HESI A2 Chemistry study guide

What this topic actually asks of you

Chemistry on this exam asks what matter is made of and what happens to it when it changes. Two habits do the work: name the particle-level reason — a proton count, a shared pair of electrons, an ion's charge, a mole of particles — and carry the units through the arithmetic. A memorized paragraph does not carry a calculation; a particle-level reason and the units do. Most of the work on this page is a count to finish: electrons lost or gained, atoms on each side of an arrow, grams per mole, moles per liter, half-lives elapsed.

Elsevier lists chemistry among the areas the HESI A2 covers. The publisher releases no national content specification — no item count, no clock, no cut score — so nothing on this page mirrors an official weighting, and nothing here claims to. The scope below is a teaching scope: matter and change, the atom, the periodic table, bonding, and then the arithmetic chemistry questions are built on — moles, solutions, pH and half-life.

The element data on this page follows the NIST periodic table and reference data and the NIH's PubChem, and the unit conventions follow NIST Special Publication 811. All three are US federal government material, which is not subject to copyright in the United States.

The seventeen ideas this page teaches

These are the ideas this page teaches, and they are its headings.

1. Matter and its states — what matter is, and how solids, liquids, gases and plasmas differ.
2. Physical and chemical change — how to tell a change of form from a change of identity, and how to classify a sample as an element, a compound or a mixture.
3. Atomic structure — protons, neutrons and electrons, and where each one sits.
4. Atomic number, mass number, isotopes and ions — the four counts that describe an atom.
5. Electron shells and valence electrons — why the outermost shell decides how an atom behaves.
6. The periodic table — groups, periods, the metal and nonmetal divide, and the three trends.
7. Ionic bonding — a transfer of electrons, and a formula built from charge balance.
8. Covalent bonding — a shared pair, and the electronegativity difference that makes a bond polar.
9. Intermolecular forces and hydrogen bonds — why water boils so high.
10. Formulas, names and polyatomic ions — writing a formula from its name and a name from its formula.
11. Reaction types and balancing — synthesis, decomposition, replacement, combustion, and the atom count that has to match on both sides.
12. The mole and molar mass — the bridge between a balance reading and a particle count.
13. Solutions and concentration — molarity, dilution and percent by mass.
14. Acids, bases, pH and buffers — the proton, the logarithm, and what a buffer resists.
15. Reaction rates, catalysts and enzymes — what speeds a reaction up without being consumed.
16. Nuclear change and half-life — the changes that are not chemistry, and the one calculation that describes them.
17. The four families of biological molecules — carbohydrates, lipids, proteins and nucleic acids, in the terms chemistry uses.

Matter and its states

Matter is anything with mass and volume. Every sample of it is either a pure substance — one kind of particle, and either an element or a compound — or a mixture of substances that keep their own identities.

The state of a sample is set by how much energy its particles have, and by how strongly they attract one another.

A change of state has a name for each direction, and those names are the vocabulary a question uses.

Two of those pairs happen at the same temperature, which is worth saying once: melting and freezing both occur at the melting point, and vaporization and condensation both occur at the boiling point. The pressure matters too — water boils below 100 °C on a mountain, because the air above it presses down less hard.

A vapor is the gas form of a substance that is a liquid or a solid at room temperature. Steam and water vapor are the same substance as liquid water; the difference is state, not identity.

Kelvin, and the three temperature scales

Three scales measure the same motion of particles, and what differs between them is where each one puts zero. Celsius puts 0 °C at the freezing point of water and 100 °C at its boiling point, both at one atmosphere. Kelvin puts 0 K at absolute zero — the point past which no further motion can be removed from a particle — and keeps Celsius's step size, so a step of one kelvin is exactly a step of one degree Celsius. Fahrenheit uses a smaller step and a different zero again.

• kelvin = °C + 273.15
• °C = K − 273.15
• °F = (°C × 9/5) + 32

Absolute zero is 0 K, −273.15 °C and −459.67 °F. Water freezes at 273.15 K (373.15 K at the boil). Normal body temperature, 37.0 °C, is 310.15 K and 98.6 °F.

Worked example. Convert 25.0 °C to both other scales. Kelvin: 25.0 + 273.15 = 298.15 K. Fahrenheit: (25.0 × 9/5) + 32 = 45.0 + 32 = 77.0 °F. Check the direction of each move: a kelvin value is always the larger of the pair for ordinary temperatures, and a Celsius reading below zero becomes a kelvin value below 273 but above zero.

