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FORMULA SHELF 18 of 370

The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.

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Chemistry 18 formulas

Avogadro's law
V is proportional to n at constant temperature and pressure
SYMBOLS · equal volumes of gas at the same temperature and pressure contain equal numbers of molecules
UNITS · varies
HOW TO USE

The rule that lets you scale up a gas reaction - a bottle of gas and a cylinder of gas behave the same way.

EXAMPLE

Double the moles in a fixed vessel and you double the pressure.

gas avogadro moles volume
Boyle's, Charles's and Gay-Lussac's laws
Boyle: P x V = constant ; Charles: V / T = constant ; Gay-Lussac: P / T = constant
SYMBOLS · T must be in kelvin (C + 273)
UNITS · varies
HOW TO USE

Each one holds the other two constant. A cold bottle warms in the sun and the pressure goes up, which is why a bottle left in a hot shed can go off.

EXAMPLE

Gas at 10 C in a bottle warms to 30 C and its pressure rises by about 7%.

gas boyle charles pressure temperature
Buffer pH (Henderson-Hasselbalch)
pH = pKa + log10 of (base / acid)
SYMBOLS · pKa = the pH at which the acid is half turned into base
UNITS · pH units
HOW TO USE

How a milk, a must, or a soil stays at a steady pH while things are added to it. A brine is a buffer, and so is the lime in a soil.

EXAMPLE

A phosphate buffer with pKa 6.8 and equal parts has a pH of 6.8.

buffer ph milk brine soil
Dilution
c1 x V1 = c2 x V2
SYMBOLS · c1, V1 = the stock solution; c2, V2 = what you want to make
UNITS · mol/L and litres
HOW TO USE

Every time you mix a concentrate with water, for a spray, a disinfectant or a test solution. Always add the concentrate to the water, never the other way round.

EXAMPLE

50 mL of 5 mol/L acid made up to 500 mL = 0.5 mol/L.

dilution concentration mixturing spray acid
Enthalpy change of a reaction
dH = sum of the enthalpy of the products - sum of the enthalpy of the reactants
SYMBOLS · negative means exothermic (gives out heat), positive means endothermic (takes heat in)
UNITS · kJ/mol
HOW TO USE

Why a compost heap gets hot, why a lime slurry in a slurry tank warms, and why a soaking cold feed makes the animal cold.

EXAMPLE

Fermenting fruit releases heat; the vat warms by a few degrees.

enthalpy heat reaction compost lime
Freezing point depression
dT(freeze) = i x Kf x m
SYMBOLS · i = the number of particles the solute splits into; Kf = the freezing constant of the solvent (water 1.86 K per mol/kg); m = molality in mol per kg of solvent
UNITS · degrees C
HOW TO USE

Why salt melts ice on a road, why a brine freezes below zero, and why a freezer with a brine tank is colder than one with water.

EXAMPLE

A 10% salt brine freezes at about -6 C.

freezing brine salt ice antifreeze
Ideal gas law
P x V = n x R x T
SYMBOLS · P = pressure (Pa); V = volume (m3); n = moles; R = 8.314 J/mol K; T = temperature (K)
UNITS · Pa m3
HOW TO USE

The rule behind a pressure cooker, a tyre, a gas cylinder and a fermenting barrel. Pressure rises with temperature and with the amount of gas, and falls as the volume grows.

EXAMPLE

A 20 L bottle at 20 C and 2 bar holds roughly 0.8 moles.

gas pressure cooker cylinder temperature
Law of conservation of mass
mass of reactants = mass of products
SYMBOLS · in a closed system, nothing is created or destroyed
UNITS · g, kg
HOW TO USE

The reason a sealed compost bin gains mass (it gains the carbon dioxide that leaves) and the reason a fire seems to lose mass - the carbon dioxide and water vapour have left the shed.

EXAMPLE

A burning log loses mass as gases escape, not because matter vanished.

mass conservation compost fire
Molarity
c = n / V
SYMBOLS · c = concentration (mol/L); n = moles; V = volume in litres
UNITS · mol/L
HOW TO USE

The standard way to say how strong a solution is. A 1 mol/L solution of sodium hydroxide is 40 g of it in a litre of water.

