Class XI: Thermodynamics (Chapter 6) notes

THERMODYNAMICS

It is the branch of chemistry which deals with energy changes in the chemical reactions and their feasibility.

System – Part of universe in which observations are made.

Surroundings -  Part of universe excluding system = Universe – System

Types of System –

a)         Open System -  There is exchange of energy and matter between system and surroundings. e.g. Open beaker.

b)         Closed system -  There is no exchange of matter but exchange of energy is possible between system and surroundings. e.g. presence of reactants in a closed vessel made up of conducting material.

c)         Isolated system -  There is no exchange of energy as well as matter between system and surroundings. e.g. Presence of reactants ina thermos flask or any insulated closed vessel.

State of the system -  The system must be described in order to make useful calculations by specifying quantitatively each of the properties such as pressure (P), volume (V) and temperature (T) as well as the composition of the system.

The state of the system is described by its measurable or macroscopic (bulk) properties.

State functions or state variables -  Those properties of a system which depend only on the state (initial and final state) of the system and do not depend upon the path of the system e.g. P.V.T.

Path functions -  Those properties of a system which do not depend upon the state (initial and final state) of the system but depend only upon the path of the system e.g. work done.

Types of processes :

a)      Isothermal process – that occurs at constant temperature.

b)      Isobaric process – that occurs at constant pressure

c)      Isochoric process – that occurs at constant volume

d)     Adiabatic  process – that occurs at constant heat i.e., there is no heat exchange between system and surroundings.

Internal energy (U or E) -  It is the energy possessed by the system. It depends upon –

a)      Heat passes into or out of the system

b)      Work is done on or by the system

c)      Matter enters or leaves the system

Internal energy is a state function as it depends upon initial and final state of the system

We cannot calculate the exact value of internal energy as it is the sum of many different kinds of energy such as mechanical energy, chemical energy, electrical energy, etc. whose values are difficult to calculate separately.

For adiabatic process, ΔU = U₂ – U₁ = W_ad

FIRST LAW OF THERMODYNAMICS –

-           According to it, energy of an isolated system is constant

-           Energy can neither be created nor be destroyed

Mathematically, ΔU = q + w

Where U = change in internal energy, q = heat absorbed by the system, W = work done on the system.

Proof – Let initial internal energy = U₁, final internal energy = U₂. If ‘W’ work is done on the system and ‘q’ heat is absorbed. Then,

            U₂ = U₁ + q + W

            U₂ – U₁ = q + W

            ΔU = q + W

Sign Conventions –

Work done by the system = (.), Work done on the system = (+)

Heat absorbed  → q = (+) and U = (+), Heat evolved → q = (–) and U = (–)

During expansion W = (–). During compression W = (+)

For adiabatic process, ΔU = – W_ad

For thermally conducting process, ΔU = – q

For closed system, ΔU = q + w

If the work is done by the system, ΔU = q – W  →  ΔU = q – W

APPLICATIONS :

1.         Work – (I = length, A = area) For 1 mole of a gas

            Change in volume  V = 1 × A

            As P = Force / area                             

            →        F on piston = P_ext . A

            Work done = F × distance = P × A × I = P × (–ΔV).           Therefore, W = – P Δ V

2.         

W = – 2.303 nRT log V₂ / V₁

Also,  As Boyle’s law  :  P₁/P₂ = V₂/V₁

→   W = – 2.303 nRT log P₁/P₂

 Now  cases :

a)      For isothermal process (T = constant) i.e., for isothermal expansion of ideal gas into vacuum,

            W = 0 and q = 0  →  ΔU = 0

b)      For isothermal irreversible change, q = W = P (V₂ – V₁)

c)      For isothermal reversible change, q = – W = nRT InV₂ / V₁

d)     For adiabatic change, q = 0 → ΔU = W_ad

Enthalpy (H) :

            It is the heat absorbed or heat evolved by the system.

