Kinetic Theory and Gases

Objectives

• Use kinetic theory to understand the concept of temperature.

• 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 the mass and speed of the particles

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

num

ber o

f pa

rticl

es Kinetic Energy

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

K = oC + 273 oC = K - 273

Kelvin temperature is directly proportional to the KE!

KE

temperature (K)

Temperature and KE

•Is 2oC twice as warm as 1oC?•What temperature would be twice as warm as 1oC?

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

Atmospheric pressure is 14.70 lbs/in2 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 KSTP: standard T and P

CAN SMASH

• Have about 1 inch of water in the bowl plus at least one large ice cube or some snow.

• Remove tab from rinsed can. Place about 1/4” of water in the can.

• Hold can with tongs—palm up!• Heat the water over the burner, shaking can

regularly. Allow water to boil—steam forms. • Shake out any excess water. • Plunge top of can into the ice water! CRUNCH!

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 G-U-E-S-S Method

• G = list the “given” values• U = list the “unknown”• E = find the correct equation• S = solve for the unknown (use algebra!)• S = substitute the values and solve

Boyle’s Law

PF

A

Boyle’s Law (T is constant )

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

P and V are inversely proportionalP V k

P V P V

1 1 2 2

temperature(in K scale)

volume

At constant temperature, 7.5 L of air at 89.6 kPa is compressed to 2.8 L. What is the new pressure?

Demo: balloon in vacuum

Charles’s Law and the P-T LawCharles’s Law (P is constant )V

Tk

V

T

V

T

1

1

2

2

V and T are directly proportional*must use Kelvin

P-T Law (V is constant )P

Tk

P

T

P

T

1

1

2

2

P and T are directly proportional*must use Kelvin

Demos: hot squirt bottle,space modulator gun

Gas Law Problems (use GUESS method)

(1) A 3.0 L balloon inside a -22oC freezer is removed and placed into a room at 19oC. What is the new volume if the pressure remains the same? What law was used?

(2) A solid container of gas at STP is heated and the pressure increases to 158 kPa. What is the new temperature of the gas? 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

Mm

n

nP V

R T

Mm

Mm R T

P V

PVRT

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 mass of 165 mL of CH4 gas if it is 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?C3H8 + 5 O2 → 3 CO2 + 4 H2O(2) How many liters of H2 gas are formed when 0.25 gNa reacts with HCl at STP?2Na + 2HCl → H2 + 2NaCl