Kinetic Theory and Gases. Objectives Use kinetic theory to understand the concepts of temperature and gas pressure. Be able to use and convert between.

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 !

Kinetic Energynu

mbe

r of

parti

cles

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

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

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.

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?

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

P-T Law (V is constant )P

Tk

P

T

P

T

1

1

2

2

P and T are directly proportional

More Gas Law Problems

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?

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?