Gaseous State Flashcards
Relation between Pressure and root mean square speed
P = mnu*u/3V
(where ‘m’ is mase of 1 molecule, ‘n’ is total no. of molecules and V is volume of container)
Most Probable Speed (alpha)
square root of (2RT/M)
Average speed
Square root of [{(nv)1 + (nv)2}/n1 + n2]
square root of (8RT/pi*M)
Root mean square speed
square root of (3RT/M)
(alpha) : average speed : u
square root 2 : square root 8/pi : square root 3
1 : 1.1 : 1.224
Relation between speed, Temperature and Most probable speed for fraction of molecules
The most the temperature, the more the speed but alpha (waise toh woh increase hi krti hai but for the fraction of molecules) decreases and vice versa.
Kinetic Energy per mole of a gas ( R/N = Boltzmann constant K )
3RT/2 or 3PV/2 [ for n moles : 3RT/2*avogadro no. = 3KT/2]
Pressure and Temperature for real gas
P = high
T = low
Compressibility Factor
Z = PV/nRT
‘Z’ for ideal gas
1
Vander Waal equation
(P + an*n/V^2)(V - nb) = nRT
where,
a = force of attraction,
b = volume reserved (4VN)
n = no. of moles
Relation between Repulsive Forces and ‘Z’
when Z > 1, repulsive forces dominate
Relation between Repulsive Forces and ‘Z’
Critical Temperature
Temperature below which a gas can be liquified
Critical Pressure
Pressure for critical temperature
Critical Volume
Volume on critical temperature
Critical Temperature for gases
Elementary Gases : Tc is low
Non Elementary Gases : Tc is high
Relation between ‘a’ and Tc
the more the value of ‘a’, the more the value of Tc and the better and easy the liquification
Formula for Tc
8a/27Rb
Formula for Pc
a/27b*b
Formula for Vc
3b
CRITICAL :
Pressure * Volume / Temperature
= 3R/8
Boyle Temperature
Temp. on which a gas acts or becomes an ideal gas
Inversion Temperature
Temperature below which a gas shows cooling effect and above which it shows heating effect
Formula for T(boyle)
a/Rb
Formula for T(inversion)
2a/Rb
Weak forces
Ion dipole interaction
Ion induced dipole interaction
DIPOLE DIPOLE INTERACTION
DIPOLE INDUCED INTERACTION
LONDON FORCES
H-bonding
type of dipole dipole interaction
Relation between distance between dipole and Interaction Energy of Dipole- Dipole interaction
1/r^3 ∝ 1/r^6
Vander Waal Forces ∝
Atomic Masses ∝ Molecular Masses ∝ 1/branching
1 atm =
76 cmHg
760 mmHg
760 torrHg
almost equal to 1 bar
Manometer
when closed :
pressure of the gas is Height gained (h) by the liquid (fundamentally - Hg)
when open :
when liquid rises towards narrow tube :
1 atm + height gained by liquid
when liquid rises towards the gas conc. :
1 atm - height gained by the liquid
THE LIQUID IS GENERALLY Hg
If the liquid in manometer is not Hg
hρ (mercury) = hρ (given liquid)
Varying values of R
STP : 0.0821
NTP : 0.0831
Joules : 25/3 or 8.31
Calories : 2
Gas Laws
Boyle’s Law
Charles’s Law
Pressure Law
Avogadro Law
Dalton’s Law of Partial Pressure
Combined Gas Law
Graham Law of Diffusion Effusion
Boyle’s Law
Pressure ∝ 1/ Volume
when T and Mass of the gas are constant
PV (initial) = PV (final)
Charles’s Law
Volume ∝ Temperature (in K)
when Pressure and mass is constant
V/T (initial) = V/T (final)
Pressure Law
Pressure ∝ Temperature (in K)
when volume and mass is constant
P/T (initial) = P/T (final)
Dalton’s Law of Partial Pressure
Sum of all partial pressures is total pressure for dry gas whereas, for moist gas, aqueous tension is also added to total pressure of dry gas
Partial Pressure = Total pressure * Mole Fraction of the gas (moles of gas/moles of mixture)
diffusion (r) and effusion
Diffusion : movement of gas from high concentration to low concentration
Effusion : movement of gas through a pinhole or small opening
Graham Law for diffusion and effusion
Graham Law
r ∝ P/(density)^2
r1/r2 = P1/P2 * (d2/d1)^2
or
r1/r2 = P1/P2 * (M2/M1)^2
Formulae for Rate of Diffusion
r = Volume of gas diffused / time
r = Distance travelled by diffused gas / time
r = no. of moles of gas diffused/ time
Avogadro Law
If two gases have same pressure, volume and temperature, their no. of molecules are equal.
(Gay Lussac Law)
If reactants and products exist in gases having same temperature and pressure, then for the gas :
Molar Ratio = Volume Ratio
Combined Gas Law
P1V1/T1 = P2V2/T2
