IMAT Chemistry · Formula sheet

Periodic Table formulas

4 formulas, 9 reference tables and 14 common traps for IMAT Chemistry Periodic Table, grouped by subtopic.

Groups, Periods, Blocks and Typical Charges

Typical ion charges from the group, and writing ionic formulas

Charge balance in an ionic formula

\sum (\text{ion charge} \times \text{number of ions}) = 0

Groups, periods and blocks of the periodic table

Block	Groups	Subshell being filled	Examples
s-block	Groups 1 and 2 (and helium)	ns	Na, Mg, Ca
p-block	Groups 13 to 18	np	C, O, Cl, Ne
d-block	Groups 3 to 12	(n−1)d	Fe, Cu, Zn
f-block	Lanthanides and actinides, drawn as two rows below	(n−2)f	Ce, U

Metals, non-metals and metalloids

Class	Where in the table	Typical physical properties	Oxides	Examples
Metals	Left and centre, below the staircase	Shiny, conduct heat and electricity, malleable; mostly solids (mercury is a liquid)	Basic; a few amphoteric	Na, Mg, Fe, Cu
Non-metals	Right, above the staircase, plus hydrogen	Dull, poor conductors (graphite conducts), brittle as solids; many are gases	Acidic ( $\mathrm{CO_2}$ , $\mathrm{SO_2}$ ) or neutral (CO, $\mathrm{H_2O}$ )	C, N, O, S, Cl
Metalloids	Along the staircase	Look metallic but are brittle; semiconductors	Weakly acidic or amphoteric	B, Si, Ge, As

Common traps

Group 13 to 18 elements have the group number minus 10 valence electrons

Chlorine is in group 17 but has 7 valence electrons, not 17. With the old numbering it is group VII, which gives 7 directly. Check which numbering the question uses.

Aluminium is a metal, not a metalloid

Aluminium touches the staircase line but is a good conductor and a typical metal. Its oxide is amphoteric, which can mislead. The metalloids are B, Si, Ge, As, Sb and Te.

Group 13 metals form 3+ ions

Aluminium, gallium and indium form

\mathrm{M^{3+}}

, so their oxides are

\mathrm{M_2O_3}

, their sulfates

\mathrm{M_2(SO_4)_3}

and their carbonates (where they exist)

\mathrm{M_2(CO_3)_3}

. A formula like

\mathrm{AlSO_4}

treats the metal as 2+ and is wrong.

Atomic Radius and Ionic Radius

Learn this subtopic in the notes

Common traps

An atom gets smaller across a period even though it gains electrons

Adding electrons sounds like it should make an atom bigger, but along a period they go into the same shell while the nuclear charge rises. The stronger pull wins. Radius increases from right to left and from top to bottom.

A positive ion is smaller than its atom, never larger

Losing electrons removes the outer shell and leaves the full nuclear charge pulling on fewer electrons. So

\mathrm{Mg^{2+}}

is smaller than Mg. It is negative ions that are larger than their atoms.

Ionisation Energy, Electron Affinity and Electronegativity

Learn this subtopic in the notes

First and successive ionisation energies

First ionisation energy

\mathrm{X(g)} \rightarrow \mathrm{X^{+}(g)} + e^- \qquad \Delta H > 0

$\mathrm{X(g)}$ a gaseous atom of the element
$\Delta H$ energy change, in kJ/mol; positive because energy is taken in

First and second electron affinity

\mathrm{X(g)} + e^- \rightarrow \mathrm{X^{-}(g)} \qquad \mathrm{X^{-}(g)} + e^- \rightarrow \mathrm{X^{2-}(g)}

first equationfirst electron affinity: one gaseous atom gains one electron
second equationsecond electron affinity: the gaseous 1− ion gains another

Electronegativity and its values

Element	Pauling value	Where it sits
Fluorine	3.98	Top of group 17: the highest of all
Oxygen	3.44	Group 16, period 2: second highest
Chlorine	3.16	Group 17, period 3
Nitrogen	3.04	Group 15, period 2
Carbon	2.55	Group 14, period 2
Hydrogen	2.20	Slightly below carbon
Sodium	0.93	Group 1, period 3
Caesium	0.79	Group 1, period 6: among the lowest

Summary of the periodic trends across a period and down a group

Property	Across a period (left to right)	Down a group	Main reason
Atomic radius	Decreases	Increases	Nuclear charge across; extra shells down
First ionisation energy	Increases (small dips at groups 13 and 16)	Decreases	How tightly the outer electron is held
Electronegativity	Increases	Decreases	Pull of the nucleus on shared electrons
First electron affinity	Generally more exothermic	Less exothermic (from chlorine down)	Pull of the nucleus on an added electron
Metallic character	Decreases	Increases	Ease of losing electrons
Reactivity of metals (groups 1, 2)	Group 1 more reactive than group 2	Increases	Ease of losing electrons
Reactivity of halogens (group 17)	Halogens most reactive in their period	Decreases	Ease of gaining an electron

Common traps

The noble gas, not the halogen, has the highest ionisation energy in a period

Ionisation energy keeps rising across a period all the way to group 18. Halogens are high but each noble gas is higher. Down a group it falls, so an element lower in the same group always has the smaller value.

Second electron affinities are endothermic

The first electron affinity of oxygen or sulfur is exothermic, but the second is strongly endothermic. Options giving both as exothermic, or the first as very exothermic and the second as exothermic too, are wrong.

