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### Chapter 9

Gases

Gases and Gas Pressure

- Gases– constituent atoms and molecules that have little attraction for one another
- Free to move in available volume

- Some properties of gases
- Mixtures are always homogenous
- Very weak attraction between gas molecules
- Identity of neighbor is irrelevant

- Compressible – volume contracts when pressure is applied
- 0.10% of volume of gas is occupied by molecules
- Exert a measurable pressure on the walls of their container

- Mixtures are always homogenous

Pressure – force exerted per unit area

SI unit equals Pascal (Pa)

1 Pa = 1 N/m2 (1 N = 1 (kg•m)/s2)

Alternative units

Millimeters of mercury (mmHg)

Atmosphere (atm)

1.0 atm = 760 mmHg = 101, 325 Pa

1.0 atm = 760 torr

Force

Unit area

Gases and Gas PressurePressure:

Atmospheric Pressure

- - pressure created from the mass of the atmosphere pressing down on the earth’s surface
- Standard atmospheric pressure at sea level – 760 mmHg

Gases and Gas Pressure

- Barometer:
- long thin mercury filled tube sealed at once end and inverted into a dish of mercury
- Downward pressure of Hg in column equals outside atmospheric pressure

Measuring Pressure

- Manometer:
- U-tube filled with mercury, with one end connected to the gas – filled container and the other end open to the atmosphere.
- Pgas < Patm; liquid level in the arm connected to the gas-filled cylinder will be higher
- Pgas + PHg = Patm

Measuring Pressure

- Pgas > Patm; liquid level in the arm connected to the gas – filled cylinder will be lower
- Pgas = Patm + PHg
- (PHg = the difference in the heights of the two mercury columns)

Example

- What is the pressure of the gas inside the following apparatus (in mm Hg) if the outside pressure is 750 mm Hg? (1 cm Hg = 10 mm Hg)

The Gas Laws

- Ideal Gas: A gas whose behavior follows the gas laws exactly.
- The physical properties of a gas can be defined by four variables:
P pressure

T temperature

V volume

n number of moles

Pressure and Volume: Boyle’s Law

- Showing the relationship between pressure and volume
- P x V = k (constant value @ specific temp and constant moles of gas)
- k = 1.40 x 103
- V = 1/P (inverse relationship)

Pressure and Volume: Boyle’s Law

- Can predict a new volume of pressure is changed
- P1V1 = k = P2V2 P1V1 = P2V2

Example

A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. Assume constant temperature.

- Will the volume of the gas increase of decrease?
- What will be the new volume of the gas?

Vinitial

Vfinal

Tinitial

Tfinal

Volume and Temperature: Charles’s Law- Relationship between Volume and Temperature
- V = bT (b is a constant)
- V / T = b
- Can predict the new volume or temperature
- (V1/T1)= (V2/T2)

Example

- A 2.0 L sample of air is collected at 298K and then cooled to 278 K. The pressure is held constant at 1.0 atm.
- Does the volume increase of decrease?
- Calculate the volume of the air at 278 K?

Vinitial

Vfinal

ninitial

nfinal

Volume and Moles: Avogadro’s Law- Relationship between volume of gas and number moles of gas
- V is directly proportional to n
- V = an or V / n = a (a = constant)
- Can predict the new volume or new moles of gas at constant pressure and temperature
- (V1/n1) = (V2/n2)

Example

- Consider two samples of nitrogen gas (composed N2 molecules). Sample 1 contains 1.5 mol of N2 and has a volume of 36.7 L at 25oC and 1 atm. Sample 2 has a volume of 16.0 L at 25oC and 1 atm. Calculate the number moles of N2 in sample 2

Vinitial

Vinitial

Vfinal

Vfinal

Tinitial

ninitial

Tfinal

nfinal

Summary=

PinitialVinitial = PfinalVfinal

9.3 The Ideal Gas law

- Different gasses show similar physical behavior (unlike solid or liquid)
- Relationship of variable – gas laws
- Ideal gas – behavior follows the gas laws exactly

- Relationship of variable – gas laws

R = 0.082058

K mol

9.3 The Ideal Gas law- Describes how the volume of a gas is affected by changes in pressure, temperature and moles.
- PV = nRT;

R = 0.082058

K mol

9.3 The Ideal Gas LawIdeal Gas Law:

PV = nRT

R is the gas constant and is the same for all gases.

