Chapter 1: The properties of gases

Question 1

Physical State

Answer 1

of a sample os as substance, its physical condition, is defined by its physical properties.

two samples of the same substance that have the same physical properties are on the same state

amount of substance (n)

volume(V)

pressure(p)

temperature(T)

Question 2

standard pressure

Answer 2

1 bar p^Ø

Question 3

mechanical equilibrium

Answer 3

the condition of wquality of pressure on either side of a movable wall.

When there are no unbalanced forces within the system and between the system and the surrounding, the system is said to be under mechanical equilibrium. The system is also said to be in mechanical equilibrium when the pressure throughout the system and between the system and surrounding is same. Whenever some unbalance forces exist within the system, they will get neutralized to attain the condition of equilibrium. Two systems are said to be in mechanical equilibrium with each other when their pressures are same.

Question 4

pascal

Answer 4

1 N m^-2 , 1 kg m^-1 s^-2

Question 5

equation of state

Answer 5

an equation that interrelates these four variables

p = f (T,V,n)

Question 6

Boyle’s law

Answer 6

For a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure.

• pV* = constant , at constant n,T
• pV* = R

P₁V₁=P₂V₂

_ex. halfing the volume increases pressure due to the increase in collsions

Question 7

Charles’s law

Answer 7

For a fixed mass of gas at constant pressure, the volume is directly proportional to temperature (in Kelvin).

V = constant X T, at constant n, p

V/T = R

p = constant X T, at constant n,V

p/T = R

temperture incresaes the averge law speed, causing collsion to happen more offten

Question 8

Avogadro’s principle

Answer 8

Avogadro’s law states that, “equal volumes of all gases, at the same temperature and pressure, have the same number of molecules”.

V = constant X n, at constant p,T

The number of molecules or atoms in a specific volume of ideal gas is independent of size or the gas’ molar mass.

Question 9

limiting law

Answer 9

a law that is strictly ture only in a certain limit,

in the case of boyles and charles law

example, p→0

Question 10

isotherm

Answer 10

a line on a map connecting points having the same temperature at a given time or on average over a given period.

a polt with changeing volume and pressure might us isotherms

Question 11

isobars

Answer 11

showing variation at constant pressure

Question 12

isochores

Answer 12

change at constant volume

Question 13

perfect gas law

Answer 13

is based on a series of empirical observation, is a limiting las that is obeyed incresingly well as the pressure of a gas tends to zero

pV = nRT

the approximate equation of any gas, and becomes increasing exact as the pressure of the gas approaches zero

Question 14

perfect gas

Answer 14

a gas that obeys the perfect gas law exactly under all conditions

Question 15

real gas

Answer 15

an actual gas, behavies more like a perfect gas the lower the pressure and is described by the perfect gas law in the linit of p→ 0

Question 16

standard temperature and pressure

Answer 16

0 degrees celces , 1 atm

V_m = 22.414 dm³ mol^-1

Question 17

partial pressure (1A.8)

Answer 17

p_j = x_jp

x = mole fraction

Question 18

Dalton’s Law (words)

Answer 18

the pressure exerted by as mixtutre of a gas is the sum of the pressures that each one would exert if it occupied the container alone

Question 19

Partial pressure

Answer 19

P_j = x_jp

Question 20

kinetic theory

Answer 20

it is assumed that the only contribution to the energy of the gas is from the kinetic energies of the molecuces.

Question 21

Root -Mean square speed

Answer 21

v_rms =〈​v²〉​^{<span>1/2</span>}

V_rms = (3RT/M)^1/2 -RMS speed - perfect gas

Question 22

elastic collision

Answer 22

a collision in which the total translational kinetic energy of the molecules is conserved

Question 23

distribution of speeds

Answer 23

the fraction of molecules that have speeds in the range v to v +dv is proportional to he width of the range, and is written f(v)dv , where f(v) is called the distribution of speeds

f(v) is the Maxwell-Boltzmann distribution of speeds

Question 24

Maxwell-Boltzmann distribution of speeds (1B.4)

Answer 24

• f(v) = 4π(M/2πRT)^3/2 v²e(-Mv² /2RT)*
• important feature*
• 1.implies the fraction of molecules with very high speeds will be very small*
• 2.heavy molecules are unlikely to be found ar very high speeds*
• 3.a greater fraction of molecules can be expected to have high speeds at high temperatures than at low temperature*
• 4. the fraction of molescules with very low speeds will also be very small ehatever their mass*
• 5. the sum of the fractions over the entire reagon of speeds from zero to infinty will be 1*

Question 25

mean speed (1B.8)

Answer 25

• v_mean = (8/3π)^1/2*
• ^{perfect gas}*

Question 26

collision frequency,z, (1B.11a)

Answer 26

the number of collisions made by one molecule divided by the time interval during which the collisions are counted.

