9Gaseous and Liquid states

📚
GASEOUS STATE
▢ Pressure Measurement:
  • •
    pure gas pressure → manometer
  • •
    mixture of gases pressure → barometer
📚
GAS LAWS
📖
Boyle's law
▢ Statement: constant temperature → volume of fixed mass of gas inversely proportional to pressure
▢ Formulae:
  1. \(V \propto \frac{1}{P}\)
  2. \(PV = K\)
  3. \(P_1V_1 = P_2V_2 = P_3V_3 = \cdots = P_nV_n = K\)
▢ Density-Pressure Relation:
  1. \(d \propto P\) at constant \(T\) and mass
  2. \(\frac{d_1}{P_1} = \frac{d_2}{P_2}\)
▢ Graphical Representation:
  • •
    \(P\) vs \(\frac{1}{V}\) → straight line through origin
  • •
    \(P\) vs \(PV\) → straight line parallel to pressure/volume axis
  • •
    \(P\) vs \(V\) → rectangular hyperbola
  • •
    \(P-V\) curves at constant temperature = isotherms
▢ Special Point: air at sea level dense due to compression by air mass; density + pressure ↓ with altitude
📖
Charles' law
▢ Statement: constant pressure → volume of fixed mass gas changes by \(\frac{1}{273}\) of volume at \(0^\circ C\) per \(1^\circ C\) change
▢ Formulae:
  1. \(V_t = V_0 + \frac{t}{273}V_0\)
  2. \(V_t = V_0\left(\frac{t+273}{273}\right)\)
  3. \(T = t + 273\)
  4. \(V \propto T\)
  5. \(\frac{V}{T} = K\)
  6. \(\frac{V_1}{T_1} = \frac{V_2}{T_2} = \cdots = \frac{V_n}{T_n} = K\)
▢ Absolute Zero:
  • •
    at \(-273^\circ C\), gas volume theoretically zero
  • •
    absolute zero = \(0K\)
  • •
    Kelvin zero = \(-273.15^\circ C\)
  • •
    at absolute zero: volume, pressure, kinetic energy, heat content → zero
  • •
    Charles' law not applicable to gases liquefying before \(-273^\circ C\)
▢ Volume Coefficient: \(\alpha_v = \frac{1}{273}\)
▢ Pressure Coefficient: \(\alpha_p = \frac{1}{273}\)
▢ Graphs:
  • •
    \(V\) vs \(T(K)\) at constant pressure → straight line through origin
  • •
    \(V\) vs \(t(^\circ C)\) at constant pressure → straight line cutting temperature axis at \(-273^\circ C\)
  • •
    constant pressure graph = isobar
▢ Density-Temperature Relation:
  1. \(V \propto T\)
  2. \(\frac{1}{d} \propto T\)
  3. \(dT = K\)
  4. \(d_1T_1 = d_2T_2\)
📖
Pressure law / gay-lussac law
▢ Statement: constant volume → pressure of fixed mass gas directly proportional to absolute temperature
▢ Formulae:
  1. \(P \propto T\)
  2. \(\frac{P}{T} = K\)
  3. \(\frac{P_1}{T_1} = \frac{P_2}{T_2} = \frac{P_3}{T_3}=\cdots\)
▢ Graph: isochore → constant volume graph
📖
Combined gas equation
▢ Basis: Boyle's law + Charles' law
▢ Formulae:
  1. \(V \propto \frac{1}{P}\) at constant \(T\)
  2. \(V \propto T\) at constant \(P\)
  3. \(V \propto \frac{T}{P}\)
  4. \(\frac{PV}{T} = R\)
  5. \(PV = RT\) for 1 mole
  6. \(PV = nRT\) for \(n\) moles
  7. \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
▢ Nature of R: work done per degree per mole
▢ Values of R:
    ◉ **type: bullet
  1. \(R = 0.0821\,L\,atm\,K^{-1}mol^{-1}\)
  2. \(R = 8.314\times10^7\,erg\,K^{-1}mol^{-1}\)
  3. \(R = 8.314\,J\,K^{-1}mol^{-1}\)
  4. \(R = 2\,cal\,K^{-1}mol^{-1}\)
  5. \(R = 0.002\,kcal\,K^{-1}mol^{-1}\)
  6. \(R = 8.314\,N\,m\,K^{-1}mol^{-1}\)
  7. \(R = 8.314\,MPa\,cm^3\,K^{-1}mol^{-1}\)
  8. \(R = 5.189\times10^{19}\,eV\,K^{-1}mol^{-1}\)
  9. \(R = 8.314\,kPa\,dm^3\,K^{-1}mol^{-1}\)
▢ Boltzmann Constant:
  1. \(k = \frac{R}{N_A}\)
  2. \(k = 1.38\times10^{-16}\,erg\,deg^{-1}\,molecule^{-1}\)
  3. \(k = 1.38\times10^{-23}\,J\,K^{-1}\)
▢ Applications:
❖ Mass / Molecular Weight:
  1. \(PV=nRT\)
  2. \(n=\frac{m}{M}\)
  3. \(PV=\frac{m}{M}RT\)
  4. \(m=\frac{PVM}{RT}\)
❖ Density:
  1. \(PV=\frac{m}{M}RT\)
  2. \(P=\frac{m}{V}\times\frac{RT}{M}\)
  3. \(P=\frac{dRT}{M}\)
