Thermochemistry | General Chemistry 2

Thermochemistry is studied in this chapter: kinetic energy, potential energy, law of conservation of energy, system and surroundings, state and state functions, internal energy, heat and work, first law of thermodynamics, enthalpy, calorimetry, heat capacity, Hess’s law, standard state, enthalpy of formation, enthalpy of reaction, bond enthalpy.

Energy and its Conservation

Energy:

Energy is the capacity to do work or transfer heat. It exists in various forms, including kinetic energy, potential energy, thermal energy, and chemical energy. The SI unit of energy is the joule (J). One joule is the energy transferred when a force of one newton acts over a distance of one meter.

1 J = 1 N.m = 1 kg.m2.s-2


Forms of energy:

Energy is classified as either kinetic or potential.

  • Kinetic energy (EK):

Kinetic energy is the energy associated with the motion of an object. The amount of kinetic energy in a moving object is given by the equation:
 

Ek = 12 mv2

Ek = kinetic energy (in J)
m = mass (in kg)
v = velocity (in m.s-1)

 

  • Potential energy (Ep):

Potential energy is the energy stored in an object due to its position or arrangement.
 

Conservation of energy law:

Energy cannot be created or destroyed; it can only be converted from one form into another. The total energy of an isolated system remains constant over time.
 

ΔEsystem + ΔEsurroundings = 0

ΔEsystem = change in energy in the system
ΔEsurroundings = change in energy in the surroundings

Introduction to Thermodynamics

Thermodynamics and thermochemistry:

  • Thermodynamics: The study of energy transformations in chemical and physical processes. It focuses on the concepts of energy, heat, work, and the laws governing these transformations.
  • Thermochemistry: The study of the energy change associated with chemical reactions.

 

System and surroundings:

  • System: The part of the universe being studied (e.g., a reaction mixture in thermochemistry).
  • Surroundings: Everything outside the system. Surroundings can exchange energy and matter if the system is open or only energy if the system is closed. There is no exchange with an isolated system.

 

Types of systems:

  • Open System: Can exchange both energy and matter with its surroundings.
  • Closed System: Can exchange energy but not matter with its surroundings.
  • Isolated System: Cannot exchange either energy or matter with its surroundings.
     
  • Open system: A pot of boiling water, where water vapor (matter) and heat (energy) are exchanged with the surroundings.
  • Closed system: A sealed container of gas, where only energy (heat) can be transferred but not matter.
  • Isolated system: An insulated thermos bottle, where neither energy nor matter is exchanged with the surroundings.

 

Process:

A process is the path of a system from an initial state to a final state. The final state is generally an equilibrium, where all the properties of the system do not change with time. A process can be:

  • Isobaric: Constant pressure.
  • Isochoric: Constant volume.
  • Isothermal: Constant temperature.
  • Adiabatic: No matter or heat transfer from the system to its surroundings.

 

State and state functions:

  • State: The condition of a system as described by its properties, such as temperature, pressure, volume, and composition.
  • State functions: Properties that depend only on the current state of the system, independent of how the state was achieved (e.g., internal energy, enthalpy, entropy, Gibbs free energy).

Internal Energy, Heat and Work

Heat (q): 

Heat is the transfer of energy based on a temperature difference, moving from a region of high temperature to a region of low temperature.

Sign convention:

  • q < 0: The reaction releases energy as heat (exothermic process).
  • q > 0: The reaction absorbs heat energy (endothermic process).

 

Work (w):

Work is defined as the force that produces the movement of an object times the distance moved:
 

 w = F x d

w = work (in J)
F = force (in N)
d = distance (in m)

 

Sign convention:

  • w < 0: Work is done by the system (expansion).
  • w > 0: Work is done on the system (compression).


When gases expand or compress, they can do work on the surroundings:
 

w = - PΔV

w = work of gas (in J)
P = external atmospheric pressure
ΔV = Vf - Vi


 

Internal energy (U):

Internal energy is the sum of the kinetic and potential energies of the particles of a system:
 

U = Ek + Ep

U = internal energy (in J)
Ek = kinetic energy (in J)
Ep = potential energy (in J)


Energy change of a system:
 

ΔU = Uf - Ui

ΔU = change in internal energy (in J)
Uf = internal energy in the final state (in J)
Ui = internal energy in the initial state (in J)

 

Recall that energy is defined as the capacity to do work or transfer heat. The overall change in the system's internal energy is given by:
 

ΔU = q + w

ΔU = change in internal energy (in J)
q = heat (in J)
w = work (in J)

 

Sign convention:

  • ΔU < 0: Energy flows from the system into the surroundings.
  • ΔU > 0: energy flows from the surroundings into the system.