Oxygen is more electronegative than chlorine

Fluorine is first and oxygen second. Chlorine and nitrogen come after oxygen. Picking chlorine because it is a halogen is the usual slip.

Metal reactivity rises down a group; halogen reactivity falls

Metals react by losing electrons, which gets easier further down, so caesium is more reactive than lithium. Halogens react by gaining electrons, which gets harder further down, so fluorine is more reactive than iodine. Melting points of the halogens rise down the group while their electronegativity and ionisation energy fall.

Alkali Metals, Alkaline Earth Metals, Halogens and Noble Gases

Learn this subtopic in the notes

Group 1: the alkali metals

Metal	Melting point (°C, approx.)	Reaction with cold water	Flame colour
Lithium	181	Fizzes steadily	Crimson red
Sodium	98	Melts into a ball and darts across the surface	Yellow-orange
Potassium	63	Melts and the hydrogen catches fire	Lilac
Rubidium	39	Violent	Red-violet
Caesium	28	Explosive	Blue-violet

Group 2: the alkaline earth metals

Metal	Reaction with water	Hydroxide	Note
Beryllium	No reaction, even with steam	$\mathrm{Be(OH)_2}$ , amphoteric	Its oxide is amphoteric, unlike the rest
Magnesium	Very slow with cold water; fast with steam, giving MgO	$\mathrm{Mg(OH)_2}$ , barely soluble	Burns with a bright white flame
Calcium	Steady fizzing with cold water	$\mathrm{Ca(OH)_2}$ , slightly soluble (limewater)	Limewater turns milky with $\mathrm{CO_2}$
Barium	Vigorous with cold water	$\mathrm{Ba(OH)_2}$ , quite soluble	$\mathrm{BaSO_4}$ is insoluble (used in X-ray imaging)

Group 17: the halogens

Halogen	State at room temperature	Colour	Oxidising power
Fluorine, $\mathrm{F_2}$	Gas	Pale yellow	Strongest
Chlorine, $\mathrm{Cl_2}$	Gas	Yellow-green	Strong
Bromine, $\mathrm{Br_2}$	Liquid	Red-brown	Moderate
Iodine, $\mathrm{I_2}$	Solid	Shiny grey-black solid; violet vapour when heated	Weakest of the four

Group 18: the noble gases

Gas	Outer-shell electrons	Typical use
Helium	2	Balloons (light and non-flammable); cooling the magnets in MRI scanners
Neon	8	Advertising signs that glow red
Argon	8	Inert atmosphere for welding; filling light bulbs
Xenon	8	Bright lamps; forms compounds such as $\mathrm{XeF_4}$

Common traps

In a metal hydride, hydrogen is negative

Hydrogen is +1 in water and acids, but in ionic hydrides of groups 1 and 2 it is the

\mathrm{H^-}

ion, oxidation state −1. The metal is always positive.

The oxide formula gives the group away

A metal oxide

\mathrm{M_2O}

points to group 1, MO to group 2 and

\mathrm{M_2O_3}

to group 13. A metal that reacts with water and forms an ionic, basic oxide MO belongs to group 2.

Halogen reactivity falls down the group

Fluorine is the most reactive halogen and iodine the least of the four common ones, the opposite of group 1. Electronegativity and first ionisation energy also fall down the group, while melting and boiling points rise.

Transition Metals and Their Oxidation States

Learn this subtopic in the notes

Finding the oxidation state of a metal in a compound or ion

Sum of oxidation states

\sum \text{oxidation states of all atoms} = \text{overall charge}

Properties of the transition metals

Ion	Electron configuration	Colour in water
$\mathrm{Cr^{3+}}$	$[\mathrm{Ar}]\,3d^3$	Green
$\mathrm{Mn^{2+}}$	$[\mathrm{Ar}]\,3d^5$	Very pale pink
$\mathrm{Fe^{2+}}$	$[\mathrm{Ar}]\,3d^6$	Pale green
$\mathrm{Fe^{3+}}$	$[\mathrm{Ar}]\,3d^5$	Yellow to orange-brown
$\mathrm{Cu^{2+}}$	$[\mathrm{Ar}]\,3d^9$	Blue
$\mathrm{Zn^{2+}}$	$[\mathrm{Ar}]\,3d^{10}$	Colourless

The configurations follow the rule from Atomic Structure: the 4s electrons leave first.

Common traps

Not every transition metal is reactive

Iron rusts and zinc reacts with dilute acids, but copper does not react with dilute hydrochloric or sulfuric acid at all. Statements that all transition metals are reactive, or that all their ions are coloured, are false.

Share the total between the metal atoms

\mathrm{K_2Cr_2O_7}

the two chromium atoms together carry +12, so each is +6. Answering with the total is a classic distractor whenever the metal appears more than once in the formula.

Periodic Table formulas

Groups, Periods, Blocks and Typical Charges

Typical ion charges from the group, and writing ionic formulas

Groups, periods and blocks of the periodic table

Metals, non-metals and metalloids

Common traps

Atomic Radius and Ionic Radius

Common traps

Ionisation Energy, Electron Affinity and Electronegativity

First and successive ionisation energies

Electronegativity and its values

Summary of the periodic trends across a period and down a group

Common traps

Alkali Metals, Alkaline Earth Metals, Halogens and Noble Gases

Group 1: the alkali metals

Group 2: the alkaline earth metals

Group 17: the halogens

Group 18: the noble gases

Common traps

Transition Metals and Their Oxidation States

Finding the oxidation state of a metal in a compound or ion

Properties of the transition metals

Common traps

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