Gas laws take kelvin, not Celsius, because a gas's volume and pressure track the speed of its particles, and only the kelvin scale starts at the temperature where that motion stops. A Celsius value substituted for a kelvin one in a gas calculation gives an answer that is wrong without looking wrong.

Energy, specific heat and a temperature change

Temperature measures the average motion of a substance's particles, and the energy that changes it arrives as heat. How far the temperature moves for a given amount of energy is a property of the substance, and the number that records it is the specific heat: the energy needed to raise one gram of the substance by one degree Celsius. Water's value is 4.18 J/(g·°C), high because much of the added energy goes into loosening the hydrogen bonds between molecules instead of speeding those molecules up. That single number explains why a pot of water takes far longer than a metal pan of the same mass to reach the same temperature: aluminum's specific heat is under a quarter of water's, so the same energy lifts its temperature nearly five times as far.

• q = m × c × ΔT — energy in joules, mass in grams, specific heat in J/(g·°C), temperature change in °C.
• A temperature fall releases the energy a rise of the same size would have taken, so the sign of ΔT carries the direction.

Worked example. How much energy raises 50.0 g of water by 10.0 °C? Energy = 50.0 × 4.18 × 10.0 = 2 090 J, a little over 2 kJ. Tipped into 50.0 g of aluminum instead, those 2 090 J raise its temperature by 2 090 ÷ (50.0 × 0.897) = 46.6 °C, which is the same compare and contrast, read backwards.

Chemists often quote the energy per mole rather than per gram; the arithmetic is unchanged, with molar mass standing where mass stood.

Physical and chemical change

A physical change alters how a substance looks, moves or is arranged, and leaves its identity alone. A chemical change produces a new substance, with different properties and a different formula.

The evidence for a chemical change is a new substance, and the everyday signs of one are: a gas produced without heating, a precipitate (a solid appearing when two clear solutions are mixed), a color change that will not wash out, a new odor, or heat and light released. Each sign is evidence, not proof — boiling water produces bubbles and gives off no new substance at all.

Samples classify on the same evidence, and the four classes are worth keeping apart.

A mixture can be made in any proportion — a spoon of salt or a cup of salt both dissolve in a liter of water — and a compound cannot. That ratio is the surest way to tell the two apart: water is always 2 hydrogens to 1 oxygen, whatever the glass.

Atomic structure

An atom is a small, dense nucleus of protons and neutrons, surrounded by electrons. Almost all of the mass sits in the nucleus, and almost all of the volume is the region the electrons occupy.

The three facts worth memorizing as one sentence: protons and neutrons are in the nucleus, electrons are in shells outside it, and the charges are +1, 0 and −1. A neutral atom has as many electrons as protons, so its charges cancel.

The figure draws carbon-12, the isotope that makes up about 99 percent of natural carbon. The counts are the point of the drawing: 6 protons fix the element, 6 neutrons bring the mass number to 12, and 2 + 4 = 6 electrons fill the first shell and half-fill the second. Every atom on the periodic table is described by the same three counts, and the three counts are what a question about an atom is really asking.

Atomic number, mass number, isotopes and ions

Four numbers describe an atom, and three of them are read from a symbol such as ¹⁴C or Cl⁻.

• Atomic number (Z) is the number of protons. It is the element's identity: 6 is always carbon, 11 is always sodium, 17 is always chlorine. In a neutral atom, Z is also the electron count.
• Mass number (A) is protons plus neutrons. It is written as a superscript before the symbol, as in carbon-14 or ¹⁴C.
• Neutrons are not listed anywhere; they are A − Z.
• Charge is protons minus electrons, written as a superscript after the symbol: Na⁺ has lost one electron, Cl⁻ has gained one.

Isotopes are atoms of the same element with different neutron counts — same Z, different A. Carbon-12 and carbon-14 are isotopes of carbon, and they behave the same way in a chemical reaction, because chemistry is decided by electrons. The atomic mass printed on the periodic table is the weighted average of an element's isotopes, which is why chlorine is 35.45 and not a whole number. Round the abundances to 75 and 25 percent and the arithmetic gives 0.75(35) + 0.25(37) = 26.25 + 9.25 = 35.50, which overshoots because the two isotopes are not exactly 35 and 37. The exact abundances — about 75.8 percent chlorine-35 at 34.9689 u and 24.2 percent chlorine-37 at 36.9659 u — give 0.758(34.9689) + 0.242(36.9659) = 26.506 + 8.946 = 35.45, the figure on the table.

