IMAT Chemistry · Formula sheet

Equilibrium, Kinetics and Energetics formulas

8 formulas, 9 reference tables and 20 common traps for IMAT Chemistry Equilibrium, Kinetics and Energetics, grouped by subtopic.

Full notes with worked examples

Exothermic and Endothermic Reactions, Bond Enthalpies and Hess's Law

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Energy profiles and the activation energy

Energy profile relations

\Delta H = H_{\text{products}} - H_{\text{reactants}} \qquad E_{a,\text{reverse}} = E_{a,\text{forward}} - \Delta H

$E_a$ activation energy, measured from the starting level up to the peak
$\Delta H$ enthalpy change of the forward reaction

Estimating ΔH from bond enthalpies

ΔH from bond enthalpies

\Delta H \approx \sum E(\text{bonds broken}) - \sum E(\text{bonds formed})

$E$ mean bond enthalpy, in kJ/mol

Hess's law and enthalpies of formation

ΔH from enthalpies of formation

\Delta H = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants})

$\Delta H_f^\circ$ standard enthalpy of formation, in kJ/mol, multiplied by the coefficient in the equation

Exothermic and endothermic reactions and the sign of ΔH

Feature	Exothermic	Endothermic
Heat flow	Released to the surroundings	Absorbed from the surroundings
Sign of ΔH	Negative	Positive
Energy of products	Lower than the reactants	Higher than the reactants
Temperature of surroundings	Rises	Falls
Examples	Combustion, respiration, neutralisation, freezing, condensation	Photosynthesis, thermal decomposition of $\mathrm{CaCO_3}$ , melting, dissolving ammonium nitrate

Common traps

Exothermic does not mean fast

Rusting is exothermic but takes weeks, and wood does not catch fire at room temperature even though burning is exothermic. Whether a reaction gives out heat (ΔH) and how fast it goes (the activation energy and the conditions) are separate questions.

Breaking bonds never releases energy

Energy is released when bonds form, and must be supplied to break them. A reaction is exothermic when the bonds formed release more energy than the bonds broken took in.

Activation energy is not the energy difference between products and reactants

The gap between reactants and products is

\Delta H

. The activation energy is the barrier from the reactants up to the transition state. Options describing

E_a

as energy released, or as the products minus the reactants, are wrong.

Bonds broken minus bonds formed, not the other way round

\Delta H \approx

(energy to break bonds) minus (energy released forming bonds). Subtracting in the other order gives the right size with the wrong sign, and that wrong sign is always one of the options.

Formation enthalpy is zero only for the standard form of an element

\Delta H_f^\circ

is zero for

\mathrm{O_2(g)}

or graphite, but not for ozone or diamond, which are not the standard states. And it is products minus reactants, each multiplied by its coefficient.

Entropy, Gibbs Free Energy and Spontaneous Change

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Gibbs free energy and whether a reaction is spontaneous

Gibbs free energy

\Delta G = \Delta H - T\Delta S

$\Delta G$ free energy change, in kJ/mol
$\Delta H$ enthalpy change, in kJ/mol
$T$ absolute temperature, in K
$\Delta S$ entropy change, in kJ/(K mol) when combined with ΔH in kJ

Entropy: a measure of the spreading of matter and energy

Change	Entropy of the system	Why
Ice melting	Increases	Particles become free to move
Steam condensing	Decreases	Gas becomes liquid
$\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)}$	Increases	A gas is produced from a solid
$\mathrm{N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)}$	Decreases	4 mol of gas become 2 mol
Salt dissolving in water	Usually increases	Ions spread through the solution

Common traps

The entropy of the system can fall in a spontaneous change

Water freezes spontaneously below 0 °C although its entropy falls. The heat released raises the entropy of the surroundings by more. The second law is about the total entropy, not the system alone.

Endothermic reactions can be spontaneous

Ice melting above 0 °C and ammonium nitrate dissolving are endothermic yet happen by themselves, because their entropy increase is large enough. A positive ΔH alone does not rule out a spontaneous change.

Spontaneous does not mean fast

ΔG tells you whether a reaction can go, not how quickly. A mixture of hydrogen and oxygen has a very negative ΔG for forming water, yet it can sit unchanged for years until a spark supplies the activation energy.