            As U = q_p – P Δ V (expansion)

            qp = ΔH = ΔU + P Δ V

Proof :  ΔU = q – PΔV

            U₂ – U₁ = q_P – P (V₂ – V₁) at constant P

            q_p = (U₂ + PV₂) – (U₁ + PV₁)

            Therefore, H = U + PV

            qp = H₂ – H₁ = ΔH ( it is also known as state function)

            Now, if H = U + PV

            ΔH = ΔU + ΔpV + pΔV

            As H = q_p (at constant Pressure) i.e. ΔP = 0

            Therefore, ΔH = ΔU + PΔV

ΔH = (+) for endothermic reaction, ΔH = (.) for exothermic reaction.

Derivation ΔH = ΔU + Δn_gRT

Proof  ΔH = ΔU + PΔV = ΔU + P (V₂ – V₁)

Now, if PV = nRT. So,  PV₁ = n₁RT  and PV₂ = n₂RT

ΔH = ΔU + n₂RT – n₁RT = ΔU + (n₂ – n₁) RT

ΔH = ΔU + Δn_gRT

Where Δng = n₂ – n₁ for gaseous state = n_p – n_r

–          Extensive Property – Property whose value depends upon the quantity of matter contained in the system. e.g. mass, volume, internal energy, enthalapy, heat capacity. etc.

–          Intensive Property -  Property whose value does not depend on the quantity or size of matter present in the system. e.g. temperature, density, pressure

–          Heat Capacity (C) – It is the amount of heat required to raise the temperature of a substance by IC.

            Specific Heat Capacity  (C_S) –Amount of heat required to raise the temperature of 1gram of a substance by 1°C (1K).

            Molar Heat Capacity (C_m) –Amount of heat required to raise the temperature of 1 mole of a substance by 1°C.

                                                            Q = m C ΔT      where ΔT = T₂ – T₁

Relationship between C_P and C_V for ideal gases –

For constant volume, q_V = C_VΔT = ΔU  and  at constant P, q_P = C_PΔT = ΔH

For 1 mole of a gas, ΔH = ΔU + R ΔT

On putting the values of ΔH and ΔU, we get       C_PΔT = C_VΔT + R ΔT

V_P = V_C + R     Therefore,  C_P – C_V = R

We can measure energy changes (ΔH and ΔU) associated with chemical or physical processes by an experimental technique called calorimetry. The process is carried out in calorimeter immersed in a known volume of a liquid.

Knowing that heat capacity of liquid in which calorimeter is immersed and heat capacity of calorimeter, it is possible to determine the heat evolved in the process of measuring temperature changes under two different values,  a) at constant volume,  b) at constant pressure.

                                                            ΔH = H_P – H_R

Enthalpy changes -  Reactants  →  Products

The enthalpy changes accompanying the reaction is known as reaction enthalpy (ΔH)

Standard enthalpy of reaction -  The reaction enthalpy changes for a reaction when all the participating substances are in their standard states [standard temperature and pressure (1 bar) [Δ,H⁰]

DEFINITIONS

1.         Standard enthalpy of fusion  (Δ_fusH⁰) -  It is the heat evolved or absorbed by the system when one mole of a solid substance melts in standard state.

2.         Standard enthalpy of vapourisation (_vapH⁰) -  Amount of heat require to vapourize mole of a liquid at constant temperature and under standard pressure (1 bar)

3.         Standard enthalpy of sublimation (Δ_subH⁰) -  Amount of heat absorbed or evolved when sublimes at constant temperature and standard pressure (1 bar)

            ΔH is directly proportionsal to the intermolecular interactions in substance

4.         Standard enthalpy of formation (Δ_tH⁰) -  Amount of heat absorbed or evolved when 1 mole of compound is formed from its elements in their most stable states (reference state) at 25°C and 1 bar.

Example - H₂ (g) + 1/2O₂ (g) → H₂O (1) Δ_tH⁰ = 285.8KJ/mol; C (graphite) + 2H₂ (g) → CH₄ (g)

5.         Standard enthalpy of combustion – (Δ_CH⁰) Enthalpy change when 1 mole of a substance is burnt in presence of air completely.