An ion is an atom that has gained or lost electrons. Losing electrons leaves more protons than electrons, so the ion is positive and is called a cation (Na⁺, Ca²⁺, Al³⁺). Gaining electrons makes it negative: an anion (Cl⁻, O²⁻, N³⁻). The nucleus never changes in an ion — only the electron count does — which is why an ion's mass number is the same as its atom's.

Electron shells and valence electrons

Electrons occupy shells at increasing distance from the nucleus, and each shell holds a limited number: 2 in the first, 8 in the second, and 8 in the third for the elements up to calcium. Electrons fill the inner shells first, so the outermost shell is where the interesting count is.

The electrons in that outermost shell are the valence electrons, and they decide nearly everything an atom does chemically: how many bonds it forms, what charge its ion carries, and which family of the periodic table it belongs to. What an atom "wants" is a full outer shell — the octet rule. Sodium has 1 valence electron and gives it away to reach the 8 in the shell below; chlorine has 7 and takes one to reach 8.

The noble gases — helium, neon, argon — have full outer shells, and that is the whole reason they barely react. Everything else reacts in order to look like one of them.

The periodic table

The periodic table arranges the elements by atomic number, and the arrangement is the information: an element's position tells you its electron count, its likely ion, and how it will bond.

• A period is a horizontal row. The seven periods are the shells being filled, so every element in period 2 has its valence electrons in the second shell.
• A group is a vertical column. There are 18, and the main-group columns have the same valence count all the way down, which is why the elements in a column behave alike.

The table also divides by character. Metals sit on the left and toward the bottom: they conduct heat and electricity, are malleable and ductile, and lose electrons to form cations. Nonmetals sit in the upper right: they are poor conductors and gain or share electrons. The metalloids sit along the staircase between them — boron, silicon, germanium, arsenic, antimony and tellurium — and behave partly like each. Hydrogen is a nonmetal that sits alone in the top-left corner, which is the table's one placement that is about electron count rather than character.

Three trends follow from the same cause, the pull of the nucleus on the outer electrons.

Electronegativity is the one that decides bonding, so it is worth knowing a few values: fluorine 4.0, oxygen 3.5, chlorine 3.0, nitrogen 3.0, carbon 2.5, hydrogen 2.1, sodium 0.9. Fluorine is the most electronegative element on the table, and francium the least.

Ionic bonding

An ionic bond is the electrostatic attraction between two oppositely charged ions. It forms when a metal gives electrons to a nonmetal: the metal becomes a cation, the nonmetal an anion, and the two are held together by charge alone.

Sodium chloride is the standard case. Sodium has 1 valence electron and chlorine has 7, so sodium gives one electron away, chlorine takes it, and both end with a full outer shell. The ions are Na⁺ and Cl⁻, and because the charges are equal and opposite they pair in a 1:1 ratio — NaCl.

Formulas follow from charge balance, and that is the whole method: the total positive charge must equal the total negative charge.

Ionic compounds share a set of properties, all of them consequences of the lattice the ions form: they are solids at room temperature with high melting points, they are brittle crystals rather than soft solids, they do not conduct electricity as solids, and they do conduct when melted or dissolved, because the ions are then free to move. They dissolve in water more readily than in oil, because water is polar.

A polyatomic ion is a group of atoms that carries a charge as a unit — NO₃⁻, SO₄²⁻, NH₄⁺. It bonds ionically just like a single atom, and the subscript outside its parentheses multiplies everything inside: in Ca(NO₃)₂ there are two nitrates, so 2 nitrogens and 6 oxygens.

Covalent bonding

A covalent bond is a shared pair of electrons between two atoms, and it forms between nonmetals, because neither of them gives electrons away. Each atom contributes one electron to the pair, and the shared pair counts toward both atoms' octets.

A molecule is the unit a covalent compound is made of, and molecules have properties the ionic lattice does not: low melting and boiling points (the forces between molecules are weak, even when the bonds inside them are strong), softness, and no conductivity in any state, because there are no free ions and no free electrons. Carbon dioxide and water are molecules; table salt is not.