  4. \(d=\frac{PM}{RT}\)
  5. \(\frac{dT}{P}=K\)
  6. \(\frac{d_1T_1}{P_1}=\frac{d_2T_2}{P_2}\)
📖
Dalton's law of partial pressures
▢ Statement: total pressure of non-reacting gas mixture = sum of partial pressures under similar temperature
▢ Formulae:
  1. \(P = P_1 + P_2 + P_3 + \cdots\)
  2. \(P*{gas} = \text{mole fraction} \times P*{total}\)
  3. \(\text{mole fraction} = \frac{\text{moles of gas}}{\text{total moles of mixture}}\)
▢ Partial Pressure: pressure exerted by a gas if present alone in same container at same temperature
▢ Non-Applicable Mixtures:
    ◉ **type: bullet
  1. \(SO_2\) + \(Cl_2\) → react
  2. \(NH_3\) + \(HCl\) → react
▢ Gas Collected Over Water:
    ◉ **type: bullet
  1. water vapour contributes aqueous tension
  2. \(P*{dry\ gas}=P*{moist\ gas}-P*{water\ vapour}\)
  3. \(P*{dry\ gas}=P*{observed}-\text{aqueous tension}\)
▢ Percentage Composition: \(\%\,gas = \frac{\text{partial pressure of gas}}{\text{total pressure of mixture}}\times100\)
▢ Partial Pressure From Mixing:
  1. \(P = \frac{P_1V_1}{V}\)
  2. \(P_1V_1\) → pressure-volume before mixing
  3. \(V\) → volume of container
📖
Graham's law of diffusion
▢ Diffusion: property of gases to mix with each other forming homogeneous mixture irrespective of gravity
▢ Effusion: special diffusion through small aperture
▢ Rate:
  1. \(r=\frac{\text{volume diffused}}{\text{time}}\)
  2. \(r_1=\frac{V_1}{t_1}\), \(r_2=\frac{V_2}{t_2}\)
  3. \(\frac{r_1}{r_2}=\frac{t_2}{t_1}\) for equal volume
▢ Main Formulae:
  1. \(r \propto \frac{1}{\sqrt{d}}\) at constant \(T,P\)
  2. \(\frac{r_1}{r_2}=\sqrt{\frac{d_2}{d_1}}=\sqrt{\frac{VD_2}{VD_1}}=\sqrt{\frac{M_2}{M_1}}\)
▢ Different Pressure:
  1. \(r \propto \frac{P}{\sqrt{d}}\)
  2. \(\frac{r_1}{r_2}=\frac{P_1}{P_2}\sqrt{\frac{d_2}{d_1}}=\frac{P_1}{P_2}\sqrt{\frac{M_2}{M_1}}\)
▢ Same Volume: \(\frac{t_1}{t_2}=\sqrt{\frac{M_1}{M_2}}\)
▢ Different Mass of Different Gases:
  1. \(t \propto \frac{m}{\sqrt{M}}\)
  2. \(\frac{t_2}{t_1}=\frac{m_2}{m_1}\sqrt{\frac{M_1}{M_2}}\)
▢ Different Masses of Same Gas:
  1. \(t \propto m\)
  2. \(\frac{t_2}{t_1}=\frac{m_2}{m_1}\)
▢ Rate Order: \(CO_2 > SO_2 > SO_3 > PCl_3\)
▢ Equal Molar Mass: gases with equal molecular mass → equal rate of diffusion
▢ Atmolysis: separation of gases from gaseous mixture using diffusion principle
▢ Special: \(NH_3\) and \(HCl\) introduced at tube ends → white \(NH_4Cl\) ring nearer to HCl end
📚
KINETIC THEORY OF GASES
▢ Postulates:
  • •
    gas molecules in constant rapid straight-line motion in all directions
  • •
    actual molecular volume negligible compared with total gas volume
  • •
    gas pressure due to collisions of molecules against vessel walls
  • •
    collisions between gas molecules perfectly elastic → no energy loss
  • •
    no effective force of attraction / repulsion between molecules
  • •
    average kinetic energy directly proportional to absolute temperature
▢ Kinetic Gas Equation:
  1. \(PV=\frac{1}{3}mnc^2\)
  2. \(P\) → pressure; \(V\) → volume; \(m\) → mass of one molecule; \(n\) → no. of molecules; \(c\) → RMS speed
  3. \(PV=RT=\frac{1}{3}mnc^2=\frac{2}{3}\times\frac{1}{2}mnc^2=\frac{2}{3}KE\)
  4. \(KE=\frac{3}{2}RT=\frac{3}{2}PV\)
  5. \(\text{Average KE per molecule}=\frac{3}{2}kT\)
▢ Absolute Zero: molecular velocities reduced to zero → molecular motion ceases
▢ Applicability: kinetic theory applies to ideal gases
▢ Kinetic Energy:
    ◉ **type: bullet
  1. total KE of gas = \(\frac{3}{2}nRT\)
  2. KE per mole same for all gases at same temperature
  3. KE per molecule / average KE = \(\frac{3}{2}kT\)
