Gases

This is Unit Seven of Chemistry, Part One: pressure, the gas laws, and mixtures. Gases are the first system in this course where a handful of variables — pressure, volume, temperature and amount — fully describe the behaviour, which is why so much of this unit is arithmetic. The through-line is unit discipline. Almost every error the book names here is a unit error rather than a conceptual one: a Celsius temperature where kelvin was required, a pressure in torr against a constant expecting atmospheres, a conversion factor applied upside down. By the end you will be able to say why pressure depends on area as much as force; say which temperature scale the gas laws require; name the two assumptions the ideal gas law makes; say why the abbreviation STP needs a convention check; and say what must be subtracted from a gas collected over water.

Three entries. What pressure is as a definition, the several units chemists use for it, and the procedure for moving between them — which is the first place this unit's unit discipline bites.

Force over area.

Chem 1201 Pressure, Defined

Pressure is the force a gas exerts divided by the area over which that force acts. A gas pushing with equal force on a smaller container wall area produces a higher pressure. Pressure depends on area as much as on force — a large force spread over a large area can still produce a small pressure.

Six ways to say it.

Chem 1203 The Pascal and Common Pressure Units

Pressure is measured in several units — the pascal, atmosphere, torr, millimetres of mercury, bar and psi — related by fixed conversion factors. One atmosphere equals 101,325 pascals, 760 torr, and about 14.7 pounds per square inch. These units measure the identical physical quantity: switching between them changes the number, never the pressure.

One factor at a time.

Chem 1206 Converting Among Pressure Units

Converting a pressure means applying the fixed relationships among those units as a chain of conversion factors, one pair at a time. A weather reading of 29.2 inches of mercury converts to about 742 torr, then to about 0.976 atmospheres, then to about 98.9 kilopascals — each step using exactly one defined relationship rather than a memorised combined formula. Applying a factor upside down is the commonest error; check that each one's units cancel before multiplying.

Four entries. Why a column of liquid can measure pressure at all, the two instruments built on that principle, and how to turn a height difference into a number — where which arm you are reading decides whether you add or subtract.

Weight of the column.

Chem 1210 Hydrostatic Pressure

Hydrostatic pressure is a fluid's pressure from gravity, equal to its density times column height times gravitational acceleration. A taller column of the same liquid exerts proportionally more pressure at its base. A denser liquid needs a shorter column for the same pressure, which is why mercury barometers are far shorter than water ones would be.

The atmosphere itself.

Chem 1213 Barometer

A barometer measures atmospheric pressure from the height of a liquid column that atmospheric pressure alone supports in a closed, inverted tube. Mercury's high density lets it stand about 760 millimetres tall at sea level, far shorter than water would need. A barometer measures the surrounding atmosphere — not the pressure of a gas trapped in a separate container.

A trapped gas.

Chem 1216 Manometer

A manometer measures a trapped gas's pressure from the height difference between its two liquid columns. A closed-end manometer references a vacuum; an open-end one references the atmosphere and must add or subtract atmospheric pressure. Ignoring which arm holds the reference gives the wrong gas pressure from the same height reading.

Height into pressure.

Chem 1219 Calculating Gas Pressure from a Manometer Reading

Calculating a gas's pressure from a manometer means measuring the height difference between the columns, converting it to a pressure unit, then adding atmospheric pressure for an open-end instrument or reading it directly for a closed-end one. A gas-side column 13.7 centimetres lower converts to 137 millimetres of mercury, and added to 760 gives 897. Adding atmospheric pressure when the gas-side column sits higher reverses the sign.

Four entries, four pairwise relationships. Each holds two of the four variables fixed and states how the remaining two move together — and three of the four carry a warning about the same thing, which is the temperature scale.

Pressure with temperature.

Chem 1224 Amontons's Law: Pressure and Temperature

At constant volume, a fixed amount of gas has pressure directly proportional to its kelvin temperature. Heating a sealed rigid canister raises the pressure inside in direct proportion to the kelvin rise. The proportionality holds only for kelvin — doubling a Celsius reading does not double the pressure.

Volume with temperature.

Chem 1227 Charles's Law: Volume and Temperature

At constant pressure, a fixed amount of gas has volume directly proportional to its kelvin temperature. A sealed balloon shrinks in a freezer and re-expands at room temperature, its volume tracking the kelvin change. Cooled far enough the proportionality would predict zero volume at absolute zero — real gases liquefy before reaching it.

Volume against pressure.

Chem 1230 Boyle's Law: Volume and Pressure

At constant temperature, a fixed amount of gas has volume inversely proportional to its pressure. Pushing a syringe's plunger halves the trapped gas's volume and doubles its pressure. Volume and pressure trade off inversely rather than directly — squeezing a gas raises its pressure, never lowers it.

Volume with amount.

Chem 1233 Avogadro's Law: Volume and Amount

At constant temperature and pressure, a gas's volume is directly proportional to its number of moles. Pumping more air into a flexible balloon increases its volume in direct proportion to the added moles. Volume tracks the mole count and molecule identity plays no role — equal moles of any gas occupy equal volume.

Four entries. The four laws collapsed into one equation, the procedure for using it, its two-state form, and then the two assumptions it quietly rests on — which Part Two returns to when it looks at where they fail.

All four at once.

Chem 1236 The Ideal Gas Law

The ideal gas law combines pressure, volume, moles and kelvin temperature into one equation, P V equals n R T, with R a fixed constant. It reproduces all four individual gas laws as special cases. R's numerical value depends on which pressure and volume units are chosen — the equation itself never changes.

Three known, one unknown.