Polar versus nonpolar is decided by electronegativity, the measure of how hard an atom pulls on a shared pair.

• If the two atoms pull equally, the electrons are shared evenly, and the bond is nonpolar covalent. The diatomic gases are the clean cases: H–H, O=O, N≡N, Cl–Cl.
• If one atom pulls harder, the pair shifts toward it, the bond gets a partial negative end and a partial positive end, and it is polar covalent. Hydrogen chloride is the textbook case; water is the one that matters in biology.

The size of the difference sets the label, roughly.

Those cutoffs are a rule of thumb rather than a law, and the table is honest about it. What the numbers buy you is the middle case: the polar covalent bond, where electrons are shared but unevenly. Water's O–H bond is the example to keep, because a water molecule with two polar bonds is bent rather than straight, and that shape leaves it with a positive end and a negative end.

Intermolecular forces and hydrogen bonds

The forces between molecules are not bonds. They are much weaker than a covalent bond, and they decide melting points, boiling points and how substances dissolve.

A hydrogen bond needs a hydrogen that is already attached to nitrogen, oxygen or fluorine. That is the whole definition, and the three atoms are the whole list. The hydrogen carries a strong partial positive charge, and it is attracted to the lone pair on a nearby N, O or F.

Three consequences are worth knowing, because they explain the rest of the science:

• Water boils at 100 °C at sea level, far above hydrogen sulfide (H₂S, boiling near −60 °C), even though the two molecules are similar in size. Each water molecule can hydrogen-bond to four neighbors, and breaking those bonds takes energy.
• Ice floats on water, which is unusual: the hydrogen-bonded lattice holds the molecules farther apart in the solid than in the liquid, so solid water is less dense.
• Water dissolves salts and sugars because it is polar, and it holds large molecules together in biology: the two strands of DNA are paired by hydrogen bonds, and a protein's folded shape is held by them.

Formulas, names and polyatomic ions

Names run in one direction for ionic compounds and another for molecular ones, and mixing the two conventions is the error this section exists to prevent.

Ionic compounds: name the cation first, then the anion with its ending changed to -ide for a single element. No prefixes, ever — the charges already fix the ratio.

Metals with more than one charge need a Roman numeral for the charge actually used, and leaving it out is an error rather than a shortcut.

Covalent compounds use prefixes, because there is no charge to count: mono-, di-, tri-, tetra-, penta-, hexa-. The first element keeps its name and takes a prefix only if there is more than one of it; the second takes a prefix always and ends in -ide.

Acids have their own set of names, and the pattern is worth having: an acid of two elements (hydrogen plus one nonmetal) is hydro-…-ic acid; an acid containing oxygen takes -ic or -ous from the polyatomic ion it comes from.

These are the polyatomic ions worth having in memory. The endings pair up: -ate is the ion with more oxygen, -ite the one with less.

To write a formula from a name, balance the charges and put the polyatomic ion in parentheses when more than one is needed: aluminum sulfate is Al₂(SO₄)₃, because two 3+ ions need three 2− ions; ammonium phosphate is (NH₄)₃PO₄, because three 1+ ions need one 3− ion; calcium hydroxide is Ca(OH)₂.

Reaction types and balancing

A chemical equation writes the reactants on the left of the arrow and the products on the right, and the arrow is read "yields". Balancing it means making the atom counts equal on both sides, which is the law of conservation of mass written down: atoms are rearranged, never created or destroyed.

A balanced equation falls into one of five patterns.

Two subtypes are worth naming. A precipitation reaction is a double replacement whose product is an insoluble solid — silver chloride in the example above. A neutralization is a double replacement between an acid and a base, and its products are always a salt and water: HCl + NaOH → NaCl + H₂O.

The balancing method is four steps, and doing them in this order is faster than guessing coefficients.

1. Count each element on both sides.
2. Balance the elements that appear in only one compound on each side first, leaving hydrogen and oxygen for later when they appear in several.
3. Balance a polyatomic ion as a unit if it appears unchanged on both sides.
4. Recount everything, and multiply through only if a coefficient is not a whole number.

