Chapter 05: Gases Flashcards
Pressure
The force exerted per unit area by gas molecules as they strike the surfaces around them
Pressure = force/area = F/A
Pressure units & conversion factors
760 mmHg = 760 torr = 1 atm = 101,325 Pa
Elements that exist as gases at 25°C and 1 atm
1A: H
5A: N
6A: O
7A: F, Cl
8A: (all)
Force (formula)
mass × acceleration
SI units of force and pressure
Force: 1 newton (N)
Pressure: 1 pascal (Pa)
Newton
1 newton = 1 kg×m/s2
Pascal
1 pascal = 1N/m2 = 1 kg/(m×s2)
Barometer
Atmospheric pressure measurment tool
Inverted tube of Hg over open dish of Hg;
height of Hg in mm is equal to atmospheric pressure
Manometer
Instrument used to measure pressure of gas trapped in container
Gas pressure is determined by difference in liquid levels in U-shaped tube
(Pressure is high if it pushes down on liquid;
low if it cannot push down on liquid)
Simple Gas Laws: Four* basic properties of a gas
P, pressure
V, volume
T, temperature (Kelvin)
t, temperature (°C)
n, amount in moles
Boyle’s law
Inverse relationship between volume and pressure
*n is constant
*T is constant
P1V1 = P2V2
Charles’ law
Direct relationship between volume and temperature (Kelvin).
*P is constant
*n is constant
V1 = V2
T1 T2
Avogadro’s law
Direct relationship between volume and quantity (number of moles)
*P is constant
*T is constant
V1 = V2
n n
Ideal Gas Law
How a hypothetical gas behaves
PV = nRT
Where R is the ideal gas constant
R, ideal gas constant
R = 0.08206 L atm/mol K
Molar volume
The volume occupied by one mole of a substance
Ideal gas molar volume
22.414 L at STP of an ideal gas
STP
standard temperature and pressure
pressure = 1 atm at STP
temperature = 0°C or 273.15 K at STP
Density of a gas (formula)
d = PM
RT
Where d = density
P = pressure in atm
M = molar mass
R = gas constant
T = temperature in Kelvin
Molar mass of a gas (formula)
M = dRT
P
Where M = molar mass
d = density
R = gas constant
T = temperature in Kelvin
P = pressure in atm
Dalton’s law
Partial pressures, Pn
Pn = nnRT
V
Ptotal = Px + Py + Pz
*volume and temperature are constant
Mole fraction
Xn = nn
ntotal
Thus, with Dalton’s law:
Pn = XnPtotal
Vapor pressure
The partial pressure of water vapor in a system
Gas stoichiometry
General conceptual plan:
P, V, T / mass or volume of gas A –> moles of gas A –>
moles of gas B –> P, V, T / mass or volume of gas B
Kinetic molecular theory
- Particle size is negligible, even those they have mass
- Constant motion, random directions, no overall loss of energy, just a transfer of energy (known as being elastic)
- Average kinetic energy is directly proportional to temperature in Kelvin
- Gas particles exert neither attractive nor repulsive forces
Average kinetic energy
average kinetic energy = KE
( KE = 1/2×mv2 )
At same temperature, gases have same average kinetic energy
Boyle’s law explained (KMT)
Decreasing volume forces gas particles into a smaller space, thus increasing collisions, and hence, pressure
*n and T are constant
Charle’s law explained (KMT)
Temperature increase increases average kinetic energy
The higher the average kinetic energy, the greater the area particles will move around
Thus, volume increases
*P & n constant
Avogadro’s law explained (KMT)
Increasing number of particles causes more collisions
To keep pressure constant, volume must then increase
*P and T are constant
Dalton’s law explained (KMT)
Because average kinetic energy is the same (at same temperature), the total pressure of the collisions is the same
Root mean square velocity
A kind of average velocity
root mean square velocity = urms
urms = (3RT/M)1/2
Where M = molar mass in kg/mol
R = gas constant in J/mol K
T = temperature in Kelvin
R, gas constant (with joules)
8.314 J/mol K
*used as R in root mean square velocity
1 Joule = ? (kg, m, s)
1 J = 1 kg×m2/s2
Mean free path
The average distance a gas molecule travels between collisions
mean free path v as pressure ^
Diffusion
Process by which gas molecules spread out
in response to concentration gradient
Heavier molecules diffuse more slowly than lighter ones
Effusion
The process by which a gas escapes from a container into a vacuum through a small hole
Heavier molecules effuse more slowly than lighter ones
Rate of effusion
Amount of gas that effuses in a given time
Inversely proportional to square root of molar mass of gas
Graham’s law of effusion
The ratio of effusion rates of two different gases is equal to the square root of the division of the molar masses
Since rate of effusion is an inverse proportion, it can be said that rateA times the squre root of A’s molar mass is equal to rateB times the squre root of B’s molar mass.
Real gases
Do not behave like ideal gases at high pressure or low temperature
Compared to ideal gases:
Low pressure: lower ratio of PV/RT
High pressure: higher ratio of PV/RT
Effect of finite volume of gas particles
Size of gas particles become important at high pressure
Because size of particles take up significant portion of total gas volume
Hence, volume of the particles must be corrected – increased
Effect of intermolecular forces
At low temperatures, pressure is less than an ideal gas’
Because gas atoms spend more time interacting and less colliding, thereby decreasing pressure
van der Waals equation
correction for intermolecular forces (P-) × correction for particle volume (V+) = nRT
1 atm = ? Pa
1 atm = 101,325 Pa
