ch 8 - The Gas Phase Flashcards
four variables that define the state of a gaseous sample
pressure (P), volume (V), temperature (T), and number of moles (n)
gas pressure units
atmospheres (atm) or millimeters of mercury (mmHg), which are equivalent to torr; SI unit is the pascal (Pa); mathematical relationship between all of these: 1 atm = 760 mmHg = 760 torr = 101.325 kPa
standard temp and pressure (STP)
conditions at 273 K (0 degrees C) and 1 atm; generally used for gas law calculations
standard state conditions
298 K, 1 atm, 1 M concentrations; used when measuring standard enthalpy, entropy, free energy changes and electrochemical cell voltage
ideal gas
represents a hypothetical gas with molecules that have no intermolecular forces and occupy no volume
ideal gas law
PV = nRT; where P = pressure, V = volume, n = number of moles, T = temp, R = ideal gas constant (8.21 x 10^-2 L x atm/mol x K or 8.314 J/K x mol which is derived when SI units of Pa and cubic meters (for volume) are substituted into the ideal gas law
density (fancy p)
ratio of the mass per unit volume of a substance; usually expressed for gases in units of grams per liter; density derived from ideal gas law: PV = nRT; n = m/Molar mass; PV = (m/molar mass) RT and density = m/V = P(molar mass)/RT
how much space does a mole of an ideal gas at STP occupy?
22.4 L
combined gas Law
can be used to relate changes in temp, volume, and pressure of gas: Psub1Vsub1/Tsub1 = Psub2Vsub2/Tsub2; where the subscripts 1 and 2 refer to the two states of the gas; this equation assumes number of moles stays constant
change in volume
Vsub2 = Vsub1[Psub1/Psub2][Tsub1/Tsub2]
change in volume used to find density
density = m/Vsub2
molar mass from density
molar mass = (density at STP)(22.4 L/mol)
Avogadro’s principle
states that all gases at a constant temp and pressure occupy volumes that are directly proportional to the number of moles of gas present; equal amounts of all gases at the same temp and pressure will occupy equal volumes: n/V = k or nsub1/Vsub1 = nsub2/Vsub2; k = a constant; nsub1 and nsub2 = number of moles of gas 1 and gas 2; Vsub1 and Vsub2 = volumes of gases 1 and 2
Boyle’s Law
for a given gaseous sample held at constant temp (isothermal), the volume of the gas is inversely proportional to its pressure: PV = k or Psub1Vsub1 = Psub2Vsub2; k = a constant; subscripts 1 and 2 = different sets of pressure and volume condidtions; in terms of gas law, n and T are constant here… As pressure increases volume decreases
Charles’s Law
states that, at constant pressure, volume of a gas is proportional to its absolute temp in kelvins: V/T = k or Vsub1/Tsub1 = Vsub2/Tsub2; k = proportionality constant; subscripts 1 and 2 = two different sets of temp and volume conditions; n and P (with reference to ideal gas law) are held constant… as temp increases, volume increase
Gay-Lussac’s law
relates pressure to temp: P/T = k or Psub1/Tsub1 = Psub2/Tsub2; subscripts 1 and 2 = two different sets of temp and pressure conditions; n and V (in terms of ideal law) are constant; as temp increases, pressure increases
combined gas law
combination of many of the preceding laws; relates pressure and volume in numerator, and variations in temp to both volume and pressure
Dalton’s Law of partial pressures
if two or more gases that do not chemically interact are found in the same container each one will act independently of the other; law states total pressure of a gaseous mixture is equal to the sum of the partial pressure of the individual components
partial pressure
pressure exerted by each gas in a container where multiple gases that do not chemically interact are found
Dalton’s Law equation
PsubT = PsubA + PsubB + PsubC + etc..; where PsubT = total pressure in container; PsubA through C = partial pressures of respective gases
determining partial pressure
PsubA = (XsubA)(PsubT); where XsubA = moles of gas A/total moles of gas and PsubT = total pressure of container
vapor pressure
pressure exerted by evaporated particles above the surface of a liquid
Henry’s Law
[A] = ksubH x PsubA or [A]sub1/Psub1 = [A]sub2/Psub2 = KsubH; [A] = concentration of A in solution; ksubH = Henry’s constant; PsubA = partial pressure of A
kinetic molecular theory
used to explain the behavior of gases; assumptions are: 1. Gases are made up of particles with volumes that are negligible compared to volume of container; 2. gas atoms or molecules exhibit no intermolecular attractions or repulsions; 3. Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls; 4. Collisions bt any two gas particles or particles and container are elastic meaning conserving momentum and kinetic energy; 5. avg kinetic energy of gas particles is proportional to the absolute temp of the gas (in kelvins), and it is the same for all gases at a given temp
kinetic energy of a gas particle
KE is proportional to the absolute temp of gas: KE = 1/2mv^2 = 3/2ksubB(T); where ksubB = Boltzmann constant (1.38 x 10^-23 J/K)
Boltzmann constant
1.38 x 10^-23 J/K, serves as a bridge between macroscopic and microscopic behaviors of gases (as a bridge between behavior of the gas as a whole and the individual gas molecules)
root-mean-square speed (u sub rms)
a way to define the average speed of gases, determined by the average kinetic energy per particle and then calculating the speed which corresponds to it; given by the equation: u sub rms = square root of (3RT/M); R = ideal gas constant; T = temp, M = molar mass
Maxwell-Boltzmann distribution curve
shows the distribution of gas particle speeds at a given temp
Graham’s Law
under isothermal and isobaric conditions, rates at which two gases diffuse are inversely proportional to the square roots of their molar masses: r sub 1/r sub 2 = square root of (Msub2/Msub1); r1 and r2 are diffusion rates of gases 1 and 2; M1 and M2 are molar masses of gases 1 and 2; noted that a gas with 4 times the molar mass of another gas will travel half as fast as the lighter gas
Effusion
the flow of gas particles under pressure from one compartment to another through a small opening; for two gases at same temp, rates of effusion are proportional to avg speeds
deviation in real gases from ideal gases due to pressure
as pressure of gas increases, the particles are pushed closer and closer together until gas condenses into a liquid; at moderately high pressure, gas’s volume is less than predicted by ideal gas law; at extremely high temps gas’s volume is more than predicted
deviation in real gases from ideal gases due to temp
as temp of a gas decreases, avg speed of the gas molecules decreases and attractive intermolecular forces become increasingly significant; as condensation temp is approached for a given pressure, intermolecular attractions eventually cause the gas to condense to a liquid; temp reduced toward condensation (boiling) point, has smaller volume than would be predicted. at extremely low temps, gas occupies more space than predicted.
van der Waals equation of state (equation does not need to be memorized)
attempts to correct for deviations from ideality (P + (n^2a)/V^2 )(V - nb) = nRT; where a and b are physical constants experimentally determined for each gas; ‘a’ corrects for the attractive forces between molecules and will be smaller for gases that are small and less polarized (such as helium), larger for gases that are larger and more polarized, and largest for polar molecules. ‘b’ corrects for volume of the molecules themselves - larger molecules have larger ‘b’
volume of ideal gas
22.4 L