Balancing the combustion of propane

• Left side: C₃H₈ + O₂ → C 3, H 8, O 2.
• Carbon: 3 carbons need 3 CO₂ on the right.
• Hydrogen: 8 hydrogens need 4 H₂O on the right.
• Oxygen: 3 × 2 + 4 × 1 = 10 oxygens on the right, so the left needs 5 O₂.
• Check: C 3 = 3, H 8 = 8, O 10 = 10, so the balanced equation is C₃H₈ + 5O₂ → 3CO₂ + 4H₂O.

A coefficient multiplies the whole formula, so 2H₂O is 4 hydrogens and 2 oxygens, not 2 hydrogens and 2 oxygens. A subscript is part of the formula and must never be changed to make a count work — change the coefficient in front instead. And a balanced equation says nothing about how fast the reaction runs, which is why the rate section further down is a separate idea.

Oxidation and reduction

Oxidation is the loss of electrons and reduction is the gain of them; the two always happen together, because an electron taken from one particle is handed to another, and a reaction that does both is a redox reaction. The memory hook is that the names describe the electrons, not the oxygen: a substance can be oxidized with no oxygen anywhere in the beaker.

• oxidized — loses electrons, and its oxidation number rises
• reduced — gains electrons, and its oxidation number falls
• the oxidizing agent is the species that takes the electrons, so it is itself reduced
• the reducing agent is the species that gives them, so it is itself oxidized

Worked example. Iron metal dropped into copper(II) sulfate solution:

Fe + Cu²⁺ → Fe²⁺ + Cu

Iron goes from 0 to +2, so iron is oxidized and is the reducing agent. Copper goes from +2 to 0, so copper(II) is reduced and is the oxidizing agent. The blue color fades as Cu²⁺ leaves the solution, and a red-brown solid appears, which is the visible half of a bookkeeping change.

Two redox pairs worth carrying into a clinical setting: oxygen is reduced as it accepts electrons at the end of cellular respiration, and the body's own antioxidant chemistry depends on one partner handing electrons to another.

The mole and molar mass

A mole is 6.022 × 10²³ particles — Avogadro's number. It is a counting unit, like a dozen, chosen so that one mole of a substance in grams weighs its formula mass in atomic mass units. That link is what makes a balance useful in chemistry.

The molar mass of a substance is the mass of one mole, in grams per mole, and it is read straight off the periodic table by adding up the atomic masses in the formula. The values below are the standard ones to two decimal places.

Three relationships carry the arithmetic, and each is the same equation rearranged.

• mass = moles × molar mass, so grams come from moles by multiplying.
• moles = mass ÷ molar mass, so moles come from grams by dividing.
• particles = moles × 6.022 × 10²³, so a particle count comes from moles by multiplying.

A few molar masses worth recognizing on sight: water H₂O is 18.02 g/mol, table salt NaCl is 58.44 g/mol, carbon dioxide CO₂ is 44.01 g/mol, glucose C₆H₁₂O₆ is 180.18 g/mol, and sulfuric acid H₂SO₄ is 98.08 g/mol.

Molar mass of a compound with a parenthesized group

• The formula Ca(OH)₂ holds 1 calcium, 2 oxygens and 2 hydrogens.
• Calcium: 1 × 40.08 = 40.08 g/mol.
• Oxygen: 2 × 16.00 = 32.00 g/mol.
• Hydrogen: 2 × 1.01 = 2.02 g/mol.
• Total: 40.08 + 32.00 + 2.02 = 74.10 g/mol.

The subscript outside the parentheses multiplies everything inside, which is the step people drop: the formula has two hydroxides, so it has two oxygens and two hydrogens, not one of each.

Converting between grams and moles

• Glucose has a molar mass of 180.18 g/mol, so 9.00 g ÷ 180.18 g/mol = 0.04995 mol, which rounds to 0.0500 mol.
• The same relation runs the other way: 0.250 mol × 58.44 g/mol = 14.61 g of NaCl, which rounds to 14.6 g.
• Checking the second one backwards: 14.61 g ÷ 58.44 g/mol = 0.250 mol, so the division and the multiplication are the same fact used twice.

The check line is not decoration. Every mole question has three quantities — mass, moles, molar mass — and if two of them are known the third follows; a wrong answer is almost always the right number divided when it should have been multiplied, and the check catches it.