z= σv_relƝ

Ɲ= N/V, the number density

σ = πd², collsion cross section

z=σv_relp/kT

Question 27

mean free path

Question 28

Compression factor (1C.1)

Answer 28

the ration of the measured molar volum of a gas V_m = V/n, to he molar volume of a perfect gas .V_m^°

Z = V_m/V_m^°

Question 29

Virial equation of state (1C.3b)

Answer 29

pV_m = RT (1 + B/V_m +C/V_m² +…)

B,C re virial coefficients and depend on temperature

Question 30

principle of corresponding states

Question 31

critical temperture T_c

Answer 31

an isotherm slighly below T_c , at a certin pressure , a liquid condences from the gas and it is distinguishable from it by the presences of a visable surface

if the compression take place at T_c itself, then a surface separating the two phases does not appear ans the volumes at each end of the horizontal part of the isotherm have merged to a single point, the critical point of a gas

above T_C the sample has a singel phase which occipies the entire volume of the container, such a phase is defined as a gas

liquid phase does not form abobe Tc

Question 32

vapour pressure

Answer 32

when both the liquid and vapour are present in equilibrium

Question 33

critical behavior

Question 34

van der Waals equation (1C.5a)

Answer 34

p = nRT/(V-nb) -an²/V²

a represents the strength of attractive interaction

b represents the strength of repilsive interactions between the molceules

depend on the gas and temp

Question 35

reduced variables

Question 36

Gas

Answer 36

in molecuar terms, a gas consists of a molecules that are in ceasless motion and which interact sigificantly with one another only when thay collide

Question 37

difference between ideal and perfect

Answer 37

ideal -> the interactions are all the same

perfect -. the interactions are the same, they are also zero

Question 38

Combined gas law (1A.7)

Answer 38

p₁ V₁/n₁T₁ = p₂ V₂/n₂T₂

Question 39

Molar volume

Answer 39

V_m= V/n

Question 40

Mole fraction

Answer 40

x_j = n_j/n

n = n_A + n_B +…

Question 41

a gas consists of ….

Answer 41

molecles of negligilbe size in ceasless random motion and obeying the laws of classical mechanics in therir collisions

note Newtons 2nd law

acceleration of a body is proportional to the force acting on it, and the conservation of linear momentum

Question 42

the kinetic model is based on three assumptions

Answer 42

1. the gas consists of molecules of mass m in ceasless random motion obeying the laws of classical mechanics
2. the size of the molecules is negligible, in the sence that their diameters are much smaller than the average distance travelled between collisions.
3. the molecules interact only through brief elastic collisions

Question 43

Attractions and repulusions between gas molecules account for……

Answer 43

modifications to the isotherms of a gas and account for critical behavior

Question 44

real gases show deviations from the perfect gs law because

Answer 44

molecules interact with one another

note

replusive forces between molesules assist expansion and attractive forces assist compression

Question 45

repulsive forces

Answer 45

assist expansion

are only significant only when molecules are almost in constatn

short range interactions

only important when molecules the averge separation of the molecles is small (in the case of high pressure when many molecules occupy a small volume)

Question 46

attractive forces

Answer 46

assist compression

have long ranges and are effective over several molecular diameters

important when moleculs are failry close together but not necessarily touching

ineffective when molecules are far apart

Question 47

intermolecular forces are important ….

Answer 47

when the temp is so low that they can be captured by one another

Question 48

at moderate pressure

Answer 48

attractive forces dominate the repulsive forces

in this case, the gas can be expected to be more compressible than a perfect gas because the forces help to draw molecules together

Question 49

at high pressures

Answer 49

when that average seporations is small , the replsive dominate and the gas can be expected to be less compressible now the forces help drive the molecules apart

Question 50

at low pressures

Answer 50

whe nthe sample occupies a large volume, the molecules are so far apart for most of the time that intermolecular forces play no significant role, and the gas beahves virtually perfect

Question 51

when a gas is compressed by a pistion,at some point….

Answer 51

it will compress without a rise in presssure( a liquid appears, and there are two phases seporated by a sharply defined surface)

as the volume decreases the amount of liquid increases

thers is no additional resistance to the pistion because the gas can respond by condensing.

the pressure corresponds to when both the liquid and vapour are present in equilibrium (vapour pressure

Question 52

molar volume of a perfect gas.

Answer 52

V_m = RT/p

Question 53

What is the compression factor of a perfect gas

Answer 53

the compression factor of a perfect gas is one

deviations of Z from one is a measure of departure from perfect behavior

z= RT/pV_m^°

Question 54

super crital fluid

Answer 54

the single phase that fils the entire volume when T > Tc may be much denser than that of normal gases

Question 55

Boyle temperature ,T_B,

Answer 55

at the boyle temperatue the properties of the real gas do coincide with those of a perfect gas as p→ 0.

Z has zero slope as p→0 if B=0