Presentation on theme: "AP Notes Chapter 11 Properties Of Gases. Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure."— Presentation transcript:
AP Notes Chapter 11 Properties Of Gases
Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure of the average kinetic energy of a collection of particles KE avg = kT Boltzman Plot Boltzman Plot
Pressure Measure of the number of collisions between gas particles and a unit area of the wall of the container Pressure = force / unit area
Torricelli Barometer h = 760 mm Hg 1 atmosphere pressure
1 atm = 760 torr (mm Hg) = kPa = bar =14.70 psi
Manometer P gas P atm h
Manometer P gas P atm h
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)
V 1/P (at constant T) Slope = k
In mathematical terms: y = mx + b Boyles 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 = 0 C + 273
Relationship between Pressure & Temperature of Gases P-T
In mathematical terms: y = mx + b P = mT + b Gay-Lussacs Law
Relationship between Volume & Moles of Gases V-n
In mathematical terms: y = mx + b V = mn + b Avogadros Law
Avogadros Hypothesis At constant temperature and pressure, equal volumes of gases contain equal number of particles
3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 37 0 C and 100 kPa. What volume of ammonia is produced at these same conditions?
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.
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. Kinetic Molecular Theory
Have 1 particle, with mass m, with velocity PARTICLE IN THE BOX
Consider the P exerted:
But: f = ?
But: f = ma where
Change in velocity = (
Thus, the pressure exerted by one particle on a wall is:
and, the distance a particle travels between collisions with the same wall is ?
Substituting into we get:
This represents the pressure (P) that one particle exerts striking opposite walls in the box.
Now assume the box contains N particles. Then, N/3 particles are traveling between opposite walls.
Thus, the total pressure on opposite walls is:
Substitute & rearrange
From classical physics where k is the Boltzman constant
where R = universal gas constant N 0 = Avogadros number
Ideal Gas Equation
Note that is similar to the Combined Gas Law derived earlier.
Variations on Ideal Gas Equation
4. What is the molar mass of methylamine if g of the gas occupies 125 mL with a pressure of 99.5 kPa at 22 0 C?
Variations on Ideal Gas Equation Bromine
5. Calculate the density of fluorine gas at: 30 0 C and 725 torr C and 725 torr. STP STP
Real Gas Behavior
Ideal Gas Equation P V = n R T
Ideal gas P (atm) PV nRT CO 2 H2H2 N2N2 CH 4
correct for volume of molecules (V - b)
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 Ne *when P(atm) & V(L)
from CRC Handbook a* b* NH H 2 O *when P(atm) & V(L)
from CRC Handbook a* b* CCl C 5 H *when P(atm) & V(L)
Cl 2 gas has a = 6.49, b = Cl 2 gas has a = 6.49, b = For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. P (ideal) = nRT/V = 49.3 atm P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm P (van der Waals) = 29.5 atm
T & P conditions where a real gas approximates an ideal gas?
203 K 293 K 673 K Ideal gas P (atm) PV nRT N 2 gas
T & P conditions where a real gas approximates an ideal gas? high temperature low pressure
Gaseous Molecular Movement
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 P T = P 1 + P 2 + P
P i V = n i R T or
therefore: n T = n i and P T sum of mols of gas
and P i = X i P T
diffusion is the gradual mixing of molecules of different gases. diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container. effusion is the movement of molecules through a small hole into an empty container.
rate of average effusion speed
thus then RMS speed
simplifying Grahams Law NH 3 -HCl
if d is constant
if t is constant
GAS LAW STOICHIOMETRY
1. Ethanol, C 2 H 5 OH, is often prepared by fermentation of sugars such as glucose, C 6 H 12 O 6, with carbon dioxide as the other product.
[A] What volume of CO 2 is produced from 125 g of glucose if the reaction is 97.5% efficient?
[B] Ethanol can also be made from ethylene, C 2 H 4 according to the following chemical system:
3 C 2 H 4 (g) + 2 H 2 SO 4 C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 then C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 + 3H 2 O 3C 2 H 5 OH + 2 H 2 SO 4
What volume (mL) of 95% ethanol is produced from dm 3 of C 2 H 4 ? The density of 95% ethanol is g/mL.
2. What is the final pressure [kPa] if g uranium reacts with sufficient fluorine gas to produce gaseous uranium hexafluoride at 32 o C in a 300. L container?
3. What mass of sodium metal is needed to produce 250 mL of hydrogen gas at 24 o C and 740 Torr?