T = 0 °C (273.15 K)

Standard Temperature and Pressure (STP) for Gases

P = 1 atm

0.082058

K mol

(1 mol)

(273.15 K)

nRT

P

(1 atm)

The Ideal Gas LawWhat is the volume of 1 mol of gas at STP?

V =

=

= 22.414 L

Example

- A helium gas cylinder of the sort used to fill balloons have a volume of 43.8 L and pressure of 1.51 x 104 kPa at 25.0oC. How many moles of helium are in the tank?
- What volume is occupied by 0.250 mol of carbon dioxide gas at 25.0oC and 371 torr?
- A 0.250 mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas?

2NaN3(s)

2Na(s) + 3N2(g)

Stoichiometric Relationships with Gases- The reaction used in the deployment of automobile airbags is the high temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0oC are produced by the decompostion of 45.0g NaN3?

Examples

- Consider the reaction represented by the equation
P4(s) + 6 H2(g) 4H3(g)

What is the amount of P4 is required to react with 5.39 L of hydrogen gas at 27.0oC and 1.25 atm?

Example

- Ammonia is commonly used as a fertilizer to provide a source of nitrogen for plants. A sample of NH3(g) occupies a volume of 5.00 L at STP. What moles will this sample occupy?

Combine Gas Law

- is an expression obtained by mathematically combining Boyle’s and Charles’ law
- P1V1 = [email protected] constant n
T1 T2

can predict P, V or T when condition is changed

Examples

- A sample of diborane gas B2H6, a substance that bursts into flames when exposed to air, has a pressure of 0.454 atm at a temperature of -15oC and a volume of 3.48L. If condition are changed so that the temperature is 36oC and the pressure is 0.616 atm, what is the new volume of the sample?

Examples

- Consider a sample of hydrogen gas of 63oC with a volume of 3.65L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35oC. Calculate the new volume of the gas

Xi =

Xi =

Pi

ni

Moles of component

Ptotal

ntotal

Total moles in mixture

13.6 Dalton’s Law of Partial Pressure- A. Gas laws apply to mixtures of gases
- B. Dalton's law of partial pressure –
- Ptotal = P1 + P2 + P3 + ….. at constant V, T
where P1, P2, ….refer to the pressure of the individual gases in the mixture

Mole Fraction (X) =

or

Partial Presssure

- C. Partial pressures refer to the pressure each individual gas would exert if it were alone in the container (P1, P2, …)
1. Total pressure depends on the total molar amount of gas present

Ptotal = ntotal (RT/V)

Examples

- A 2.0 L flask contains a mixture of nitrogen gas and oxgyen gas at 25.0oC. The total pressure of the gas mixture is 0.91 atm, and the mixture is known to contain 0.050 mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present

Examples

- Mixture of helium and oxygen are use in the “air” tanks of underwater divers for deep dives. For a particular dive, 12.0L of O2 at 25.0oC and 1.0 atm and 46.0 L of He at 25oC and 1.0 atm were both pumped into a 5.0 L tank. Calculate the partial pressure, moles fraction of each gas and the total pressure in the tank at 25.0oC

The Kinetic Molecular Theory of Gas

A. Model that can explain the behavior of gases

.Assumptions

1. A gas consists of particles in constant random motion

2. Most of the volume of a gas is empty spaces

3. The attractive and repulsive forces between molecules of gases are negligible

4. The total kinetic energy of the gas particles is constant at constant T

5. Average Ek α T

Graham’s Law: Diffusion and Effusion of Gases

- Diffusion: The mixing of different gases by molecular motion with frequent molecular collisions

a

Rate

m

Graham’s Law: Diffusion and Effusion of GasesEffusion: The escape of a gas through a pinhole into a vacuum without molecular collisions.

Graham’s Law:

The Behavior of Real Gases

The volume of a real gas is larger than predicted by the ideal gas law.

The Behavior of Real Gases

Attractive forces between particles become more important at higher pressures.

The Behavior of Real Gases

van der Waals equation

Correction for intermolecular attractions.

a

n2

P

+

V - n

b

= nRT

V2

Correction for molecular volume.

examples

Assume that you have 0.500 mol of N2 in a volume of 0.600L at 300K. Calculate the pressure in the atmosphere using both the ideal gas law and the van der Waals equation. For N2, a = 1.35 (L2·atm)mol2, and b = 0.0387 L/mol

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