6.         Enthalpy of atomization (ΔaH⁰) – It is enthalpy change on breaking 1 mole of bonds completely to obtain atoms in the gas phase.

Example -    CH4 (g)   →   C (g)  + 4H (g)                     Na (s)  →  Na (g)

7.         Bond enthalpy (Δ_bondH⁰) -  Energy is required break a bond and released to form a bond.

            The amount of heat absorbed or released due to break or form one mole of bonds of reactants is known as bond enthalpy.               Δ_rH⁰ = BE_R – BE_P

8.         Enthalpy of solution (Δ_solH⁰) – It is the enthalpy change when 1 mole of a substance is dissolved in specified amount of solvent.

 9.         Lattice enthalpy – It is the enthalpy change which occurs when 1 mole of an ionic compound dissociates into its ios in gaseous state (Δ_Lattice H or U)

10.       Heat of hydration -  Amount of enthalpy change when 1 mole of the anhydrous salt combines with required number of moles of water so as to change into the hydrated salt.                                         CuSO₄ + aq → CuSO₄.5H₂O

11.       Heat of neutralization of an acid by a base -  It is the heat change when 1 gram equivalent of the acid is neutralized by a base, the reaction is carried out in dilute aqueous solution.

            When 1 gram equivalent of HCI is neutralized by NaOH or vice-versa, 57.1 kJ of heat is produced

–          Heat of neutralization is taken for 1 gram equivalent of acid and base because neutralization involves combination of 1 mole of H⁺ ions with 1 mole of ^–OH ions. 1 gram of any acid on complete dissociation gives 1 mole of H⁺ ions but 1 mole of an acid may not give 1 mole of H⁺ ions.

Example -  1 mole H₂SO₄ → 2 moles of H⁺ ions on complete dissociation,

            1 gram equivalent H₂SO₄  → 1 mole of H⁺ ion

Hess’s law of constant heat summiation –

According to it, if a reaction takes place in several steps then its standard enthalpy is the sum of the standard enthalpies of the intermediate reaction into which the overall reaction may be divided at same temperature.                                                         OR

According to it, if a reaction takes place in one step or in many number of steps, the amount of energy released or absorbed (enthalpy change) always remain constant at constant temperature.

Example -        C (graphite, s) + O₂ (g) → CO₂

            Step 1 : C (s) + ½ O₂ → CO (g);   Step 2 :  CO (g) + ½ O₂ →  CO₂ (g)  i.e. ΔH = H₁ + H₂

Class XI: States of matter (Chapter-5) notes

States of matter

Intermolecular forces – forces of attraction and repulsion between interacting particles (atoms and molecules). These are also known as Vander Waals force of attraction. Types of Vander Waal forces:-

1)            Ion-dipole forces: attractive forces between an ion and a dipole. E.g. NaCl + H₂O.

2)        Dispersion forces or London forces: atoms or non-polar molecules are electrically symmetrical and have no dipole moment. But a dipole may develop momentarily even in such atoms and molecules. If the momentarily electronic charge distribution in one of the atoms becomes unsymmetrical, this results in the development of instantaneous dipole on the atom for very short interval of time. This distorts the electron density of other atoms which are closer to it and as a result the dipole is induced in other atoms. These are temporary dipoles. E.g.: Noble gases, H₂, etc.

3)      Dipole-dipole forces: present between the molecules possessing permanent dipoles. E.g.: H₂O, HCl.

4)            Dipole-Induced dipole: between polar molecules having permanent dipoles and molecules which are non-polar. Permanent dipole of polar molecules induces dipole on the electrically neutral molecule by deforming its electronic clouds. E.g.: Cl₂ and H₂O.

5)            Hydrogen bond: requires (i) H-Atom, (ii) small size electronegative atom (F, O, N). E.g.: water, ammonia.  

   

Thermal Energy : It is the measure of average kinetic energy of particles  of the matter and their motion.

Order of intermolecular force of attraction: Gas < liquid < solid.