The metric prefix ladder

Every metric prefix is a power of ten, and the ladder runs the same way above and below one. Five prefixes above the base unit and six below carry the whole chemistry range:

Moving down the ladder multiplies by 1 000 and shifts the decimal three places to the right; moving up divides by 1 000 and shifts it three places left. Only the steps through milli are three at a time; deci and centi are one step of ten and two steps of ten, and micro, nano and pico resume the thousand pattern.

Worked example. A dose is 0.25 mg. In micrograms that is 0.25 × 1 000 = 250 µg, because micro is three places below milli. In grams it is 0.25 ÷ 1 000 = 0.000 25 g. The same 250 µg written as 2.5 × 10⁻⁴ g is scientific notation applied to the same shift, which is why the two skills are taught together.

A prefix attaches to a unit and nothing else: µg is a microgram, mg a milligram, and ng a nanogram, and a result in the wrong prefix is a thousandfold error that reads as a small one.

Solutions and concentration

A solution is a homogeneous mixture of a solute dissolved in a solvent. When the solvent is water the solution is aqueous. "Like dissolves like" is the working rule: polar solvents dissolve ionic compounds and polar molecules, and nonpolar solvents dissolve nonpolar substances. Water and oil do not mix for that reason, not because either is unusual.

Molarity (M) is the concentration to reach for first: moles of solute per liter of solution, not per liter of solvent.

M = moles of solute ÷ liters of solution

Diluting a solution adds solvent and leaves the moles of solute alone, so the concentration falls in step with the volume. That gives the only dilution equation worth memorizing:

C₁V₁ = C₂V₂

where C is concentration and V is volume, in any matching units. The units cancel, so milliliters may be used on both sides as long as they are used on both sides.

Percent by mass is the other concentration a question uses, and it is the mass of the solute over the mass of the whole solution, times 100.

Molarity from a measured mass

• 4.00 g of NaOH, whose molar mass is 22.99 + 16.00 + 1.01 = 40.00 g/mol.
• Moles: 4.00 g ÷ 40.00 g/mol = 0.100 mol.
• Volume: 250 mL = 0.250 L.
• Molarity: 0.100 mol ÷ 0.250 L = 0.400 M.

Diluting a stock solution

• A stock of 2.00 M is needed at 0.500 M, and 100.0 mL of the dilute solution is wanted.
• Rearranged: V₁ = (C₂ × V₂) ÷ C₁.
• Substitute: (0.500 M × 100.0 mL) ÷ 2.00 M = 25.0 mL of stock.
• Add enough water to the 25.0 mL to reach 100.0 mL, and the result is 0.500 M — a 4-fold dilution, which matches the 4-fold drop from 2.00 M.

Acids, bases, pH and buffers

An acid is a substance that donates a hydrogen ion (H⁺, a proton) in water. A base is a substance that accepts one. In water, that makes an acid a source of H₃O⁺ (usually written H⁺) and a base a source of OH⁻.

A strong acid or base ionizes completely in water; a weak one ionizes only partly. HCl is strong, acetic acid is weak, NaOH is strong, ammonia is weak. Strength is not the same thing as concentration: a dilute strong acid can be less corrosive than a concentrated weak one.

An acid and a base neutralize each other, and the products are a salt and water: HCl + NaOH → NaCl + H₂O. That is the reaction a buffer works against, and the reason an antacid helps.

The pH scale is a logarithm, and that is the only hard part of it. pH is the negative logarithm of the hydrogen-ion concentration:

pH = −log[H⁺], and the inverse runs the same road backwards: [H⁺] = antilog(−pH)

Because it is a logarithm, each step of one pH unit is a tenfold change in [H⁺]. pH 3 has ten times the H⁺ of pH 4, and a hundred times the H⁺ of pH 5. At 25 °C the scale is anchored by [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ and pH + pOH = 14, so neutral water has [H⁺] = 1.0 × 10⁻⁷ M, pH 7.00 and pOH 7.00.

The figure is a scale rather than a graph: the position of a substance is its pH, and the colors run from red at the acid end to blue at the base end. The two rows of substance labels are staggered only so that neighbors do not collide — read each one down its leader line to the scale. Blood at about 7.4 sits just on the basic side of neutral; lemon juice near 2 sits far on the acid side, five steps from neutral where blood is four-tenths of a step from it.

