Chapter 12 Properties Of Gases
Pressure Measure of the number of collisions between gas particles and a unit area of the wall of the container Pressure = force / unit area
Force/area English system: pounds/in2 (psi) Metric system: Newton/m2 (pascal)
Torricelli Barometer h = 760 mm Hg 1 atmosphere pressure
1 atm = 760 torr (mm Hg) = 101.325 kPa = 1.01325 bar =14.70 psi
Patm Manometer h Pgas
Patm Manometer h Pgas
Volume Total space of a container that gases occupy due to the free random motion of the gas molecules
Relationship between Volume & Pressure of Gases P-V
V P (at constant T)
Slope = k V 1/P (at constant T)
In mathematical terms: y = mx + b Boyle’s Law
Relationship between Volume & Temperature of Gases V-T
In mathematical terms: y = mx + b V = mT + b Charles’ Law
Where T must be in Kelvin (K) temperature K = 0C + 273
Relationship between Pressure & Temperature of Gases P-T
In mathematical terms: y = mx + b P = mT + b Gay-Lussac’s Law
Relationship between Volume & Moles of Gases V-n
In mathematical terms: y = mx + b V = mn + b Avogadro’s Law
Avogadro’s Hypothesis At constant temperature and pressure, equal volumes of gases contain equal number of particles
Combined Gas Law
Ideal & Real Gasses
Kinetic Molecular Theory 1. Gases consist of small particles that are far apart in comparison to their own size. These particles are considered to be tiny points occupying a negligible volume compared to that of their container.
Kinetic Molecular Theory 2. Molecules are in rapid and random straight-line motion. This motion can be described by well-defined and established laws of motion.
Kinetic Molecular Theory 3. The collisions of molecules with the walls of a container or with other molecules are perfectly elastic. That is, no loss of energy occurs.
Kinetic Molecular Theory 4. There are no attractive forces between molecules or between molecules and the walls with which they collide.
Kinetic Molecular Theory 5. At any particular instant, the molecules in a given sample of gas do not all possess the same amount of energy.
Ideal Gas Equation
Note that is similar to the Combined Gas Law derived earlier.
Variations on Ideal Gas Equation
Variations on Ideal Gas Equation Bromine Variations on Ideal Gas Equation
Real Gas Behavior
Ideal Gas Equation P V = n R T
N2 2.0 CH4 H2 PV nRT 1.0 Ideal gas CO2 0 200 400 600 800 1000 P (atm)
“correct” for volume of molecules (V - b)
attractive forces between molecules also “correct” for attractive forces between molecules
van der Waals’ Equation for 1 mole
van der Waals’ Equation for n moles
from CRC Handbook a* b* He 0.03412 0.02370 Ne 0.2107 0.01709 *when P(atm) & V(L)
from CRC Handbook a* b* NH3 4.170 0.03707 H2O 5.464 0.03049 *when P(atm) & V(L)
from CRC Handbook a* b* CCl4 20.39 0.1383 C5H12 19.01 0.1460 *when P(atm) & V(L)
Cl2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl2 in a 4.0 L tank at 27oC. P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm
T & P conditions where a real gas approximates an ideal gas?
N2 gas PV nRT 203 K 293 K 1.8 1.4 673 K Ideal 1.0 gas 0.6 0 200 400 600 800 P (atm)
T & P conditions where a real gas approximates an ideal gas? high temperature low pressure
Gaseous Molecular Movement
pressure exerted by each component in a mixture of gases Partial Pressure pressure exerted by each component in a mixture of gases
this assumes that NO interactions occurs between the molecules of gas
must conclude 1. each gas acts as if it is in container alone 2. each gas collides with the container wall as an “event”
where n = # components Or Dalton’s Law PT = P1 + P2 + P3 + ...
Pi V = ni R T or
thus:
or
therefore: nT = ni and PT sum of mols of gas
Mole Fraction
Since: and
Then
and Pi = Xi PT
diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container.
rate of average effusion speed
But ... where
thus then RMS speed
substituting:
simplifying Graham’s Law NH3-HCl
if “d” is constant
if “t” is constant
GAS LAW STOICHIOMETRY