Order of thermal energy:    Gas > liquid > solid.

Gaseous State:

Only 11 elements exist as gas under normal conditions: He, Ne, Ar, Kr, Xe, Rn, F, Cl, O, N, H.

They are highly compressible and diffusible.

Parameters:

a) Volume: 1L=1 dm³= 1000cm³= 1000 ml.

b) Pressure : measured by barometer ( atmospheric pressure) and manometer ( P of gas). 1 atm = 760mm = 760 torr = 1 bar = 101,325 Pa.

c) Temperature (^oC, K or F)

Gas laws:

1) Boyle’s law : At constant temperature, pressure of fixed mass of gas is inversely proportional to  volume. i.e  P α 1/V  OR     PV=Constant.         

            P₁V₁ = P₂V₂

Isotherm: Graph between P and V at constant temperature.

Significance of Boyle’s law: The gases are compressible. The more it is pressed, the denser it becomes. Therefore, at constant temperature, density of gas is directly proportional to pressure. At altitudes, as atmospheric pressure is low, the air is less dense. As a result, less oxygen is available for breathing. That is why the mountaineers have to carry oxygen cylinders with them.

2) Charles’ law: (given by Jacques Charles and extended by Joseph Gay Lussac) At constant Pressure, volume of a given mass of a gas increases or decreases by 1/273.15 of its volume at 0^oC for every one degree centigrade rise or fall in temperature.

  

This implies that a gas at -273.15⁰C will have zero or no volume, i.e., it will cease to exist.

Absolute zero: The lowest hypothetical or theoretical temperature of -273.15^oC at which a gas is supposed to have zero volume is called absolute zero.

Lord Kelvin suggested a new scale of temperature starting with -273.15⁰C as its zero. This scale of temperature is known as Kelvin or absolute scale of temperature. (273K to 373K)

Also, at constant temperature for a fixed mass of gas, Volume α Temperature.

V/T = constant.

Isobar: Graph between V and T at constant Pressure.

Significance of Charles’ law: Air expands on heating and hence its density decreases. Thus hot air is lighter than the atmosphere air and is used in filling hot air in the balloons which rise up for meteorological observations.

3) Gay- Lussac’s law or Amonton’s law: At constant volume, Pressure of a given mass of a gas increases or decreases by 1/273.15 of its pressure at 0⁰C for every centigrade rise or fall in temperature.

Also, at constant temperature for a fixed mass of gas, Pressure α Temperature.

P/T = constant.

Isochore: Graph between P and T at constant Volume.

4) Avogadro’s law: According to it, equal volumes of all gas under the same conditions of temperature and pressure contain equal number of molecules. Volume α no. of moles

5) Ideal Gas: A gas that follows Boyle’s law, Charles’ law and Amonton’s law strictly is called an ideal gas. Such a gas is hypothetical.

Ideal Gas Equation:

Boyle’s law: PV = Constant at constant T and n

Charles’law: V/T = Constant at constant P and n

Amonton’s law: P/T = Constant at constant V and n

Avogadro’s law: V α n at constant P and T.

PV/T = Constant   i.e. PV = nRT

Where R = Universal Gas Constant

= 8.314 J/K/mol = 0.0831 L atm/k/mol.

This is an equation of state. It is a relation between four variables and it describes the state of any gas.

Combined gas law:

Units of R:

6) Dalton’s law of partial pressure: (given by John Dalton)

According to it, the total pressure exerted by the mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. In a mixture of gases, pressure exerted by the individual gas is called partial pressure of a gas.

P_total = P₁ + P₂ + P₃ + …….. at constant temperature and volume

P_{dry gas} = P_total – aqueous tension.

Aqueous tension = Pressure exerted by saturated water vapours.