A buffer is a solution that resists a change in pH when a small amount of acid or base is added, because it contains a weak acid and its conjugate base, and the pair absorbs what is added. Blood is buffered near pH 7.4, mainly by the bicarbonate system, and that narrow range is why a pH of 7.0 in a blood gas result is a clinical alarm rather than a curiosity.

pH from a hydrogen-ion concentration

• Given [H⁺] = 2.5 × 10⁻⁵ M, take the logarithm: log(2.5 × 10⁻⁵) = log 2.5 + log 10⁻⁵ = 0.40 − 5 = −4.60.
• pH = −log[H⁺] = −(−4.60) = 4.60.
• Check the direction: 4.60 is below 7, so the solution is acidic, and 2.5 × 10⁻⁵ M is larger than the 1.0 × 10⁻⁷ M of pure water, which agrees.
• Check the value: the antilog of −4.60 is 2.5 × 10⁻⁵, so the return trip lands on the number you started with.

Hydrogen-ion concentration, and pOH, from a pH

• Given pH = 8.20, find [H⁺] = antilog(−8.20) = 6.3 × 10⁻⁹ M.
• Then pOH = 14.00 − 8.20 = 5.80, because pH + pOH = 14.00 at 25 °C.
• And [OH⁻] = antilog(−5.80) = 1.6 × 10⁻⁶ M.
• Check: (6.3 × 10⁻⁹)(1.6 × 10⁻⁶) = 1.0 × 10⁻¹⁴, which is the water constant, so the pair is consistent.

Reversible reactions and equilibrium

Some reactions run in both directions at once, written with a double arrow: N₂ + 3 H₂ ⇌ 2 NH₃. The forward reaction makes ammonia and the reverse reaction takes it apart, and both are happening in the same vessel. Equilibrium is the state in which the two rates are equal. It is not a state in which nothing is happening, and it is not a state in which the amounts are equal — a reaction can sit at equilibrium with far more product than reactant, or the other way round.

What the amounts settle at depends on the conditions, and the shifts follow one rule: a system at equilibrium that is disturbed moves in the direction that partly undoes the disturbance.

• Add a reactant — the forward rate rises, and the position shifts toward products.
• Remove a product — the reverse rate falls, and the position again shifts toward products.
• Add a product, or remove a reactant — the shift goes the other way, toward reactants.
• Raise the temperature — the position moves in the direction of the endothermic side.
• Add a catalyst — both rates rise by the same amount, so equilibrium arrives sooner at the same position. A catalyst changes the speed, never the yield.

Worked example. Carbon dioxide in blood is carried largely as carbonic acid, and the two interconvert:

CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻

Rapid breathing removes CO₂, so the left-hand side is emptied, the position shifts left, H⁺ is consumed and the pH rises — which is why hyperventilation produces alkalosis. A slower breathing rate pushes the same equilibrium the other way and lowers the pH. A buffer is a pair of species that sits on either side of an equilibrium like this one, so an added acid or base is partly absorbed instead of moving the pH.

Reaction rates, catalysts and enzymes

A reaction happens when particles collide with enough energy and the right orientation. Everything that changes the rate changes one of those three things.

A catalyst is not consumed by the reaction, and it does not change the reactants, the products or the final amounts — only how fast the reaction gets there. Activation energy is the energy barrier the colliding particles must clear; a catalyst provides a lower path over it.

An enzyme is a protein that catalyzes a reaction in a living thing, and the same rules apply: more substrate speeds it up until every active site is busy, and a higher temperature speeds it up only until the protein denatures — loses its folded shape — after which the rate collapses. That collapse is why a sustained high fever is a clinical problem: a brief low fever is part of the immune response, but heat enough to misfold a cell's enzymes stops the chemistry they run. It is also why an enzyme has an optimum pH and temperature rather than a preference for more of both.

Nuclear change and half-life

Chemistry rearranges electrons; a nuclear change alters the nucleus, and the two should never be described with the same words. Three emissions do the work here.

Alpha emission moves the element two places left on the periodic table; beta emission moves it one place right. Gamma emission changes neither, which is why it is often released alongside the other two. Ionizing power runs the other way: alpha does the most damage to tissue it reaches, and gamma the least per centimeter traveled.