Reaction Rate, Collision Theory, Catalysts and Rate Laws

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Measuring the rate of a reaction

Average rate

\text{rate} = \frac{\Delta[\text{reactant or product}]}{\Delta t}

$\Delta[\ ]$ change in concentration, in mol/dm³ (taken as positive)
$\Delta t$ time taken, in s

Rate laws and orders of reaction are found by experiment

Rate law

\text{rate} = k\,[\mathrm{A}]^m\,[\mathrm{B}]^n

$k$ rate constant, fixed at a given temperature
$m, n$ orders with respect to A and B, found by experiment

Collision theory and the factors that change the rate

Factor increased	Effect on rate	Why
Concentration of a solution	Faster	More particles per volume, so more frequent collisions
Pressure of a gas	Faster	Particles closer together, so more frequent collisions
Surface area of a solid	Faster	More particles exposed, so more frequent collisions
Temperature	Faster	Mainly a larger fraction of collisions with energy at least $E_a$
Catalyst added	Faster	Lower activation energy, so more collisions succeed

Catalysts: a lower-energy route, not more product

Feature	What a catalyst does
Activation energy	Lowers it, for both the forward and the reverse reaction
Rate	Increases the rates of both directions equally
ΔH	No change
Equilibrium position, K and yield	No change; equilibrium is reached sooner
Amount at the end	Same as at the start
Examples	$\mathrm{MnO_2}$ for $\mathrm{H_2O_2}$ decomposition, iron in ammonia synthesis, enzymes

Common traps

A faster reaction does not make more product

Speeding a reaction up gets to the end sooner, but the amount of product is fixed by the limiting reactant. Doubling the amount of the limiting reactant doubles the product; doubling only the rate does not.

Pressure and concentration change how often particles collide, not how hard

Raising the pressure of a gas at constant temperature speeds a reaction because collisions become more frequent. It does not give more molecules energy above the activation energy: only a rise in temperature does that, and a catalyst lowers the barrier instead.

A catalyst never increases the yield

A catalyst gets a reversible reaction to equilibrium faster, but the equilibrium mixture is exactly the same as without it. Options saying a catalyst increases the yield, shifts the equilibrium or changes K are always wrong.

Orders are not the coefficients of the equation

The rate law of a reaction cannot be read from its balanced equation, because most reactions go through several steps. Options like rate = k[A][B] written straight from A + B → C are guesses; the right answer is that the rate law is found by experiment. For a simple reaction, the products do not normally appear in it.

Dynamic Equilibrium and the Equilibrium Constant Kc

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Writing the Kc expression

Equilibrium constant

K_c = \frac{[\mathrm{C}]^c\,[\mathrm{D}]^d}{[\mathrm{A}]^a\,[\mathrm{B}]^b}

$[\ ]$ equilibrium concentration, in mol/dm³
$a, b, c, d$ coefficients in the balanced equation

Calculating Kc and what its size means

Concentration from amount

c = \frac{n}{V}

$c$ concentration, in mol/dm³
$n$ amount at equilibrium, in mol
$V$ volume of the vessel, in dm³

Dynamic equilibrium in a closed system

Feature	At dynamic equilibrium
Forward and reverse rates	Equal, and both greater than zero
Concentrations	Constant, but usually not equal
System	Closed: no matter enters or leaves
Starting point	The same equilibrium is reached from either side
Evidence that it is dynamic	A labelled isotope added to one side soon appears on the other side

Common traps

Equilibrium does not mean equal amounts

At equilibrium the rates are equal, not the concentrations. The mixture may be almost all products, almost all reactants, or anything between, depending on K.

Solids and pure liquids are not in Kc

A solid's concentration is fixed by its density, so it is left out of Kc. Adding or removing some of a solid therefore does not shift an equilibrium. To shift it, change the concentration of a gas or a dissolved species, or the temperature.

A small Kc means few products, not fewer moles on one side

A Kc much smaller than 1 tells you the equilibrium lies to the left, with mostly reactants. It says nothing about which side of the equation has more moles, and nothing about how fast equilibrium is reached.