  4. total KE depends on temperature and mass of gas
  5. KE per unit mole + average KE depend only on temperature
📚
MOLECULAR SPEEDS
📖
**c
📝
Types
  1. Root mean square speed
  2. Average speed
  3. Most probable speed
📝
RMS Speed
  1. \(c=\sqrt{\frac{c_1^2+c_2^2+c_3^2+\cdots+c_n^2}{n}}\)
  2. \(c*{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3PV}{M}}=\sqrt{\frac{3P}{d}}=\sqrt{\frac{3kT}{m}}\)
📝
Average Speed
  1. \(\bar{c}=\frac{c_1+c_2+c_3+\cdots+c_n}{n}\)
  2. \(\bar{c}=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8kT}{\pi m}}\)
  3. \(\bar{c}=0.9213\times c*{rms}\)
📝
Most Probable Speed
  1. \(c*{mp}=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2kT}{m}}\)
  2. \(c*{mp}=0.8164\times c*{rms}\)
📝
Ratio
\(c*{mp}:\bar{c}:c*{rms}=\sqrt{2}:\sqrt{\frac{8}{\pi}}:\sqrt{3}=1:1.128:1.224\)
📝
Order
\((V)*{rms}>(V)*{av}>V*{mp}\)
📝
Average Velocity
average velocity of molecules = 0
📝
Same Temperature Relation
\(m_1u_1^2=m_2u_2^2\)
📚
REAL GASES AND IDEAL GASES
📖
Deviation from ideal behaviour
▢ Cause: intermolecular attraction
▢ Condition: high pressure + low temperature
▢ Real Gases: do not obey gas laws strictly under all temperature and pressure
▢ Ideal Gas: obeys gas laws strictly under all conditions; actually no gas is perfectly ideal
📖
Van der waals equation
▢ Corrections:
    ◉ _*type: bullet
  1. volume correction: \(V_i = V-b\)
  2. pressure correction: \(P_i=P*{obs}+\frac{a}{V^2}\)
▢ Equation:
  1. \(\left(P+\frac{a}{V^2}\right)(V-b)=RT\) for 1 mole
  2. \(\left(P+\frac{n^2a}{V^2}\right)(V-nb)=nRT\) for \(n\) moles
▢ Constants:
  • •
    \(a\) → intermolecular attraction constant
  • •
    \(b\) → excluded volume / molecular volume constant
  • •
    unit of \(a\): \(atm\,L^2mol^{-2}\) or \(Pa\,m^6mol^{-2}\)
  • •
    unit of \(b\): \(L\,mol^{-1}\) or \(m^3mol^{-1}\)
  • •
    \(b=\frac{16}{3}\pi r^3N_A\)
  • •
    higher \(a\) → stronger attraction → gas liquefies easily
▢ Special:
  • •
    H\(_2\), He → positive deviation from ideal behaviour
  • •
    equation applicable to real gases
📖
Compressibility factor
▢ Definition: extent of deviation of real gas from ideal gas
▢ Formula: \(Z=\frac{PV}{nRT}\)
▢ Cases:
  • •
    \(PV>nRT\Rightarrow Z>1\) → positive deviation; gas less compressible than expected
  • •
    \(PV
  • •
    \(PV=nRT\Rightarrow Z=1\) → ideal gas
📖
Ideal gas vs real gas

Table 1: Difference between ideal gas and real gas

Feature
Ideal Gas
Real Gas
Gas laws
obeys \(PV=RT\) under all temperature and pressure
obeys gas laws only at low pressure + high temperature
Existence
hypothetical; no real existence
all gases are real
Molecular volume
negligible compared with container volume
not negligible
Intermolecular force
no intermolecular attraction
attraction present; pressure less than calculated from gas laws
Examples close to ideal
N\(_2\), He, H\(_2\) difficult to liquefy → nearer ideal
easily liquefiable gases deviate more
📖
Critical phenomena
▢ Critical Temperature:
  1. temperature above which gas cannot be liquefied by pressure
  2. \(T_c=\frac{8a}{27bR}\)
▢ Critical Pressure:
  1. minimum pressure required to liquefy gas at critical temperature
  2. \(P_c=\frac{a}{27b^2}\)
▢ Critical Volume:
  1. volume occupied by 1 mole gas at critical temperature and critical pressure
  2. \(V_c=3b\)
▢ Boyle's Temperature:
  1. temperature above which gas behaves like ideal gas
  2. \(T_B=\frac{a}{Rb}\)
  3. at this temperature gases behave ideally over wide pressure range
▢ Inversion Temperature:
  1. \(T_i=\frac{2a}{bR}=2\times T_B\)
  2. compressed gas allowed to expand in low pressure region → cooling below inversion temperature