 

First Law of thermodynamics:

The first law of thermodynamics and based on the law of conservation of energy and states that energy cannot be created or destroyed, but it can be transformed from one form to another. In an isolated system, the sum of all forms of energy is constant:

ΔUuniverse = ΔUsystem + ΔUsurroundings = 0

Enthalpy

Enthalpy (H):

Enthalpy is a thermodynamic quantity that represents the total heat content of a system. It is defined as:
 

H = U + PV

H = enthalpy (in J)
U = internal energy (in J)
P = pressure (in Pa = N.m-2)
V = volume (in m3)

 

Enthalpy change (ΔH):

Since U, P, and V are all state functions, H is also a state function. Therefore, the change in H depends only on the initial and final states:
 

ΔH = ΔU + Δ(PV)

ΔH = change in enthalpy (in J)
ΔU = change in internal energy (in J)
​​​​​​P = pressure (in N.m-2)
V = volume (in m3)

 

At constant pressure, ΔH = ΔU + PΔV

 

Enthalpy of reaction (ΔHrxn):

The enthalpy of reaction is the change in enthalpy during a reaction and is defined as the difference between the enthalpies of the products and the enthalpies of the reactants:
 

ΔHrxn = Hprod – Hreact

ΔHrxn = enthalpy of reaction (in J)
Hprod = enthalpies of the products (in J)
Hreact = enthalpies of the reactants (in J)

 

  • ΔH < 0: Exothermic process (heat is released by the system).
  • ΔH > 0: Endothermic process (heat is absorbed by the system).

Calorimetry and Heat Capacity

Calorimetry:

Calorimetry is the measurement of heat flow in a chemical reaction or physical process. It involves using a device called a calorimeter to measure the heat absorbed or released during a reaction.

Types of calorimetry:

  • Constant-pressure calorimetry: Performed at constant atmospheric pressure, it measures the change in enthalpy (ΔH) of a reaction.
  • Constant-volume calorimetry: Performed at constant volume, it measures the change in internal energy (ΔU) of a reaction.

 

Heat capacity (C):

Heat capacity is the amount of heat required to raise the temperature of an object or substance by one Kelvin.
 

C = qT

C = heat capacity (J.K-1)
q = quantity of heat absorbed or released (in J)
ΔT = Tf - Ti = change in temperature (in K)

 

Sign convention:

  • q < 0: Exothermic process (heat is released by the system).
  • q > 0: Endothermic process (heat is absorbed by the system).

 

Types of heat capacity

  • Specific heat capacity (s):

The amount of heat required to raise the temperature of one gram of a substance by one Kelvin.
 

s = qmT

s = specific heat capacity (in J.g-1.K-1)
q = quantity of heat absorbed or released (in J)
m = mass of the substance (in g)
ΔT = Tf - Ti = change in temperature (in K)

 

  • Molar heat capacity (Cm):

The amount of heat required to raise the temperature of one mole of a substance by one Kelvin.
 

Cm = qnT

Cm = molar heat capacity (in J.mol-1.K-1)
q = quantity of heat absorbed or released (in J)
m = number of moles (in mol)
ΔT = Tf - Ti = change in temperature (in K)

Hess's Law

Hess’s Law:

Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the number of steps in the reaction. This is based on the fact that enthalpy is a state function, which means it depends only on the initial and final states of the system, not on the path taken to get from one to the other.

 

Consequences of Hess's law:

  • Additivity of enthalpy changes: The enthalpy change for a multi-step reaction is the sum of the enthalpy changes for each individual step.

ΔH2-step rxn = ΔH (step 1) + ΔH (step 2)
 

  • Reversibility of chemical equations: The enthalpy change for the reverse of a reaction is equal in magnitude but opposite in sign to the enthalpy change of the forward reaction.

ΔHrxn (reverse) = - ΔHrxn (forward)
 

  • Multiplication of chemical equations: When a chemical equation is multiplied by a factor, the enthalpy change for the reaction is also multiplied by that same factor.

ΔHn x step = n x ΔHrxn (step)


 

Applications of Hess's law:

Hess's Law allows for the calculation of the enthalpy change for reactions that are not easily measured directly by breaking them down into simpler steps.
 