Le Chatelier's Principle: Concentration, Pressure, Temperature and Catalysts

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Changing a concentration shifts the equilibrium to oppose it

Change	Shift	Reason
Add a reactant	To the right	The forward reaction uses up the extra reactant
Remove a product	To the right	The forward reaction replaces it
Add a product	To the left	The reverse reaction uses up the extra product
Add a substance that reacts with a product	To the right	That product is being removed
Add more of a pure solid	No shift	A solid is not in Kc

Changing the pressure: count the moles of gas

Equilibrium	Moles of gas, left : right	Higher pressure shifts
$\mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3}$	4 : 2	To the right
$\mathrm{N_2O_4 \rightleftharpoons 2NO_2}$	1 : 2	To the left
$\mathrm{H_2 + I_2 \rightleftharpoons 2HI}$	2 : 2	No shift
$\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$	0 : 1	To the left

Changing the temperature: the only change that alters K

Forward reaction	Raise the temperature	Lower the temperature
Exothermic (ΔH negative)	Shifts left; K decreases	Shifts right; K increases
Endothermic (ΔH positive)	Shifts right; K increases	Shifts left; K decreases
Self-ionisation of water (endothermic)	Kw increases; pH falls below 7; still neutral	Kw decreases; pH rises above 7; still neutral

Putting the factors together: the compromise in ammonia synthesis

Condition	Effect on equilibrium yield	Effect on rate	Choice in the Haber process
Higher pressure	Increases	Increases	About 200 atm
Lower temperature	Increases	Decreases	A compromise near 450 °C
Catalyst	No effect	Increases	Iron
Removing ammonia	Increases the conversion	Keeps the forward reaction going	Ammonia condensed out

Common traps

Adding a solid does not shift an equilibrium

In an equilibrium with a solid on one side, adding or removing some of that solid changes nothing, because a solid does not appear in Kc. Only the gases and dissolved species can be used to push the equilibrium.

A reagent that removes a product shifts the equilibrium right

You do not have to add a reactant to drive an equilibrium forward. Adding a substance that reacts with one of the products (an alkali removing

\mathrm{H^+}

, for example) also shifts it to the right. Adding a substance that supplies a product shifts it to the left.

Count gas moles only

In an equilibrium with solids or liquids, only the gases decide the effect of pressure. For

\mathrm{C(s) + CO_2(g) \rightleftharpoons 2CO(g)}

the count is 1 : 2, not 2 : 2.

Heating an exothermic equilibrium lowers K

For an exothermic forward reaction, raising the temperature shifts the equilibrium left and decreases K; lowering the temperature increases K. Options pairing an exothermic reaction with a K that rises on heating are wrong.

Pure water is neutral at every temperature

Neutral means

[\mathrm{H^+}] = [\mathrm{OH^-}]

, not pH 7. Hot pure water has a pH below 7 because more of it ionises, but the two ion concentrations stay equal, so it is still neutral.

Equilibrium, Kinetics and Energetics formulas

Exothermic and Endothermic Reactions, Bond Enthalpies and Hess's Law

Energy profiles and the activation energy

Estimating ΔH from bond enthalpies

Hess's law and enthalpies of formation

Exothermic and endothermic reactions and the sign of ΔH

Common traps

Entropy, Gibbs Free Energy and Spontaneous Change

Gibbs free energy and whether a reaction is spontaneous

Entropy: a measure of the spreading of matter and energy

Common traps

Reaction Rate, Collision Theory, Catalysts and Rate Laws

Measuring the rate of a reaction

Rate laws and orders of reaction are found by experiment

Collision theory and the factors that change the rate

Catalysts: a lower-energy route, not more product

Common traps

Dynamic Equilibrium and the Equilibrium Constant Kc

Writing the Kc expression

Calculating Kc and what its size means

Dynamic equilibrium in a closed system

Common traps

Le Chatelier's Principle: Concentration, Pressure, Temperature and Catalysts

Changing a concentration shifts the equilibrium to oppose it

Changing the pressure: count the moles of gas

Changing the temperature: the only change that alters K

Putting the factors together: the compromise in ammonia synthesis

Common traps

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