▢ Critical-Boyle Relation: \(T_c=\frac{8}{27}T_B\)
▢ Note: Boyle's temperature and inversion temperature differ for different gases
📖
Heat capacity ratio
▢ Monoatomic: \(\frac{C_p}{C_v}=\gamma=1.66\)
▢ Diatomic: \(\frac{C_p}{C_v}=\frac{7R/2}{5R/2}=1.40\)
▢ Triatomic: \(\frac{C_p}{C_v}=\frac{8R}{6R}=\frac{4}{3}=1.33\)
▢ Symbols:
  1. \(C_p\) → molar heat capacity at constant pressure
  2. \(C_v\) → molar heat capacity at constant volume
📖
Degrees of freedom table

Table 1: Atomicity, heat capacities and kinetic energy

Atomicity
Translatory
Rotational
Total \(f\)
\(C_v=\frac{f}{2}R\)
\(C_p=(\frac{f}{2}+1)R\)
\(\gamma=\frac{C_p}{C_v}\)
KE per molecule
Monoatomic
3
0
3
\(\frac{3}{2}R\)
\(\frac{5}{2}R\)
1.67
\(\frac{3}{2}kT\)
Diatomic
3
2
5
\(\frac{5}{2}R\)
\(\frac{7}{2}R\)
1.4
\(\frac{5}{2}kT\)
Triatomic / Polyatomic
3
3
6
\(3R\)
\(4R\)
1.33
\(3kT\)
📖
Make calculation easy
▢ Pressure:
  1. \(1\,atm=760\,mmHg=760\,torr=1.01\times10^5\,Pa=1.01325\,bar\)
▢ Energy:
  1. \(1J=10^7\,erg=0.239\,cal\)
▢ Molar Volume: \(1\,g\,mole=22.4\,L\) gas at STP
▢ Density Relation:
  1. \(n=\frac{W}{M}\)
  2. \(P=\frac{DRT}{M}\)
  3. \(D\) → density
  4. \(M\) → molar mass
▢ Temperature Conversion: \(\frac{C}{100}=\frac{K-273}{100}=\frac{F-32}{180}\)
📚
READ AND DIGEST - GASES
▢ Important Points:
    ◉ _*type: bullet
  1. closed-limb manometer used for gases with pressure < atmospheric pressure
  2. Boltzmann constant: \(k=\frac{R}{N_A}=1.38\times10^{-23}\,J\,K^{-1}\)
  3. average translational KE per molecule = \(\frac{3}{2}kT\) for all gases
  4. total average KE per molecule: monoatomic = \(\frac{3}{2}kT\), diatomic = \(\frac{5}{2}kT\), triatomic/polyatomic = \(3kT\)
  5. total average KE per mole: monoatomic = \(\frac{3}{2}RT\), diatomic = \(\frac{5}{2}RT\), triatomic/polyatomic = \(3RT\)
  6. ideal gas possesses only KE, not PE
  7. ideal gas liquefaction impossible because cohesive force negligible
  8. \(PV=nRT\) holds best at high temperature + low pressure
  9. internal energy of ideal gas depends only on temperature
  10. internal energy of real gas depends on temperature and volume
  11. gas in fast-moving train → temperature remains unchanged
  12. electric fan in closed room → air slightly heated
  13. insect: walking surface → 2 degrees of freedom; flying in room → 3 degrees of freedom
  14. RMS speed at \(0^\circ C\) becomes double at \(819^\circ C\) / \(1092K\)
  15. gas with RMS speed \(400\,m/s\) has \(u*{mp}=800\sqrt{2}\,m/s\)
  16. Gay-Lussac's law of gaseous volume derived from experimental volume
  17. ideal gas cannot be liquefied because intermolecular forces negligible
  18. van der Waals real gas behaves ideal at high temperature + extremely low pressure
  19. Dalton's law not applicable to \(SO_2+Cl_2\) due to reaction forming sulphuryl chloride \(SO_2Cl_2\)
  20. gas molecules behave as elastic rigid spheres
  21. average velocity at equilibrium = 0, but average speed \(\propto \sqrt{T}\)
  22. He molecule two times heavier than H molecule at \(298K\); average KE same = \(\frac{3}{2}kT\)
  23. at \(27^\circ C\), RMS velocity ratio ozone:oxygen = \(\sqrt{\frac{2}{3}}\)
  24. Joule-Thomson heating at ordinary temperature → \(H_2\)
  25. polar substances have higher critical temperature than non-polar due to stronger attractive forces
📚
LIQUID STATE
▢ General Properties:
  • •
    liquids are \(10^5\) times less compressible than gases
  • •
    liquids are about 10 times more compressible than solids
  • •
    liquids neither perfectly ordered nor totally disordered
  • •