Chem 1239 Solving Problems with the Ideal Gas Law

Solving an ideal-gas-law problem means identifying which three of pressure, volume, moles and temperature are given, converting each into the units matching the chosen gas constant, then rearranging to isolate the fourth. Plugging in a Celsius temperature, or a pressure in torr while using the atmosphere-based constant, produces an answer wrong by a large factor — often an order of magnitude rather than a rounding error.

Two states, one gas.

Chem 1243 The Combined Gas Law

For a fixed amount of gas changing between two conditions, pressure times volume divided by temperature stays constant, linking initial and final states directly. It is the ideal gas law with the mole count and R cancelling out. The relationship assumes a constant mole count — introducing or removing gas breaks it.

What it takes for granted.

Chem 1246 Ideal Gas Assumptions

The ideal gas law assumes gas particles have zero volume and exert no forces on each other. Two ideal particles could occupy the same point and pass through each other with no force between them. Real gas particles have volume and do attract each other, and Part Two returns to exactly where those two assumptions break down.

Three entries on a genuine ambiguity. The abbreviation STP has two live definitions, one historical and one current, they give different answers, and the book teaches both rather than picking one — because published data uses both.

The older one.

Chem 1249 Standard Temperature and Pressure: the 1 atm Convention

Standard temperature and pressure historically fixed pressure at exactly one atmosphere and temperature at 273.15 kelvin — the convention most pre-1982 chemistry literature still uses. This is not obsolete fiction: a great deal of still-cited data, and this course's own earlier units, use it by default.

The current one.

Chem 1251 Standard Temperature and Pressure: the Current IUPAC Convention

IUPAC redefined standard pressure from one atmosphere to exactly one bar in 1982, while standard temperature stayed at 273.15 kelvin. Reading STP without checking which pressure convention a source uses silently swaps in the wrong standard molar volume.

Two answers.

Chem 1254 Standard Molar Volume, Computed Under Both STP Conventions

Computing the standard molar volume means substituting one mole and 273.15 kelvin into the ideal gas law and solving for volume, once under each convention. The one-atmosphere convention gives the familiar 22.4 litres per mole; the one-bar IUPAC convention gives about 22.7. Treating 22.4 as universal picks the wrong one for an IUPAC-sourced problem, and reading 22.7 into an older source is the same error reversed.

Seven entries. Two quantities that fall out of rearranging the ideal gas law, then what happens when several gases share one container — including the practical case where the gas you collected has water vapour mixed into it.

Mass per volume.

Chem 1259 Gas Density from the Ideal Gas Law

Rearranging the ideal gas law shows a gas's density equals its molar mass times pressure, divided by the gas constant times kelvin temperature. Unlike a solid or a liquid, a gas's density changes whenever its temperature or pressure changes, even with identical composition.

Identify the unknown.

Chem 1262 Determining Molar Mass from Measured Gas Properties

Determining an unknown gas's molar mass means measuring a sample's mass, pressure, volume and temperature, then substituting into the rearranged ideal gas law and solving for molar mass directly. Forgetting to convert the flask's Celsius temperature and millimetre-of-mercury pressure into kelvin and atmospheres first produces a molar mass off by a large unit-driven factor, rather than something near the true value.

Add them up.

Chem 1266 Dalton's Law of Partial Pressures

In a mixture of gases that do not react, the total pressure equals the sum of each gas's own partial pressure. Each gas contributes its pressure as though the others were not present — mixing dilutes no individual gas's contribution.

Share of the moles.

Chem 1269 Mole Fraction and Partial Pressure

A gas's partial pressure equals its mole fraction — its moles divided by total moles — multiplied by the mixture's total pressure. Mole fraction is a ratio of moles rather than of mass, so a heavier gas at the same mole fraction contributes the same pressure share as a lighter one.

One gas at a time.

Chem 1272 Calculating Partial Pressures in a Gas Mixture

Calculating each gas's partial pressure means finding each component's moles, then applying that component's own P equals n R T over V to isolate its contribution. Using the mixture's total moles instead of one gas's own overstates every component — and the individual partial pressures should always sum back to the measured total, which is the check worth running.

Water comes too.

Chem 1276 Collecting a Gas Over Water

A gas collected by bubbling it into an inverted, water-filled container becomes mixed with water vapour, so the trapped gas's total pressure includes both. The measured total overstates the collected gas's own pressure until the water vapour's contribution is subtracted out.

Look it up, subtract it.

Chem 1279 Correcting for Water Vapor Pressure

Correcting a gas-over-water measurement means looking up water's vapour pressure at the collection temperature from a reference table, then subtracting it from the measured total to isolate the dry gas's pressure. Using the vapour pressure listed for a different temperature — the value changes quickly with temperature — corrupts the dry-gas result and every calculation built on it.

Five things to carry out of this part. Pressure is force divided by area, so it depends on the area as much as on the force — a large force spread wide can give a small pressure, which is why a denser liquid needs a shorter column to register the same reading. The gas laws require kelvin, not Celsius: the proportionalities in Amontons's and Charles's laws hold against absolute temperature, so doubling a Celsius reading does not double anything, and plugging Celsius into the ideal gas law is the error the book flags hardest. The ideal gas law makes two assumptions — that gas particles have zero volume, and that they exert no forces on one another — and Part Two is largely about where those two fail. The abbreviation STP needs a convention check because it has two live definitions: the historical one at one atmosphere, still used across much published data, and IUPAC's since 1982 at one bar. They give different standard molar volumes, 22.4 litres per mole against about 22.7, and reading one into a source that used the other is a silent error. And from a gas collected over water you must subtract water's vapour pressure at the collection temperature, looked up for that temperature specifically, before the reading describes your gas alone. Part Two takes up gas stoichiometry, effusion, kinetic-molecular theory, and real gases.