonded atoms. ΔEN near 0 is non-polar covalent (equal sharing), roughly 0 to ~2 is polar covalent (unequal sharing, partial δ±), and greater than ~2 is ionic (electron effectively transferred). Treat the cutoff as a guide — bonding is a continuum, not a hard wall.
What is on the exam for this topic?
Expect a numeric short-answer item on solution prep or dilution (find a mass, concentration or volume to 3 s.f.), and high-frequency MCQs asking you to rank elements or ions by radius, ionisation energy or electronegativity. Marks for trend questions are in the justification — always cite Z_eff and shielding, not just the direction.
Exam move
Drill the concentration triangle until it is automatic: memorise c = n/V, n = m/M and the dilution relation c₁V₁ = c₂V₂, and make converting mL → L the first thing you do on every problem — that one habit kills the most common lost mark. For periodic trends, learn radius as your anchor (smaller across a period, bigger down a group) and treat ionisation energy and electronegativity as its mirror image, so one fact gives you three trends. Practise justifying every prediction with effective nuclear charge and shielding, because in trend questions the marks are in the reason, not the direction. Molar masses and constants are on the provided datasheet, so spend zero memory there and all of it on the four relations and the trend directions.