A half-life is the time it takes for half of a sample to decay. The decay is random for any one atom and completely predictable for a large sample, so the calculation is always the same: find how many half-lives have passed, then halve the amount that many times.

amount remaining = starting amount × (1/2)ⁿ, where n is the number of half-lives elapsed

The mass left after a known time

• Starting amount 80.0 mg, half-life 6.0 h, and 18.0 h have passed.
• Half-lives elapsed: 18.0 h ÷ 6.0 h = 3 half-lives.
• Amount remaining: 80.0 mg × (1/2)³ = 80.0 ÷ 8 = 10.0 mg.
• Check forwards: 80.0 → 40.0 → 20.0 → 10.0 mg, one halving per 6.0 h, which agrees.

Carbon-14, with a half-life of about 5,730 years, is the isotope used to date once-living material: after two half-lives, about 11,460 years, a quarter of the original carbon-14 is left. Nothing about the sample's chemistry changes across those years — only the nucleus, one atom at a time.

The four families of biological molecules

Chemistry meets biology in four families of large molecules, and each is described by the same four questions: what it is made of, what its building block is, what bond joins the blocks, and what it does.

Two details make the table usable. Sugars, starches and cellulose are the same monomer — glucose — joined differently: starch is glucose linked mostly by α-1,4 bonds, cellulose by β-1,4 bonds our enzymes cannot cut, which is why cellulose is fiber to us and starch is food. And a protein's shape is held by hydrogen bonds, while its sequence is held by peptide bonds, so heat that disrupts hydrogen bonds denatures the protein without breaking the chain, which is exactly what happens to egg white in a pan.

The traps, collected

The wrong answer on this topic is almost always a count used in the wrong place, or a term applied one level beside where it belongs.

Two more are worth stating in words rather than in a table. Balancing changes coefficients, never subscripts — H₂O is water, and 2H₂O is two waters; H₂O₂ is hydrogen peroxide, a different substance altogether. And a coefficient is not a ratio of masses: 2H₂ + O₂ → 2H₂O uses 4 g of hydrogen to 32 g of oxygen, a 1:8 mass ratio, even though the coefficients read 2:1.

How to practice this

• Count first, name second. For any atom, ion or formula, write the protons, neutrons and electrons before you look at the options. The count decides the answer, and the name only confirms it.
• Balance by recounting out loud. Say each element's count on both sides; a balanced equation is one where every count matches, and nothing else about it is negotiable.
• Work the mole arithmetic with units attached. "9.00 g ÷ 180.18 g/mol" carries its own check — the grams cancel and moles are left. A bare number cannot tell you whether to divide or multiply.
• Convert milliliters to liters before any molarity line, every time. A concentration that mixes mL and L is wrong by a factor of 1,000, and it will look plausible.
• Draw the pH scale and place the number on it. A pH of 4.6 means little on its own; "between coffee and pure water, on the acid side" is a fact you can reason from.
• Check a half-life answer by halving forwards. Three half-lives from 80 mg must pass through 40 and 20 on the way to 10; if the sequence does not agree, the division is wrong.

Where to go next

• The subject's own page — Chemistry lists what is published for this subject, including its guide and its practice set as they land.
• The cell this chemistry builds — Biology: the four families of molecules above, assembled into membranes, enzymes and genetic material.
• The units chemistry is measured in — Measurement and Conversion: grams, liters and the metric prefixes that molarity and half-life questions both use.
• The arithmetic a concentration question leans on — Ratio and Proportion: the same cross-multiplication as the dilution equation, written in the general case.

Sources. The element data on this page follows the NIST periodic table and reference data (nist.gov/pml/periodic-table-elements) and the NIH's PubChem (pubchem.ncbi.nlm.nih.gov); the unit conventions follow NIST Special Publication 811, Guide for the Use of the International System of Units (SI). All three are US federal government material, which is not subject to copyright in the United States. The teaching prose, the tables, the worked examples and both diagrams are written and drawn for this course in our own words and lines; no publisher's text is reproduced, and the OpenStax chemistry text is not used here because its current editions are licensed NonCommercial-ShareAlike. Standard values are stated as standard: Avogadro's number 6.022 × 10²³, the water constant 1.0 × 10⁻¹⁴ at 25 °C, carbon-14's half-life of about 5,730 years, and blood's buffered pH of about 7.4. The publisher's own account of the areas the exam covers is quoted from its HESI A2 page. Accessed 2026-10-27.

HESI A2 is a trademark of Elsevier Inc. Elk Ridge Academy is an independent study resource and is not affiliated with, endorsed by, or sponsored by Elsevier Inc. Exam names are used descriptively only.