Chapter 14 – Gases

Kinetic Molecular Theory (KMT)

Defn – describes the behavior of gases in terms of particle motionMakes assumptions of size, motion, &

energy of gas particles

KMT and Gases

Ideal Gases – imaginary gas that conforms to assumptions of KMT

Assumptions of KMT

A) gas particles do not attract or repel each other

no intermolecular forces occurring. gases are free to move in their containers without interference from other particles

Assumptions of KMT

B) gas particles have NO volume

almost all of the volume of a gas is empty space. The particles are insignificant in size compared to all the space

Assumptions of KMT

C) gas particles are in constant motion

they move in straight lines until they collide with each other or the walls of container

Assumptions of KMT

D) no kinetic energy is lost when gas particles collide with each other or walls

aka elastic collision. There is no loss in speed of the particles

Assumptions of KMT

E) ALL gases have same average kinetic energy at a given temperature

as temperature increases, more energy. As temp decreases, less energy

Assumptions of KMT

***KEEP IN MIND IDEAL GASES DO NOT EXIST!!!!!!!***

APPLIES AT ALL TEMPERATURES AND ALL PRESSURE

Real Gases

Defn – do not behave according to assumptions of KMT

Characteristicsi) real gas particles have volumeii) real gas particles exert attractive

forces on each other

Real Gases

When do real gases act like ideal gases?

at very low pressure and very high temp- at low P, molecules far from each

other- at high temp, molecules move too fast to have intermolecular interactions

Characteristics of Gases

1) expansion2) fluidity3) low density4) compressibility5) diffusion

4 measurable variables of gases

PressureTemperatureVolumeAmount

Pressure

Defn – force/area; pressure caused by collisions of molecules

Units: atmosphere (atm), millimeter of mercury (mm Hg), torr, kiloPascal (kPa)

Conversions:1 atm = 760 mm Hg = 760 torr = 101.3 kPa

Sample problem #1

Convert 2.3 atm to torr

2.3 atm

1 atm

760 torr= 1748 torr

Sample problem #2

Convert 450 mm Hg to kPa

450 mmHg

760 mm Hg

101.3 kPa= 60 kPa

Measuring air pressure

What device is used to measure air pressure?????

BAROMETER

Standard Temp and Pressure (STP)

P = 1 atmT = 0°C

Temperature

Unit Kelvin (K)

Kelvin = °C + 273

Temperature

Convert 45°C to Kelvin

45°C + 273= 318 K

Temperature

Absolute zero – 0 KMolecules stop moving

Question: what is absolute zero temperature in Celsius?

-273°C

Volume

Units:mLL

Amount

Unitsgramsmoles

Gas Laws

Each gas law relates the 4 variables:PressureTemperatureVolumeAmount

For the next 4 gas laws, amount is not a factor

We will only pay attention to P, T, & V

Boyles’ Law: P/V relationship

Defn – at constant T, volume of a fixed amount of gas varies inversely with pressureinversely – as one variable increases,

other variable decreases

P

V

Boyle’s Law

FormulaP1V1 = P2V2

P1 & V1 are initial conditions

P2 & V2 are final conditions

Boyle’s Law

A balloon filled with helium gas has a volume of 500 mL at 1.00 atm. When it rises to a higher altitude, the pressure is reduced to 0.50 atm. If the temperature is constant, what is the volume of the balloon?

1000 mL

Charles’ Law: V/T relationship

Defn – at constant P, volume of fixed amt of gas varies directly with Kelvin tempDirectly – as one variable increase, the

other increases

V

T

Charles’ Law

Formula

V1 & T1 are initial conditionsV2 & T2 are final conditions

2

2

1

1

T

V

T

V

Charles’ Law

A helium balloon has a volume of 2.75 L at 20°C. On a cold day, the balloon is placed outside where it shrinks to 2.46 L. What is the temperature outside?

262 K

Gay-Lussac’s Law: P/T relationship

Defn – at constant V, pressure of fixed amt of gas varies directly with Kelvin tempDirectly – as one variable increase, the

other increases

P

T

Gay-Lussac’s Law

Formula

P1 & T1 are initial conditionsP2 & T2 are final conditions

2

2

1

1

T

P

T

P

Gay-Lussac’s Law

Before a trip from Sugar Land to South Padre, the pressure in an automobile tire reads 2.1 atm at 27°C. Upon arriving in Padre, the gauge reads 2.3 atm. What is the temperature in South Padre?

329 K

Combined Gas Law: P/T/V

Defn – relationship between P,V, & T of fixed amount of gas

Formula

2

22

1

11

T

VP

T

VP

Combined Gas Law

The volume of a gas is 27.5 mL at 22.0°C and 740 mm Hg. What will be its volume at 15°C and 755 mm Hg?

26 mL

Avogadro’s Principle

Defn – equal volumes of gases at same temp and pressure contain equal number of molecules- the size of the molecule does not influence the

volume a gas occupies

- for example, 1000 relatively large Kr gas molecules occupies the same volume as 1000 smaller He gas molecules

Molar Volume of a Gas

Molar Volume – volume that one mole of a gas occupies at STP (0°C, 1 atm)

1 mole = 22.4 L

Molar Volume of a Gas

Ex prob #1: calculate the volume 0.881 mol H2 will occupy at STP.

0.881 mol H2

0.881 mol H2 x 22.4 L H2

1 mol H2

= 19.7 L H2

Molar Volume of a Gas

What is the mass of 0.0752 L of oxygen gas at STP? 0.0752 L O2

0.0752 L O2 x 1 mol O2

22.4 L O2

0.0752 L O2 x 1 mol O2 x 32 g O2

22.4 L O2 1 mol O2

= 0.107 g O2

Ideal Gas Law

Defn – relationship between P,V,T and # of moles, n

FormulaPV = nRT

ideal gas constant

Ideal Gas Constant

3 different R constants

R = 0.0821 L·atm

mol·K = 62.4 L· mm Hg

mol·K = 8.314 L·kPa

mol·K

pay attention to what unit of pressure is given in problem then use the appropriate R

Ideal Gas Law

Ex prob 1: what is the volume of 0.250 moles of oxygen gas at 20°C and 740 mm Hg?

which R do we use?

6.18 L O2

Ideal Gas Law

Ex prob 2: calculate the pressure, in atm, of 4.75 L NO2 containing 0.86 mol at 27°C.

4.46 atm

Ideal Gas Law

Ex prob 3: calculate the grams of N2 present in a 0.600 L sample kept at 1.0 atm and 22°C.first determine # of moles

0.025 mol N2

convert to grams0.70 g N2

4 gas laws vs. ideal gas law

The differences between ideal gas law and the other 4 are:

1) Ideal gas law utilizes an amount (moles), other 4 don’t

2) The 4 gas laws have a change in condition; ideal gas law does not