    partially ordered liquid structure = quasi-lattice structure
📚
SOLUTION
▢ Definition: homogeneous mixture
▢ Components:
  • •
    dispersed phase → solute
  • •
    medium → solvent
  • •
    larger amount component → solvent
▢ Azeotropic Solution: solution with definite composition and boiling point
▢ Saturated Solution: maximum solute dissolved at given temperature
▢ Unsaturated Solution: less solute than saturated solution at given temperature
▢ Supersaturated Solution: more solute than saturated solution at given temperature
▢ Crystallisation: crystals prepared from supersaturated solution
📖
Types of solution

Table 1: Solvent-solute types

Solvent
Solute
Example
Solid
Solid
alloys, stones
Solid
Liquid
hydrated salts like \(CuSO_4.5H_2O\)
Solid
Gas
gases in minerals
Liquid
Solid
sugar in \(H_2O\)
Liquid
Liquid
alcohols in \(H_2O\)
Liquid
Gas
cold drinks / carbonated water
Gas
Solid
\(I_2\)
Gas
Liquid
steam / water vapours
Gas
Gas
air
📖
Molarity
▢ Definition: moles of solute dissolved in 1000 ml solution
▢ Formula: \(M=\frac{\text{moles of solute}}{\text{volume of solution in ml}}\times1000\)
▢ Temperature Effect: temperature ↑ → molarity ↓
▢ Most Convenient: molarity = convenient way of expressing concentration
📖
Solubility of solid in liquid
▢ Definition: mass of solute dissolved in 100 g solvent at given temperature
▢ Formula: \(\text{Solubility}=\frac{\text{mass of solute in g}}{\text{mass of solvent in g}}\times100\)
▢ Depends On:
  1. nature of solute
  2. nature of solvent
  3. temperature
▢ Temperature Effect:
  • •
    endothermic dissolution: solubility \(\propto T\); e.g. \(NaCl, KCl\)
  • •
    exothermic dissolution: solubility \(\propto \frac{1}{T}\); e.g. \(KOH, NaOH, Ca(OH)_2, Na_2SO_4, Na_2CO_3, CaO\)
▢ Solubility Curve:
  • •
    plot of solubility vs temperature
  • •
    sharp break in curve → transitional temperature of hydrated salt
  • •
    slope negative for exothermic dissolution
  • •
    slope positive for endothermic dissolution
📖
Solubility of gases in liquids
▢ Temperature: decreases with increase in temperature
▢ Pressure: increases with increase in pressure
▢ Henry's Law:
  1. mass of gas dissolved in given volume liquid directly proportional to partial pressure of gas in equilibrium
  2. \(m \propto p\)
  3. \(m=Kp\)
  4. \(p\) → partial pressure of gas
  5. \(K\) → proportionality constant
▢ Critical Solution Temperature: temperature at which partially miscible liquid pair becomes completely miscible; also called consulate temperature
📚
EVAPORATION AND VAPOUR PRESSURE
📖
Evaporation
▢ Definition: spontaneous escape of liquid molecules from surface
▢ Volatility: tendency of liquid molecules to escape from surface
▢ Boiling / Vaporization: conversion of liquid into vapour at boiling point
▢ Nature:
  • •
    surface phenomenon
  • •
    endothermic process
  • •
    causes cooling
  • •
    average KE and temperature of liquid fall due to evaporation
▢ Factors Affecting Rate:
❖ Temperature: evaporation \(\propto T\)
❖ Surface Area: larger exposed surface → greater evaporation
❖ Nature of Liquid:
  1. rate inversely proportional to intermolecular force
  2. intermolecular force: ether < ethyl alcohol < water
  3. rate of evaporation: ether > ethyl alcohol > water
▢ Heat of Vaporization: heat required to vaporize 1 mole liquid at constant temperature
📖
Vapour pressure
▢ Dynamic Equilibrium: rate of condensation = rate of evaporation
▢ Definition: pressure exerted by vapour in equilibrium with liquid at given temperature
▢ Saturated Vapour Pressure: pressure under equilibrium with liquid
▢ Important Points:
  • •
    non-polar liquids like \(CCl_4, CHCl_3\) have higher vapour pressure than polar liquids
  • •
    liquid boils at lower temperature at mountain than sea level
  • •
    deliquescent / efflorescent character due to vapour pressure
  • •
    low intermolecular force → high vapour pressure
▢ Deliquescent Substance: absorbs moisture from air and dissolves; e.g. \(NaOH, KOH, CaCl_2\)
▢ Deliquescence Condition: vapour pressure of saturated solution < water vapour pressure in air
▢ Efflorescent Substance: loses water of crystallisation; e.g. \(Na_2CO_3.10H_2O\)
▢ Efflorescence Condition: vapour pressure of hydrated crystals > water vapour pressure in air
▢ Factors Affecting Vapour Pressure:
❖ Nature of Liquid: weaker cohesive force → higher escape tendency → higher vapour pressure
❖ Temperature: \(\text{vapour pressure}\propto T\); increases rapidly near boiling point
❖ Impurities: non-volatile impurities lower vapour pressure
📖
Boiling point
▢ Definition: temperature at which vapour pressure of liquid equals atmospheric pressure
▢ Boiling vs Evaporation:

Table 1: Boiling and evaporation

Boiling
Evaporation
takes place only at particular temperature
takes place at all temperatures
involves formation of bubbles throughout liquid bulk
surface phenomenon
vapour pressure = atmospheric pressure
no such condition
📚
SURFACE TENSION OF LIQUIDS
▢ Definition 1: tangential force acting along liquid surface at right angle to unit length line drawn on surface
▢ Definition 2: work required to increase free surface area of liquid by 1 unit at constant temperature and pressure
▢ Unit: dyne/cm or N/m
▢ Applications:
  • •
    spherical raindrops
  • •
    spherical mercury globules
  • •
    rise of liquid in capillary tube
  • •
    shaving blade / thin metallic needle floats on water surface when placed carefully
▢ Factors:
❖ Intermolecular Attraction:
  1. \(\text{intermolecular force}\propto\text{surface tension}\)
  2. water > ethyl alcohol > ether
❖ Pressure: pressure ↑ → surface tension ↑ slightly; effect not large
❖ Temperature:
  1. \(\text{surface tension}\propto\frac{1}{T}\)
  2. temperature ↑ → surface tension ↓
  3. at critical temperature, surface tension = 0
📚
VISCOSITY OF LIQUIDS
📖
**c
📝
Definition
internal resistance to flow of liquid
📝
Layer Concept
slow-moving layer tends to retard adjacent fast-moving layer
📝
Nature
self-governing force
📝
Formulae
  1. \(F\propto A\frac{dv}{dx}\)
  2. \(F=\eta A\frac{dv}{dx}\)
📝
Symbol
\(\eta\) → coefficient of viscosity
📝
Coefficient of Viscosity
force per unit area required to maintain unit relative velocity between two liquid layers unit distance apart
📝
Units
  1. SI: \(N\,s\,m^{-2}\)
  2. CGS: poise
📝
Arrhenius Equation
\(\eta=Ae^{B/RT}\)
📝
Molecular Weight
molecular weight ↑ → viscosity ↑ due to van der Waals force ↑
📝
Fluidity
\(\phi=\frac{1}{\eta}\)
📝
Temperature Effect
  1. \(\eta*{liquid}\propto\frac{1}{T}\)
  2. \(\eta*{gas}\propto T\)
📚
COLLIGATIVE PROPERTIES
▢ Definition: properties depending on number of molecules / ions / particles, not nature
▢ Types:
  • •
    lowering of vapour pressure
  • •
    elevation of boiling point
  • •
    depression of freezing point
  • •
    osmotic pressure
▢ Relations:
  1. colligative properties \(\propto\) no. of particles
  2. colligative properties \(\propto\frac{1}{\text{molecular mass of solute}}\)
📖
Lowering of vapour pressure
▢ Relative Lowering: \(\frac{P-P_s}{P}\)
▢ Symbols:
  1. \(P\) → vapour pressure of pure solvent
  2. \(P_s\) → vapour pressure of solution
▢ Raoult's Law: relative lowering of vapour pressure = mole fraction of solute
