# AP Notes Chapter 11 Properties Of Gases.

## Presentation on theme: "AP Notes Chapter 11 Properties Of Gases."— Presentation transcript:

AP Notes Chapter 11 Properties Of Gases

Temperature An indirect measure of the average kinetic energy of a collection of particles KEavg = kT 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

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) = kPa = 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

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
3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 370C 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.

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.

PARTICLE IN THE BOX Have 1 particle, with mass m, with velocity 

Consider the P exerted:

But: f = ?

But: f = ma where



 

  Change in velocity = (

Thus, the pressure exerted by one particle on a wall is:

But,

But, and, the distance a particle travels between collisions with the same wall is ?

Substituting into we get:

Simplifying:

but,

This represents the pressure (P) that one particle exerts striking opposite walls in the box.

Now assume the box contains N particles
Now assume the box contains N particles. Then, N/3 particles are traveling between opposite walls.

the total pressure on opposite walls is:
Thus, the total pressure on opposite walls is:

Substitute & rearrange

From classical physics
where k is the Boltzman constant

R = universal gas constant
where R = universal gas constant N0 = Avogadro’s 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 220C?

Variations on Ideal Gas Equation
Bromine Variations on Ideal Gas Equation

5. Calculate the density of fluorine gas at:
300C and 725 torr. STP

Real Gas Behavior

Ideal Gas Equation P V = n R T

N2 2.0 CH4 H2 PV nRT 1.0 Ideal gas CO2 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 Ne *when P(atm) & V(L)

from CRC Handbook a* b* NH H2O *when P(atm) & V(L)

from CRC Handbook a* b* CCl C5H *when P(atm) & V(L)

Cl2 gas has a = 6.49, b = 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
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 PT = P1 + P2 + P

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

1. Ethanol, C2H5OH, is often prepared by fermentation of sugars such as glucose, C6H12O6, with carbon dioxide as the other product.

[A] What volume of CO2 is produced from 125 g of glucose if the reaction is 97.5% efficient?

[B] Ethanol can also be made from ethylene, C2H4 according to the following chemical system:

3 C2H4(g) + 2 H2SO4  C2H5HSO4 + (C2H5)2SO4 then C2H5HSO4 + (C2H5)2SO4 + 3H2O  3C2H5OH H2SO4

What volume (mL) of 95% ethanol is produced from 142. 5 dm3 of C2H4
What volume (mL) of 95% ethanol is produced from dm3 of C2H4? 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 32oC in a 300. L container?

3. What mass of sodium metal is needed to produce 250 mL of hydrogen gas at 24oC and 740 Torr?