7) Relationship between density of a gas and its molar mass:

As PV = nRT and no. of moles = given mass (w)

                                                            Molar mass (M)

Kinetic molecular theory of gases: (given by Bernoulli and then Clausius)

Postulates or assumptions-

a) Every gas is made up of large number of molecules that are so small and so far apart that the actual volume of molecules is negligible in comparison to the empty space between them. They are considered as point masses. (This assumption explains compressibility of gas).

b) There is no force of attraction between particles of a gas at ordinary temperature and pressure. (It explains that gases expand and occupy all the space available to them)

c) Particles of a gas are always in constant and random motion. (Explains indefinite shape of gas)

d) Particles of gas move in all possible directions in straight lines with different velocities due to which they collide with each other as well as on the container.

e) Collisions of gas molecules are perfectly elastic collision, i.e., the total energy of molecules before and after the collision remain same.

f) At any particular time, the molecules are moving with different velocities and possess different kinetic energy. Average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.

Deviations from ideal gas behavior- (Real Gases)

Real gases are those gases which do not obey ideal gas equation. They show deviations from ideal gas behavior. The extent to which a real gas deviates from ideal gas behavior can be conveniently studied in terms of a quantity ‘Z’ called as the compressibility factor which is the ratio of product PV and nRT.

(i) For an ideal gas, PV = nRT i.e. Z = 1

(ii) For real gas, PV = nRT

Therefore, when Z<1, gas shows negative deviation i.e. gas is more compressible than expected from ideal behavior.

When Z>1, gas shows positive deviation i.e. gas is less compressible than expected from ideal behavior.

Extent of deviation depends upon the nature of the gas.

Q Why do gases deviate from ideal behavior?

Causes: Two assumptions of the kinetic theory do not hold good-

a) There is no force of attraction between the molecules of gas.

b) Volume of molecule of gas is negligibly small in comparison to the space occupied by the gas.

If assumption a) is correct, the gas will never liquefy. If assumption b) is correct, pressure Vs volume graph of real gas and ideal gas should coincide.

Equation of state for real gases - (Vander Waal’s equation)

For one mole of gas:

For n moles of gas:

Where a and b are Vander Waal’s constants. Their values depend upon nature of gas.

Derivation- by modifying ideal gas equation PV = nRT

(i)    Correction for volume- When the molecules are moving, their effective volume is four times the actual volume i.e. 4v. Thus, the free volume available to the gas molecule for the movement i.e. corrected volume = (V-b) for 1 mole or (V-nb) for n moles, where b = 4v = excluded volume or co-volume.

(ii) Correction of pressure- A molecule lying within the vessel is attracted equally by other molecules on all sides but a molecule near the wall is attracted by the molecules inside. Corrected P = P + p

Where p α (density)²   and  density α (n/V) for n moles or (1/V) for 1 mole.

Corrected P = P + an²/V².

Therefore, Vander Waal’s equation: (P + an²/V²) (V – nb) = nRT

Significance of Vander Waal’s constants:

(i) ‘a’ – It is a measure of the magnitude of the attractive forces among the molecules of gas. Greater the value of ‘a’, larger are the intermolecular forces of attraction.

(ii) ‘b’ – It is a measure of effective size of gas molecules. It is equal to the four times the actual volume of gas molecules. It is called excluded or co-volume.

Units of ‘a’ and ‘b’:

‘a’ :  P = an²/V²      a = PV²/n² = atm L² mol^-2

‘b’ : V = nb            b = V/n = L/mol

Real gases obey ideal gas equation at- (i) low pressure, (ii) high temperature

(as a/V² and b become negligible at these conditions)

Boyle temperature or boyle point: The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called boyle temperature.

Also Z = V_real / V_ideal

Liquifaction of gases: First complete data on P-V-T relations of a substance in both gaseous and liquid state was obtained by Thomas Andrews on CO₂. He plotted isotherms of CO₂ at various temperatures. Andrews noticed that at high temperature isotherms look like that of an ideal gas and the gas cannot be liquefied even at very high pressure.

Critical Temperature (T_c) – The temperature above which a gas cannot be liquefied howsoever high pressure may be applied on the gas. Volume of one mole of the gas at critical temperature is called critical volume (V_c) and pressure at this temperature is called critical pressure (P_c). For CO₂, T_c = 31.1⁰C or 30.98⁰C.

