CHM 101 Ch 5 Properties of Gases PDF

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Taken with Shahla Yekta,...

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Chapter 5 Properties of gases: only 11 elements are gases under normal atmospheric conditions (refer to Table 5.1 for gaseous elements and compounds); gases assume the volume and shape of their containers, are the most compressible of the states of matter, will mix evenly and completely when confined to the same container, and have much lower densities than liquids and solids, exert pressure Pressure: force applied per unit area (pressure= force ÷ area); SI unit is the Pascal (Pa) and is defined as one newton per square meter → 1 Pa = 1 N/m2 Atmospheric pressure: pressure exerted by Earth’s atmosphere; measured by the barometer (manometer measures pressure of gases other than the atmosphere) Standard atmospheric pressure (1 atm): equal to the pressure that supports a column of mercury exactly 760 mm or 76 cm high at 0 degrees Celsius → 1 atm = 760 mmHg or 760 torr, 1 atm = 101, 325 Pa Boyle’s law (P-V relationship): when temperature is held constant, the volume (V) of a given amount of a gas decreases as the total applied pressure (P) (atmospheric pressure plus the pressure due to added mercury) is increased; if applied pressure is decreased, on the other hand, the gas volume becomes larger Boyle’s law: states that the pressure of a fixed amount of gas maintained at constant temperature is inversely proportional to the volume of the gas; if P and V are multiplied, then where product of the pressure and volume of a gas at a constant temperature and amount of gas is a constant

1 P proportional to V (at constant n and T) 1 k 1⋅ V P=

or

PV  k1

P=( nRT ) Can be condensed to

or

1 V

P 1 V 1=P2 V 2 (where both sides are equal to k ) 1 , where nRT is constant

Absolute zero: theoretically the lowest attainable temperature → -273.15 °C Absolute/Kelvin temperature scale: absolute zero is starting point → 0 K= -273.15°C (scale: 1 K = 1°C) Freezing point: 273.15 K = 0°C ; Boiling point of water: 373.15 K = 100°C

Charles’ law (V-T or P-T relationships): the volume of a fixed amount of gas maintained at constant temperature is directly proportional to the absolute temperature of gas (k2 = nR/P) V proportional to T (at constant n and P)

V =k 2 T

V =k T 2

or

V1 V 2 = T1 T2

or

(where both sides are equal to k2) OR

P is proportional to T

P=k 3 T

P =k T 3

or

P1 P2 = T1 T 2

or

(where both sides are equal to k3)

CONDENSED TO

V=

( nRP )⋅T

where nR/P is constant → P can be replaced by V

Avogadro’s law: states that at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of the gas present V is proportional to n (at constant P and T)

V =k 4 n V= Can be condensed to

( RTP )⋅n

PV =nRT

Combination of all 3 gas laws:

where RT/P is constant where R, the proportionality constant, is called the gas constant

and equals 0.0821 L•atm/K•mol

R= Ideal gas equation: describes the relationship between P, V, T, and n →

PV nT (n=number of moles)

Ideal gas: a hypothetical gas whose PVT behavior can be completely accounted for by the ideal gas eq. STP: the conditions 0 degrees Celsius and 1 atm

P1 V 1 Changes in PVT:

n1 T 1

=R=

P2 V 2 P 1 V 1 P 2 V 2 = or n2 T 2 T1 T2 M=

Density of a gaseous substance:

dRT P

Gas stoichiometry: do problems to understand* Dalton’s law of partial pressures: the total pressure of a mixture of gases is just the sum of the pressures that each gas would exert if it were present alone (do problems to understand)* Mole fraction: dimensionless quantity that expresses the ratio of number of moles of one component to the number of moles of all components present*

Kinetic energy (KE): energy of motion Kinetic molecular theory of gases: number of generalizations about gas behavior that include: 1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions (“points”) 2. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collision among molecules are perfectly elastic; thus, energy can be transferred from one molecule to another by collision (total energy of all the molecules in system remains same) 3. Gas molecules exert neither attractive nor repulsive forces on one another 4. The average kinetic energy of the molecules is proportional to T of gas in K; thus, any two gases at

the same temperature will have the same kinetic energy →

1 KE= mu 2 2

Application of kinetic molecular theory of gases to gas laws: 

Compressibility of gases: gases can be compressed easily to occupy less volume



Boyle’s law: pressure exerted by a gas results from the impact of its molecules on the walls of the container (number of molecular collisions=density of a gas)



Charles’ law: because the average KE of gas molecules is proportional to the sample’s absolute temperature, raising the temperature increases average KE



Avogadro’s law: pressure of gas is directly proportional to both density and temp of gas



Dalton’s law: total pressure is given by the sum of individual gas pressures (no attract/repel)

Diffusion: gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic prop. Effusion: process by which a gas under pressure escapes from one compartment of a container to another by passing through a small opening Ideal behavior: molecules in the gaseous state do not exhibit any force, either attractive or repulsive, on one another; volume of the molecules is negligibly small compared with that of the container Deviation from the ideal gas law: do problems to understand*

Key Skills

Book Section

Work with units of pressure

5.2

Suggested Problems (from the end of chapter) 2, 13, 14

Understand the gas laws and use them to calculate T, P and V changes Understand what an ideal gas is and using the ideal gas law; Using combined gas law Calculate molecular weight and molecular formulas of gases using mass and volume Work stoichiometry problems with the gas laws

5.3

15, 18, 19, 22, 24, 83

5.4

27, 29, 32, 35, 36, 38, 41, 48

5.4

47, 49

5.4

52, 54, 85, 96

Work with partal pressures

5.5

55, 57, 60, 64

Understand kinetc molecular theory and use it t o explain gas laws Explain what an ideal gas is and what it means for a gas to deviate from ideal behavior

5.6

67, 71

5.7

78

Important Types of Problems to Study: ideal gas problems (Boyle, Charles, Avogadro, Combined Gas Law, molar mass of a gas), stoichiometry problems with gas laws, collecton of a gas over water, partal pressure problems...