▢ Formula: \(\frac{P-P_s}{P}=\frac{n}{n+N}\)
▢ Ideal Solution Conditions:
  • •
    solute-solute interaction = solvent-solvent interaction = solute-solvent interaction
  • •
    \(\Delta V=0\)
  • •
    \(\Delta H=0\)
  • •
    \(\Delta S\ne0\)
▢ Examples: chlorobenzene + bromobenzene; benzene + toluene; methanol + ethanol
▢ Positive Deviation:
  1. \(\Delta V>0\), \(\Delta H>0\), \(\Delta S\ne0\)
  2. observed vapour pressure > predicted by Raoult's law
  3. example: benzene + methanol
▢ Negative Deviation: \(\Delta V<0\), \(\Delta H<0\)
📖
Elevation of boiling point
▢ Formula: \(\Delta T_b=K_bm=\frac{w}{W}\times\frac{1}{M}\times1000\times K_b\)
▢ Symbols:
  1. \(m\) → molality of solute
  2. \(K_b\) → molal elevation constant / ebullioscopic constant
  3. \(w\) → mass of solute
  4. \(W\) → mass of solvent
  5. \(M\) → molar mass of solute
▢ Water: \(K_b=0.52\,K\,kg\,mol^{-1}\)
▢ Constant Relation: \(K_b=\frac{RT_b^2}{1000l_v}\); \(l_v\) = latent heat of vaporization
📖
Depression of freezing point
▢ Formula: \(\Delta T_f=K_fm=\frac{w}{W}\times\frac{1}{M}\times1000\times K_f\)
▢ Symbols:
  1. \(K_f\) → molal depression constant / cryoscopic constant
  2. \(l_f\) → latent heat of fusion
▢ Constant Relation: \(K_f=\frac{RT_f^2}{1000l_f}\)
▢ Water: \(K_f=1.86\,K\,kg\,mol^{-1}\)
📖
Osmotic pressure
▢ Symbol: \(\pi\)
▢ Formulae:
  1. \(\pi V=nRT\)
  2. \(\pi=C_MRT\)
▢ Measurement: Berkley and Hartley's method
▢ Isotonic Solutions: two solutions with same molar concentration at same temperature → same osmotic pressure
📖
Van't hoff factor
▢ Symbol: \(i\)
▢ Formulae:
  1. \(i=\frac{M_c}{M_o}=\frac{\text{calculated molecular mass}}{\text{observed molecular mass}}\)
  2. \(i=\frac{\text{observed magnitude of colligative property}}{\text{normal magnitude of colligative property}}\)
  3. \(i=\frac{\text{normal molar mass}}{\text{observed molar mass}}\)
  4. \(M_c=i\times m\)
▢ Corrected Formulae:
  1. \(\Delta T_b=iK_bm\)
  2. \(\Delta T_f=iK_fm\)
  3. \(\pi V=inRT\)
  4. \(\pi=iC_MRT\)
📚
READ AND DIGEST - LIQUIDS
📖
**c
📝
Important Points
    ■ **type: bullet
  1. liquefied metal expanding on solidification: Ga
  2. at critical temperature, meniscus between liquid and vapour disappears
  3. H-bonding in liquid hydrogen chloride expected dipole-dipole
  4. acetic acid molecular weight becomes 120 due to dimerization
  5. normality of 10% \(\frac{w}{v}\) acetic acid = 1.7 N
  6. mercury → convex meniscus; water → concave meniscus
  7. at critical temperature, densities of gaseous and liquid states become same; no distinction between 2 states
  8. evaporation is surface phenomenon
  9. Trouton's rule: ratio of molar heat of vaporization to boiling point = constant
  10. at critical temperature, surface tension of liquid = 0
  11. temperature ↑ → viscosity of liquid ↓; viscosity of gas ↑
  12. isotonic solutions have same osmotic pressure
  13. liquid in equilibrium with vapour at boiling point → two phases have equal total energy
  14. molality independent of temperature
Q1.
At constant temperature, in a given mass of an ideal gas
Q2.
A gas is initially at 1 atm pressure. To compress it to 1/4th of its initial volume, pressure to be applied is
Q3.
Which of the following expressions at constant pressure represents Charles' law?
Q4.
The correct value of R is close to
Q5.
The constant R is
Q6.
Pressure of a gas is due to
Q7.
If two moles of an ideal gas at 546 K occupy a volume of 44.8 litres, the pressure must be
Q8.
300 mL of a gas at \(27^\circ C\) is cooled to \(-3^\circ C\) at constant pressure, the final volume is
Q9.