Methods for gas liquefaction: a) By increasing pressure, b) By decreasing temperature.

Importance of T_c : T_c is a measure of strength of intermolecular forces of attraction of that gas. Weaker are the intermolecular forces of attraction, difficult it is to liquefy that gas and hence lower would be the T_c of gas.

Vander Waal’s constant ‘a’ is a measure of intermolecular forces of attraction.

Greater the value of ‘a’ is, higher would be the value of T_c of that gas.

Liquid state - Various properties:

a) Vapour Pressure – It is the pressure exerted by the vapours on the surface of liquid molecules when an equilibrium is established between liquid phase and vapour phase. It is known as equilibrium or saturated vapour pressure.

Boiling point – Temperature at which vapour pressure of a liquid is equal to the external pressure.

Normal boiling point - at 1atm pressure and Standard boiling point – at 1bar pressure. [as 1 bar < 1atm, therefore, normal boiling point (100⁰C) > standard boiling point (99.6⁰C) {1 atm = 1.03 bar}]

At high altitudes atmospheric pressure is low, therefore, liquids boil at lower temperature at high altitudes in comparison to that at sea level. Since, water boils at low temperature on hills, pressure cooker is used for cooking food.

Factors affecting vapour pressure:

(i) Nature of liquid – If intermolecular forces of attraction are weak, molecules can easily leave the liquid and come into the vapour phase and exert more vapour pressure.

(ii) Temperature – Temperature increases, vapour pressure increases.

b) Surface tension – Force acting at right angles to the surface along one cm length of surface. Unit of γ = N/m.         γ = Force / length

The energy required to increase the surface area of liquid by 1 unit is called surface energy. Unit = J / m².

A molecule lying inside the liquid is surrounded by other molecules and so is attracted by them equally in all directions. Hence, net force acting by them equally in all directions. Hence, net force acting on it is zero. While, a molecule at the surface is attracted more by the molecules lying in the bulk of liquid than by the molecules lying above it in the vapour phase. Thus, a molecule lying at the surface experiences a net inward attraction. Thus, surface behaves as if it is under tension. As a result, surface of liquid tends to contract to the smallest possible area for a given volume of a liquid.

Surface tension tries to decrease the surface area of liquid to minimum. The drops of liquid are spherical because for a given volume, a sphere has minimum surface area.

Liquid tends to rise (or fall) in the capillary because of surface tension. It is surface tension which gives stretching property to the surface of liquid.

Cohesive forces – Attracting forces existing between the molecules of same substance. E.g. – molecules of water.

Adhesive forces - Attracting forces existing between the molecules of different substances. E.g. – molecules of water and glass.

In case of water that wets glass has concave or lower meniscus (curved surface of liquid) because adhesive forces are stronger than cohesive forces while coloured liquids show upper meniscus in glass tube because in these liquids, cohesive forces are stronger.

Factors affecting surface tension:

(i) Temperature – Temperature increases, kinetic energy of molecules increases and intermolecular forces decrease, so surface tension decreases.

(ii) Intermolecular forces of attraction – increases, surface tension increases.

c) Viscosity – It is the measure of resistance to flow which arises due to the internal friction between layers of fluid as they slip past one another while liquid flows.

Laminar flow: Flow in which there is regular gradation of velocity in passing from one layer to the next. 

F = η.A.dV/dx   

where η = coefficient of viscosity, F = Force of viscosity, A = area, dV/dx = velocity gradient.

η = It is the force of friction between the layers of liquid when velocity gradient is unity and the area of contact is unit area.

Unit of η = Ns/m²  (in SI unit) = Poise (in cgs unit- named after Jean Louise Poiseuille)

Factors affecting viscosity:

(i) Temperature – Temperature increases, kinetic energy of molecules increases, liquid starts flowing faster, viscosity decreases.

(ii) Intermolecular forces of attraction – increases, viscosity increases.