EXAMPLE

50 g of NaOH (40 g/mol) in 2 L = 0.625 mol/L.

QUICK CALCULATOR c = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

molarity concentration solution moles
Moles and molar mass
n = m / M
SYMBOLS · n = moles; m = mass (g); M = molar mass (g/mol) from the periodic table
UNITS · mol
HOW TO USE

The bridge between grams and reactions. Every recipe that uses chemicals is really counting molecules.

EXAMPLE

36 g of water is 2 moles, because H2O is 18 g/mol.

QUICK CALCULATOR n = result
Enter values above.

Convenience only. Double-check the result against the worked example or a second method before you use it.

moles molar mass chemistry
Parts per million
ppm = mg per kg (or mg per litre for dilute solutions)
SYMBOLS · 1% = 10,000 ppm; 1 ppm = 1 mg per kg
UNITS · ppm, mg/kg
HOW TO USE

For trace elements in soil and feed, nitrate in water, and anything described as 'trace'. A soil test of 30 ppm copper is very different from 30 percent.

EXAMPLE

1 g per tonne = 1 ppm.

ppm trace soil water analysis
Percentage concentration
% (w/w) = (mass of solute / mass of solution) x 100 ; % (v/v) = (volume of solute / volume of solution) x 100
SYMBOLS · solution = solute plus solvent
UNITS · %
HOW TO USE

For a 2% milk replacer mix, a 1% iodine solution, a 5% bleach mix or a salt brine. Note that the denominator is the solution, not the water.

EXAMPLE

25 g of powder in 1 litre of water is about 2.4% w/v.

concentration percentage brine mix replacer
Percentage yield
yield % = (actual amount / theoretical amount) x 100
SYMBOLS · theoretical = what the equation says you should get; actual = what you ended up with
UNITS · %
HOW TO USE

How well a process actually ran. A lime neutralisation that only reaches 80% means you need more lime than the label says.

EXAMPLE

You need 50 kg of chalk and get 41 kg of product = 82% yield.

yield efficiency lime reaction
Stoichiometry from a balanced equation
moles of product = moles of reactant x the ratio of coefficients
SYMBOLS · read the coefficients off the balanced equation
UNITS · mol, g
HOW TO USE

For making a solution of a known strength, for a lime neutralisation calculation, and for anything where the reaction has to be right rather than roughly right.

EXAMPLE

CaCO3 + 2HCl gives CaCl2, so 1 mole of chalk needs 2 moles of acid.

stoichiometry reaction balanced equation chemistry
Titration
c1 x V1 = c2 x V2
SYMBOLS · c1, V1 = the solution in the burette; c2, V2 = the flask
UNITS · mol/L, mL
HOW TO USE

For working out the strength of a bought solution, and for checking a soil or water test against the method. The end point is the colour change, so get it right before you read the burette.

EXAMPLE

25 mL of unknown acid neutralised by 20 mL of 0.1 mol/L alkali is 0.08 mol/L.

titration acid alkali neutralisation test
Water hardness
hardness (mg/L as CaCO3) = (mg/L of Ca x 2.5) + (mg/L of Mg x 4.1)
SYMBOLS · hard water is over 200 mg/L; very hard is over 400 mg/L
UNITS · mg/L
HOW TO USE

To decide whether a borehole needs a softener, and why soap will not lather and the kettle furs up.

EXAMPLE

40 mg/L of calcium gives 100 mg/L of hardness.

water hardness softener borehole kettle
pH
pH = -log10 of hydrogen ion concentration
SYMBOLS · each whole pH step is a tenfold change in acidity
UNITS · pH units
HOW TO USE

Soil, water, antacids and preserves. A change of one unit is ten times more or less acid, which is why a small pH change matters so much. See Soil Ph And Lime.

EXAMPLE

pH 6 is ten times more acid than pH 7.

ph acidity soil water preserving
pH, pOH and the pH scale
pH + pOH = 14 (at 25 C) ; pH = 14 - pOH
SYMBOLS · pOH = -log10 of hydroxide ion concentration
UNITS · pH units
HOW TO USE

For checking that a caustic solution is strong enough, and for understanding why a wash and a rinse need different strengths.

EXAMPLE

A solution at pH 12 has pOH 2.

ph poh alkali caustic cleaning
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