Chapter 10- Gases

Chemistry: The Central Science AP Edition, 14th ed. published by Pearson

Boyle’s Law

the volume of a fixed quantity of gas is inversely proportional to its pressure; V = constant x 1/P or PV = constant

Charles Law

the volume of a fixed quantity of gas at constant pressure increases as the temperature increases; V = constant x T or V/T = constant

Gay-Lussac’s Law of combining volumes

at a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers; the pressure and Kelvin temperature of a gas are directly proportional, provided the volume remains constant; P₁/T₁ = P₂/T₂

Combined Gas Law

relationship between pressure, volume, and temperature of a fixed amount of gas; combination of Boyle’s, Charles's, and Gay-Lussac’s laws; (P₁V₁)/T₁ = (P₂V₂)/T₂

Avogadro’s Hypothesis

equal volumes of gas at the same temperature and pressure will contain the same number of molecules

Avogadro’s Law

the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas; 22.4 L of any gas at 0 degrees C contain 6.02 × 10²³ gas molecules; V = constant x n

Gases

composed of nonmetallic elements, simple moleculars formulas, and low molar masses; made up of molecules or atoms that are arranged without structure; no fixed shape or volume

Vapor

substances that are liquids of solids under ordinary conditions that also exist in the gaseous state; H₂O exists as liquid water, solid ice, or water vapor

Iiquid

has a definite volume but no definite shape; made up of atoms or molecules that are connected by bonds and their particles can flow freely; less rigid than solids but more rigid than gases

Solid

a substance that has definite shape and volume; particles are arranged in a specific arrangement; firm or hard

Properties of Gas

expand spontaneously (to fill a container); highly compressible; form homogeneous mixtures; nonmetallic elements; different chemical properties

Absolute Zero

0 K or -273.15 degrees C; William Thomson proposed an absolute-temperature scale known as Kelvin scale

Density as it relates to gases

d = (nM)/V = (PM)/(RT); depends on its pressure, molar mass, and temperature; the higher the molar mass and pressure, denser the gas; higher temperature, less dense the gas; less dense gas will lie above a denser gas without mixing (hotter gas is less dense so it rises); molar mass of a gas = M = (dRT)/P

Kinetic Molecular Theory

the theory of moving molecules; pressure of a gas caused by collisions with container but its magnitude is determined by how often and how forcefully the collisions happend; proportional to temperature so at any temperature, same average kinetic energy; if absolute temperature is doubled, average kinetic energy of its molecules doubles; KE = ½ mu²

5 Parts of Kinetic Molecular Theory

random motion (gases consists of molecules in continuous random motion); negligible molecular volume (combined volume of all of the gas’ molecules is relative to its total volume); negligible forces (attractive and repulsive forces between gas molecules are insignificant); constant average kinetic energy(as temperature stays constant, the average kinetic energy of molecules does not change; energy can be transfered during collisions though); average kinetic energy proportional to temperature (proportional to absolute temperature; at any temperature, all gas molecules have same average kinetic energy)

Diffusion

spread of one substance throughout a space for a second substance; faster for light gas molecules; significantly slower than RMS speed; slowed by gas molecules colliding with each other

Effusion

escape of gas molecules through a tiny hole; Graham’s Law

Graham’s Law of Effusion

r₁/r₂ = sqrt(M₂/M₁); r₁ and r₂ - effusion of two gases; M₁ and M₂ - molar masses; a lighter gas has the higher effusion rate; rate of effusion is proportional to the rms speed (root mean square speed- speed of molecule having the same kinetic energy and average kinetic energy)

Maxwell Boltzmann

the distribution of speeds for a gas at a certain temperature; higher temperatures increase average particle speed; high molar mass, average particle speed decreases; average kinetic energy increases as temperature increases because temperature increase increases particle speed that is directly proportional to kinetic energy; molar mass does not affect average kinetic energy because increasing molar mass decreases particle speed which cancel out so kinetic energy stays the same

What causes deviations from the ideal gas law?

higher pressure = greater deviation → gas molecules get closer, intermolecular distance decreases so attractive forces take over; temperature increase = more ideal gas → because gas molecules move faster and apart so more energy is available to break intermolecular forces; increase with increasing molecular complexity (volume + attractive forces) and increasing mass (volume); volumes of real gases are larger and have smaller pressures of ideal gases

Ideal Gas

V = (nRT)/P; molecules do not interact with each other; molecules’ combined volume is much smaller than the volume the gas occupies

Standard Temperature and Pressure

0 C and 1 atm

Pressure (P)

force per unit; SI is pascals (Pa); bars (bar = 10⁵ Pa); atmosphere (atm) and torr (torr or mmHg); barometer measures atmospheric pressure; manometer measures pressure of enclosed gases

Volume (V)

liters

Temperature

kelvins

Dalton’s Law of partial pressure

each gas exerts if present alone under same conditions; add all of the partial pressures up to make total pressure; partial pressure = mole fractions times total pressure

Mole Fraction

ratio of moles of one component of a mixture to the total moles of all components

root-mean-square (RMS) speed, u_rms

varies in proportion to the square root for the absolute temperature and inversely with the square root of the molar mass; = sqrt((3RT)/M) but most probably speed of a gas molecules is u_mp = sqrt((2RT)/M)

Mean free path

mean distance traveled between collisions; moving molecules has short path; collisions between molecules limit diffusion rate

as pressure increases, volume

decreases

as volume increase, pressure

decreases

as temperature increases, volume

increases

as pressure increases, n

increases