Lecture 6_190614 Flashcards
Gas laws
involve the relationship between P (pressure) V (volume) T (temperature) n (number of particles)
Boyle’s Law
Volume – Pressure relationship, constant T & moles
↑pressure → ↓volume
P1 * V1 = P2 * V2
– P is in absolute pressure (not gauge pressure b/c always off by 1atm)
Charles’s Law
Volume – Temperature relationship, constant P & moles
↑temperature → ↑volume
V1 / T1 = V2 / T2
– T is in absolute temp (use Kelvin)
Also expressed as, V = k * T
– k is the value (V2 / T2) at any temperature
Predicts the existence of absolute 0, the temperature at which V goes to 0
Gay-Lussac’s Law
Temp – Pressure relationship, constant V & moles
↑temperature → ↑pressure
P1 / T1 = P2 / T2
– T is in absolute temperature (use Kelvin)
Also expressed as, P = k * T
– k is the value (P2 / T2) at any temperature.
This equation predicts the existence of absolute vacuum
**Pressure cooker = increased P = increase boiling pt = increased temperature
Avogadro’s Law
Volume – Mole relationship, constant T & P
↑particles → ↑volume
V1 / n1 = V2 / n2
- n is the number of gas molecules (expressed in moles)
*every particle takes up same amount of space
The Ideal Gas Law
P * V = n * R * T
– n is moles, and R is the “universal gas constant”
*based on Combined gas Law
P1 * V1 / (n1 * T1) = P2 * V2 / (n2 * T2)
R = 8.314 J / (mol * K) R = 0.08205 L * atm / (mol * K)
STP (Standard Temperature & Pressure)
T = 0ºC = 273.15K
P = 1 bar = 100 kPa ≈ 0.987 atm ≈ 750 mmHg
1 mole of “any” gas occupies 22.71 L
Gas Density
ρ = m / V
mass, m, computed from moles * molecular weight
Dalton’s Law: Partial Pressures
Ptotal = P1 + P2 + …. Pn
- P1 is the pressure of substance 1, etc.
Pi = Χi * Ptotal
- Pi is the pressure, Χi is the “mole fraction” of the i-th substance.
Χi = mi / mtotal
- mi is the moles of i-th substance and mtotal is total number of moles.
*Like osmolarity, with pressure it’s 1 particle 1 vote
Relative Humidity
measure of the degree of saturation of water in the air
Relative humidity = amount of H2O in air / solubility of H2O in air (%)
Dew Point
Warm air holds more water than cool air,
air cools, amount of water in the air exceeds solubility,
water will condense and form dew or rain
Vapor pressure
Water dissolved in air is a gas and exerts a pressure like any other gas.
Vapor pressure of water = partial pressure exerted by the saturation density of water
Ideal Gases and Real Gases
1) gas molecules are small compared to the volume of the gas, so we can ignore the size of the molecule
* concentration is increased at high pressure
2) gas molecules are in constant, random motion
* true
3) gas molecules show a range of kinetic energies, but the average depends on the temperature
* true
4) gas molecules are not attracted or repulsed from each other, so all collisions are elastic (billiard balls)
* gas particles are very weakly attracted, so if the particles move slowly enough, at very low temperatures, this attraction matters
**very high pressure or very low temperature real gases do not behave like ideal gases
Kinetic Energies
The average kinetic energy of particles is (temp dependent):
KE = ½ * m * v2 = 3/2 * k * T
- k is Boltzmann’s constant = R / Avogadro’s number,
- T is temperature in Kelvin
- m is the mass is per atom basis = molecular weight / Avogadro’s number
KE = ½ * M * v2 = 3/2 * R * T
- M is molecular weight,
- R is universal gas constant,
- T is temperature (Kelvin
Velocity of Gas Molecules & Graham’s Law of Effusion (or Diffusion)
v = √(3 * R * T / M)
Smaller particles move faster! And heating them up also moves them faster!!
Rate of effusion ~ √(T/M) or √(1/M) if constant temp
