Atoms, Molecules, and Ions

This is Unit Two of Chemistry, Part Two: atomic mass, formulas, and the table. Part One established that isotopes of an element differ in neutrons. This part starts from the consequence: an element's tabulated mass is a weighted average across its isotopes, weighted by how common each one is. And no actual atom weighs that number. Every real atom weighs close to one isotope's mass, never the blend. The calculation runs both directions. Given the isotopes and their abundances, you can find the average. Given the average and the isotope masses, you can solve for the abundances. Both procedures have a specific failure mode, and both warnings are worth carrying. Then three entries on what a table's number actually is. The abundances come from mass spectrometry rather than from assumption; the weight itself is a measured figure a committee revises; and some elements have no such figure at all, showing a bracketed mass number instead. Then formulas — three kinds, showing different things — and the periodic table, ordered by atomic number rather than the atomic mass Mendeleev used. By the end you will be able to do five things. One: say why no atom weighs the average. Two: solve for abundance from an average. Three: say what a tabulated weight is. Four: tell the three formulas apart. Five: say what the periodic law orders by.

Four entries. A reference standard, the average built from it, and two procedures running the same equation in opposite directions. Both procedures' warnings are about setup rather than arithmetic, which is the usual place these go wrong.

The reference.

Chem 0232 The Atomic Mass Unit

The atomic mass unit, or dalton, is defined as exactly one twelfth the mass of a single carbon-twelve atom — a proton at about one point zero zero seven three and a neutron at about one point zero zero eight seven are both measured against that shared reference. The older name and the standardised one describe one identical definition.

Weighted by abundance.

Chem 0235 Average Atomic Mass as a Weighted Average

An element's average atomic mass is the weighted average of its isotopes' masses, each weighted by its fractional abundance — boron's figure combines its two isotopes in proportion to how much of each occurs naturally. No single boron atom has this average mass; every real atom weighs close to one isotope's mass, never the blend.

Isotopes to average.

Chem 0238 Calculating Average Atomic Mass from Isotopic Data

The procedure multiplies each isotope's mass by its fractional abundance and sums the products. Neon occurs as three isotopes — about ninety-two percent of one, under half a percent of another, and about eight percent of the third. Converting each percentage to a decimal fraction, multiplying by that isotope's mass, and adding the three products gives about twenty point one five for the sample. Forgetting to convert percentages to fractions first inflates the result a hundredfold; the fractions must sum to one.

Average to abundances.

Chem 0241 Calculating Isotopic Abundance from Average Atomic Mass

The same equation, solved the other way. Set one isotope's unknown fraction as x, write the other as one minus x, and solve. Chlorine's average mass of thirty five point four five three comes from two isotopes; solving gives about zero point seven six for the lighter one, so chlorine is roughly seventy-six percent chlorine-thirty-five and twenty-four percent chlorine-thirty-seven. Substituting back checks it. Entering the two isotope masses in the wrong order flips which percentage belongs to which isotope, and the average still checks out arithmetically.

Three entries asking where a periodic table's numbers actually come from. The answer runs against the way a table looks: those figures are measurements under review, not constants, and some of them are not atomic weights at all.

The instrument.

Chem 0244 Mass Spectrometry as the Method Behind Isotopic Data

Mass spectrometry measures isotopic abundance by ionising a sample, deflecting the ions by mass and charge, and counting arrivals — a spectrum's peaks show which isotopes are present and each peak's height shows what fraction of the sample it is. The abundance percentages used in mass calculations come from measurements like these, not from a table alone.

Revised over time.

Chem 0247 Standard Atomic Weight Is a Measured, Revisable Value

A standard atomic weight is a measured, weighted-average figure that an international commission reviews and revises as new abundance data arrive — and because natural abundance varies slightly by geographic source, some elements are listed as an interval rather than one number. A tabulated atomic weight is a measured figure open to revision, not a fixed constant of nature.

No average to take.

Chem 0249 Elements Without a Standard Atomic Weight

Elements whose isotopes are all radioactive have no natural abundance to average, so tables list the mass number of their most stable isotope instead — technetium, promethium and most elements from polonium onward show that number in brackets. A bracketed number is one isotope's mass number, not an atomic weight and not a mass in grams.

Four entries. Three formulas showing progressively different things, and a procedure reducing one to another. The distinction that matters is what each one leaves out — and the third leaves out enough that two different compounds can share it.

Counting atoms.

Chem 0252 Molecular Formula

A molecular formula lists each element's symbol in a molecule with a subscript giving how many of that element's atoms are present — water's formula shows two hydrogen atoms bonded to one oxygen in every water molecule. A missing subscript always means exactly one atom; no implied one is ever written.

Adding connections.

Chem 0255 Structural Formula

A structural formula shows the same atom counts as a molecular formula, and additionally shows which atoms are bonded directly to which — methane's draws four lines from a central carbon to four hydrogens, a pattern the plain formula leaves out. The lines represent bonds, not distances or angles; geometry is a separate question.

Reduced to a ratio.

Chem 0258 Empirical Formula

An empirical formula reports atom counts reduced to lowest terms, dividing out any factor shared across the molecular subscripts — benzene's six-and-six reduces to one carbon and one hydrogen. Two very different-sized molecules can share one empirical formula while describing entirely different substances.

