Kinetic Theory and Gases

Objectives

• Use kinetic theory to understand the concepts of temperature and gas pressure.

• Be able to use and convert between the Celsius and Kelvin temperature scales.

Kinetic Theory

kinetic theory: all matter is made of particles (atoms,ions, molecules) that are in constant, random motion

kinetic energy (or KE): theenergy of motion; depends on both the mass and speed of the moving particles

temperature (T): a measure of the average KE of allthe particles in a substanceNOT T-E-M-P !

average KE ~ temperature

num

ber o

f pa

rticl

es

Kinetic Theory Applet

Kelvin Scaleabsolute zero: the coldest possible temperature; there is no molecular motion (= -273oC or 0 Kelvin)

K = oC + 273 oC = K - 273

Kelvin temperature is directly proportional to the KE! 0 K = 0 KE 0 oC ≠ 0 KE600K is 2X more KE than 300K

Objectives

• Understand the concept of atmospheric pressure.

• Be able to explain how a barometer works.• Be able to convert between pressure

measurements.

Gases and Pressure

pressure: force applied over an area

PF

A metric pressure unit:

1 pascal (Pa) = 1 N/m2

barometer: instrument that measures atmospheric pressure

14.70 pounds of air push down oneach square inch of the earth’s surface (at sea level) spheres DEMO!

Gases exert pressure by collisions.

Pressure Conversions

What is the current pressure in kPa and atm?

standard pressure (P)= 14.70 psi = 760.0 mm Hg = 29.92 in Hg = 101.3 kPa= 1.000 atm

standard temperature (T)= 0oC or 273 K

STP: standard T and P

Objectives

• Be able to use the pressure equation to explain pressure, temperature, and volume changes in gases.

• Understand how to solve word problems using the “GUESS” method.

• Be able to use the various gas laws to solve problems.

The Gas Laws

PF

A

V

Tk

V

T

V

T

1

1

2

2

Boyle’s Law(constant T)

• force (F) relates to temperature (T)• area (A) relates to volume (V)

P and V are inversely proportional

Charles’s Law(constant P)

P-T Law(constant V)

P V k

P V P V

1 1 2 2

V and T are directly proportional

P and T are directly proportional

P

Tk

P

T

P

T

1

1

2

2

temperature(in K scale)

volume

Gas Law Problems Using GUESS Method

(1) At constant temperature, 7.5 L of air at 89.6 kPa is compressed to 2.8 L. What is the new pressure? What law was used?

(2) A 3.0 L balloon at 22oC is placed into a freezer at-15oC. What is the new volume if the pressure remainsthe same? What law was used? (3) A fixed volume of gas at STP is heated to 482oC.What is the pressure in kPa at this temperature? What Law was used?

Objectives

• Understand how the various gas law equations are derived.

• Be able to use the ideal gas law, gas molar mass equation, and gas density equation to solve problems.

More Gas Laws

P V

n TR

P V n R T

P V

Tk

P V

T

P V

T

1 1

1

2 2

2

Mm

n

nP V

R T

Mm

Mm R T

P V

PVRT

Combined Gas Law

Ideal Gas Law

R = 8.31 kPaL/molK

n = # moles

Gas Molar Mass

Gas Density

DP M

R T

More Gas Law Problems1. What is the molar mass of a gas that has a mass

of 0.35 g and occupies 165mL at 95oC and 87.0 kPa?

2. How many moles of air are in a 3.2 L balloon under the current temperature and pressure conditions in this room?

3. What is the density of N2 gas at 95 kPa and 25oC?

Objectives

• Understand Avogadro’s law by considering the ideal gas law.

• Be able to use the law of combining gas volumes to solve simple gas stoichiometry problems.

• Be able to use the ideal gas law to solve more complex gas stoichiometry problems.

Avogadro’s Law

Avogadro’s Law: equal volumes of gases at the sameT and P contain equal numbers of molecules (n)

O2 He CO2

Why? Look at theIdeal Gas Law!P V n R T

nP V

R T

Law of Combining Gas Volumes

N2(g) + 3H2(g) → 2NH3(g)

Coefficients can represent gas volumes if thereactants and products are at equal T and P.

1 vol. 3 vol. 2 vol. 1 L 3 L 2 L

How many liters of H2 are needed to completelyreact with 2.5 L N2? Assume same T and P.

Gas Stoichiometry

g A → mol A → mol B → g B

g A → mol A → mol B → L B (use V = nRT/P)

(1) How many liters of CO2 at 23oC and 89.5 kPa areformed when a 468 g container of C3H8 is burned?(2) How many liters of H2 gas are formed when 0.25 gNa reacts with HCl at STP?