Pressure remaining constant, at what temperature will the volume of a gas be double of its volume at \(0^\circ C\)?
Q10.
Volume of 4.4 g of \(CO_2\) at NTP is
Q11.
Volume of 0.5 mole of a gas at 1 atm pressure and \(273^\circ C\) is
Q12.
If the weight of 5.6 litres of a gas at NTP is 11 gram, the gas may be
Q13.
A gas A diffuses 5 times faster than gas B. Density of A compared with B is
Q14.
Molecular weight of a gas that diffuses twice as rapidly as the gas with molecular weight 64 is
Q15.
The relative rate of diffusion of a gas of molecular weight 128 as compared to oxygen is
Q16.
The atomic weight of helium is 4 times of hydrogen. Its rate of diffusion as compared to hydrogen is
Q17.
The rates of diffusion of \(SO_2\) and \(O_2\) are in the ratio
Q18.
The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is
Q19.
The internal energy of one mole of an ideal gas is given by
Q20.
The rms velocity at NTP of the species can be calculated from the expression
Q21.
Which set of conditions represents easiest way to liquefy a gas?
Q22.
When an ideal gas undergoes unrestrained expansion, no cooling occurs because the molecules
Q23.
The gas that is heated up during Joule-Thomson effect at ordinary temperature is
Q24.
For easily liquefiable gases like \(SO_2\), \(NH_3\), etc., the critical temperature is generally
Q25.
Positive deviation from ideal behaviour takes place because of
Q26.
The van der Waals' equation reduces itself to the ideal gas equation at
Q27.
Air at sea level is dense. This is a practical application of
Q28.
Pressure cooker reduces cooking time because
Q29.
A closed flask contains water in all its three states: solid, liquid and vapour at \(0^\circ C\). In this situation, the average kinetic energy of water molecules will be
Q30.
Vibrational energy is
Q31.
The ratio between the root mean square speed of \(H_2\) at 50 K and that of \(O_2\) at 800 K is
Q32.
Which of the following expressions correctly represents the relationship between the average molar kinetic energy of CO and \(N_2\) molecules at the same temperature?
Q33.
Gas equation \(PV=nRT\) is obeyed by
Q34.
With increase of temperature, coefficient of viscosity of a liquid
Q35.
Steam distillation is based on
Q36.
For easily liquefiable gases like \(SO_3\), \(NH_3\), etc., the critical temperature is generally
Q37.
PV=nRT is applicable to
📅MOE 2062
Q38.
Which gas diffuses more rapidly?
📅MOE 2063
Q39.
The compound A, B, C and D has 1, 2, 3 and 4 mole respectively kept in identical vessel at same temperature. The greatest pressure is exerted by
📅MOE 2003
Q40.
Which is true about O2 and SO2?
📅MOE 2002
Q41.
A certain mass of gas occupies 40 litres at 760 mmHg. What will be its volume at 5 atm?
📅MOE 2002
Q42.
One litre of gas at 0°C is heated to 100°C keeping mass and the pressure constant. What will be the new volume at 100°C?
📅MOE 2058
Q43.
The gas pressure in an aerosol can is 1.5 atm at 250°C. Assuming that the gas inside obeys Charles Law, what would be the pressure if the can were heated to 450°C?
📅MOE 2000
Q44.
2 gm of O2 at NTP has volume
📅MOE 2000
Q45.
Equal weight of N2 and O2 contained in separate containers with same volume and temperatures have
📅MOE 1997
Q46.
A gas is heated in such a way that its volume and absolute temperature are both doubled. Then the pressure of the gas increases by
📅IOM 1996
Q47.
Which of the following gases has the lowest rate of diffusion?
📅MOE 2009
Q48.
A compound has high intermolecular attraction, then it has
📅MOE 2008
Q49.
Evaporation of water is
📅MOE 2062
Q50.
How many grams of water is required to make saturated solution of 100 gram of KNO3 at 100°C if solubility at 100°C is 20?
📅IOM 2000
Q51.
If a gas at constant temperature and pressure expands then its
📅BPKIHS 2001
Q52.
The ratio of the rate of diffusion of Helium (He) and Oxygen (O2) is
📅BPKIHS 2007
Q53.
Equal weight of methane and oxygen are mixed in an empty container at 25°C. The fraction of total pressure exerted by oxygen is
📅I.E. 2005
Q54.
Which of the following mixture of gases does not obey Dalton's law of partial pressure?
📅I.E. 2004
Q55.
Which of the following is a colligative property?
📅BPKIHS 2007
Q56.
Which of the following is not an example of colligative property?
📅BPKIHS 2005
Q57.
Boiling point of liquid depends on all of the following factors except
📅BPKIHS 2005