Calculate the enthalpy change of combustion of methane knowing that:

  • CH4 ​(g) + 2 O2​ (g) → CO2 ​(g) + 2 H2​O (l) [ΔH = -890.4 kJ.mol-1]
  • H2O (l) → H2O (g) [ΔH = 44 kJ.mol-1]

The equation for the combustion of methane is: CH4 ​(g) + 2 O2​ (g) → CO2 ​(g) + 2 H2​O (g)

We can break down this equation in 2 steps:

  1. CH4 ​(g) + 2 O2​ (g) → CO2 ​(g) + 2 H2​O (l) [ΔH1 = -890.4 kJ.mol-1]
  2. Step 2: 2 H2O (l) → 2 H2O (g) [ΔH2 = 2 x 44 kJ.mol-1 = 88 kJ.mol-1]

According to Hess's law, the enthalpy change of combustion of methane is:

ΔH = ΔH+ ΔH2 = -890.4 kJ.mol-1 + 88 kJ.mol-1 = -802.4 kJ.mol-1

Standard Enthalpies of Formation

Thermodynamic standard state:

The standard state of a substance is its pure form at a specified set of conditions, typically 1 bar (or 1 atm) pressure and a specified temperature, usually 298.15 K (25°C). For solutions, the standard state is a concentration of 1 mol.L-1. Measurements made under these standard conditions are indicated by the addition of the superscript o to the symbol of the quantity reported.

 

Standard enthalpy of formation (ΔHof ):

The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states. The standard enthalpy of formation of the most stable form of an element is 0 J.
 

ΔHof of H2 (g) = 0 J
ΔHof of O2 (g) = 0 J
ΔHof of C (graphite) = 0 J

 

Standard enthalpy of reaction (ΔHorxn):

The standard enthalpy of reaction is the enthalpy change when reagents in their standard states change to products in their standard states. It is calculated using the standard enthalpies of formation of the reactants and products.
 

ΔHorxn = nΔHof (products) - nΔHof (reactants)

 

where n = stoichiometric coefficients in the reaction.

 

The formation of AgCl from silver cation and chloride ion: Ag+ (aq) + Cl- (aq) → AgCl (s)

ΔHorxn= ΔHof (AgCl) - [ΔHof (Ag+) + ΔHof (Cl-)]

ΔHorxn= -127 kJ.mol-1 - 105.9 kJ.mol-1 + 167.2 kJ.mol-1 = -65.7 kJ.mol-1

 

ΔH0rxn of the combustion of propane: C3H8 (g) + 5 O2 (g) → 3 CO2 (g) + 4 H2O (l)

ΔH0rxn = 3 ΔHof (CO2) + 4 ΔHof (H2O) - ΔHof (C3H8) - 5 ΔHof (O2

Bond Enthalpies

Bond enthalpy (BE):

Bond enthalpy (or bond dissociation energy) is the energy required to break one mole of a specific type of bond in a gaseous molecule, resulting in the formation of neutral atoms or radicals. The unit for bond enthalpy is typically kJ.mol-1.

Bond enthalpies provide insight into the strength of chemical bonds. Higher BE values indicate stronger bonds that require more energy to break. BE > 0 because heat must be supplied to break a bond.

 

Enthalpy of reaction (ΔHo):

The enthalpy of reaction is the difference in enthalpy change betwen products and reactants. It can be estimated by counting the total energy input to break bonds minus the total energy released by bond formation. Therefore, the enthalpy of reaction in the gas phase is given by:
 

ΔHo =  BE (reactants) -  BE (products)

 

  • ΔHo < 0: The reaction is exothermic (heat is released).
  • ΔHo > 0: The reaction is endothermic (heat is absorbed).

 

Calculate the ΔHo of the following reaction: CH4 (g) + 3 Cl2 (g) → CHCl3 (g) + 3 HCl (g)

Data: BE (C-H) = 413 kJ.mol-1; BE (Cl-Cl) = 243 kJ.mol-1; BE (C-Cl) = 339 kJ.mol-1; BE (H-Cl) = 427 kJ.mol-1


ΔHo = 4 BE (C-H) + 3 BE (Cl-Cl) – BE (C-H) – 3 BE (C-Cl) – 3 BE (H-Cl)

ΔH= -330 kJ.mol-1

ΔHo < 0 ⇒ the reaction is exothermic