Reducing one to the other.

Chem 0261 Determining Empirical Formula from Molecular Formula

The procedure divides every subscript by the largest whole number dividing all of them evenly. Acetic acid's subscripts two, four and two divide by two, giving one, two, one. Glucose's six, twelve and six divide by six and give exactly the same reduced formula, even though the two molecules differ in size. Hydrogen peroxide's two and two divide by two, giving subscripts already at their smallest. Dividing only one subscript instead of every one produces a ratio that no longer matches the molecule's actual atom counts.

Two entries. One is a list the book says outright must be memorised rather than worked out, and the other is the sharpest limit on what a molecular formula conveys.

Never alone.

Chem 0264 Diatomic Elements

Seven elements exist naturally as two-atom molecules rather than single atoms — hydrogen, nitrogen, oxygen, fluorine, chlorine, bromine and iodine. A sample of pure oxygen gas is made of two-atom molecules, never lone atoms. These seven are memorised as a fixed list, not derived from a rule; no simple pattern on the table predicts them.

Same formula, different substance.

Chem 0267 Isomers

Isomers are compounds sharing the same molecular formula but differing in how their atoms are arranged, which gives them different properties — acetic acid and methyl formate share a formula, and one is the sour acid in vinegar while the other is a distinct industrial solvent. An identical formula never guarantees identical behaviour.

Two entries. The first is a disputed priority claim the course states without settling, and the second is the ordering principle — which is not the one either man actually used.

Two proposals.

Chem 0270 Mendeleev, Meyer, and the Periodic Table's Origin

Dmitri Mendeleev and Lothar Meyer independently proposed periodic arrangements of the elements around eighteen sixty-nine and eighteen seventy, and historians still debate how credit should be divided — Mendeleev's table predicted then-unknown elements later found to match. Crediting only one oversimplifies a genuinely disputed claim, and the course states both without adjudicating.

Repeating properties.

Chem 0273 The Periodic Law

Under the periodic law, elemental properties repeat at regular intervals when the elements are ordered by atomic number rather than atomic mass — which places lithium, sodium and potassium in one column with similar reactive behaviour. Mendeleev's own table used atomic mass; the later shift to atomic number resolved ordering problems the mass-based table could not fix.

Four entries on the table's own structure. Rows and columns, the three-way metal split returning at a new depth, the broad column classes, and the family names — which come with one exception people trip on.

Rows and columns.

Chem 0276 Periods and Groups

A period is a horizontal row of the periodic table; a group is a vertical column whose elements share similar chemical properties — sodium and potassium share group one while sitting in different periods. The one-through-eighteen group numbering has replaced the older Roman-numeral labelling still seen on some tables.

The staircase.

Chem 0279 Metals, Nonmetals, and Metalloids at Periodic-Table Depth

Metals, nonmetals and metalloids occupy distinct regions of the table, with metalloids forming a staircase boundary between the other two — silicon sits along it and conducts moderately, unlike aluminium's strong conductivity or sulfur's poor conductivity nearby. This is the same three-way split taught in Unit One, revisited here at table-position depth rather than as new material.

Three broad classes.

Chem 0282 Main-Group, Transition, and Inner Transition Elements

Main-group elements occupy columns one, two, and thirteen through eighteen; transition metals fill the columns between; inner transition metals form the two rows below the table's main body. Group twelve is often called a transition-metal column out of habit, though the standard definition excludes it from that category.

The family names.

Chem 0285 Named Families of the Periodic Table

Several groups carry family names beyond their number, and identifying an element's family means matching its group to that name. Group one, hydrogen aside, are the alkali metals; group two the alkaline earth metals; group seventeen the halogens; group eighteen the noble gases. Chlorine is a halogen, calcium an alkaline earth metal, krypton a noble gas. Groups fifteen and sixteen have names too, less used in practice. Hydrogen sits above group one on most tables and is not an alkali metal — its nonmetallic behaviour places it outside that family.

Five things to carry out of Part Two. No atom weighs an element's average atomic mass, because that figure is a weighted average across the element's isotopes, each weighted by how common it is in nature. Every real atom weighs close to one isotope's mass. To compute it, convert each abundance to a decimal fraction, multiply by that isotope's mass, and sum — with the fractions adding to one. Running it backward gives abundance. Set one isotope's fraction as x and the other as one minus x, write the weighted-average equation, and solve. Then substitute back to check. Entering the two isotope masses in the wrong order swaps which percentage belongs to which, and the arithmetic still comes out right — so the check is on setup, not the answer. A tabulated atomic weight is a measured figure, not a constant of nature. The abundances behind it come from mass spectrometry. A commission revises the figures as data arrive, and some elements are listed as an interval because abundance varies by source. Elements with only radioactive isotopes show a bracketed mass number instead, which is not an atomic weight at all. The three formulas show different things. A molecular formula gives atom counts. A structural formula adds which atoms bond to which, without giving geometry. An empirical formula reduces the counts to lowest terms, which is why two differently sized molecules can share one. And the periodic law orders elements by atomic number, not by atomic mass. Mendeleev used mass, and the shift to atomic number resolved ordering problems the mass-based table could not. A period is a row, a group is a column, and elements in one group behave alike. Part Three turns to bonding, ion charges, and the naming system built on them.