Energy Changes in Chemical Reactions CH10 by Owen Borville 10.21.2025
The system is a part of the universe that is of specific interest. The surroundings constitute the rest of the universe outside the system. The system is usually defined as the substances involved in chemical and physical changes. Universe = System + Surroundings.
Thermochemistry is the study of heat (the transfer of thermal energy) in chemical reactions. Heat is the transfer of thermal energy. Heat is either absorbed or released during a process.
The SI energy unit is a Joule, (J). The joule is the modern, standard international (SI) unit for all forms of energy, including heat and work. Often calories are used as a unit of energy and one (1) calorie is the amount of heat required to raise 1 gram of water by 1 degree Celsius. [1 calorie (cal) = 4.184 Joules (J)]
The heat calorie is not the same as a nutritional Calorie (Cal). (1 Cal = 1000 cal). Therefore the heat calorie is usually denoted with a lowercase "c" and the nutritional calorie is usually denoted by an uppercase C. A nutritional calorie is the amount of energy needed to raise the temperature of 1 kilogram of water by 1 degree Celsius ( So 1 Calorie = 1000 calories).
Exothermal processes occur when heat is transferred from the system to the surroundings. Such as: 2H2(g) + O2(g) => 2H2O(l) + energy.
Endothermal processes occur when heat is transferred from the surroundings to the system. Such as: energy + 2HgO(s) => 2Hg(l) + O2(g)
Thermodynamics is the study of the interconversion of heat and other kinds of energy. In thermodynamics, there are three types of systems.
Open systems can exchange mass and energy with the surroundings. Closed systems allow the transfer of energy but not mass. Isolated systems do not exchange either mass or energy with its surroundings.
State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. The magnitude of the change depends only on the initial and final states of the system. Energy, Pressure, Volume, Temperature.
The First Law of Thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed.
ΔUsys + ΔUsurr = 0
ΔU is the change in the internal energy. Symbols (sys) and (surr) refer to the system and surroundings. (ΔU = Uf-Ui) is the difference in the energies of the initial and final states.
(ΔUsys = -ΔUsurr)
Work and Heat: The overall change in the system's internal energy is ΔU = q + w
q (heat) is positive for an endothermic process (head absorbed by the system)
q is negative for an exothermic process (heat released by the system)
w (work) is positive for work done ON the system
w is negative for work done BY the system
ΔU = q + w
Sign conventions for Heat (q) and Work (w)
Heat absorbed by the system (endothermic process) = (q is positive)
Heat released by the system (exothermic process) = (q is negative)
Work done ON the system BY the surroundings (such as a volume decrease) = (w is positive)
Work done BY the system ON the surroundings (such as a volume increase) = (w is negative)
Enthalpy: Reactions Carried Out at Constant Volume or at Constant Pressure
Sodium azide reacts to give a large quantity of nitrogen gas: 2NaN3(s) => 2Na(s) + 3N2(g)
Under constant volume conditions, pressure increases.
Pressure-volume, or PV work, is done when there is a volume change under constant pressure.
w = -PΔV
P is the external opposing pressure. ΔV is the change in the volume of the container.
w = -PΔV
ΔU = q + w (substitute -PΔV for w)
ΔU = q-PΔV
When a change occurs at constant volume, ΔV = 0 and no work is done.
qv = ΔU
Under conditions of constant pressure:
ΔU = q + w
ΔU = q-PΔV
qp = ΔU + PΔV
The thermodynamic function of a system called enthalpy (H) is defined by the equation H = U + PV
SI Units: Pressure: pascal: 1Pa = 1 kg/(m*s^2)
Volume: cubic meters, m^3
PV: 1 kg/(m*s^2) x m^3 = 1(kg*m^2)/(s^2) = 1J
Enthalpy: joules
U, P, V, and H are all state functions.
For any process, the change in enthalpy is: ΔH = ΔU + Δ(PV) (equation 1)
If pressure is constant: ΔH = ΔU + PΔV (equation 2)
Rearrange to solve for ΔU: ΔU = ΔH - PΔV (equation 3)
Remember, qp: qp = ΔU + PΔV (equation 4)
Substitute equation (3) into equation (4) and solve: qp = (ΔH - PΔV) + PΔV (equation 5)
qp = ΔH for a constant-pressure process.
Enthalpy of reaction (ΔH) is the difference between the enthalpies of the products and the enthalpies of the reactants.
ΔH = H(products) - H(reactants)
Assumes reactions in the lab occur at constant pressure.
ΔH > 0 (positive) endothermic process
ΔH < 0 (negative) exothermic process
Thermochemical Equations:
H2O(s) => H2O (l)
ΔH = +6.01 kJ/mol Heat absorbed by the system from the surroundings. Enthalpy increasing.
Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH > 0 endothermic
CH4(g) + 2O2(g) => CO2 (g) + 2H2O(l) ΔH = -890.4 kJ/mol Heat is given off by the system to the surroundings.
-890.4 kJ/1 mol CH4
-890.4 kJ/2 mol O2
-890.4 kJ/1 mol CO2
-890.4 kJ/2 mol H2O
Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH < 0 exothermic
Enthalpy is an extensive property. Extensive properties are dependent on the amount of matter involved.
H2O(l) => H2O(g) ΔH = +44 kJ/mol
Double the amount of matter, Double the enthalpy
2H2O(l) => 2H2O(g) ΔH = +88 kJ/mol
Regarding thermochemical equations: (1) Always specify the physical states of reactants and products because they help determine the actual enthalpy changes (such as (g) or (l)). Different states of matter have different enthalpy values. (2) When multiplying an equation by a factor (n), multiply the ΔH value by the same factor.
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol
2CH4(g) + 4O2(g) => 2CO2(g) + 4H2O(g) ΔH = -1604.8 kJ/mol
(3) Reversing an equation changes the sign but not the magnitude of ΔH
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol
CO2(g) + 2H2O(g) =>CH4(g) + 2O2(g) ΔH = +802.4 kJ/mol
---------------------------------------------------------------------------------
Calorimetry is the measurement of heat changes. Heat changes are measured in a device called a Calorimeter. The Specific Heat of a substance is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius. Different substances, element, and compounds have different specific heat values.
Specific Heat and Heat Capacity: The heat capacity (C) is the amount of heat required to raise the temperature of an object by 1 degree Celsius. The object may be a given quantity of a particular substance.
The heat capacity of 1 kg of water = 4.184 J/1g*degrees Celsius (specific heat capacity of water) x 1000g = 4184 J/degrees Celsius (heat capacity of 1 kg of water).
Specific heat capacity has units of J/(g*degrees C). Heat capacity has units of J/degrees Celsius.
The heat associated with a temperature change may be calculated by: (q = smΔT ) and (q = CΔT)
m=mass
s=specific heat
ΔT=change in temperature (ΔT = Tfinal -Tinitial)
C= heat capacity
Ex. What is q of 1.o1 kg water from 0.05degC to 35.81degC? q = 1.o1 kg(1000g/1kg)(4.184 J/g*degC)(35.81degC-0.05degC) = 151000 J = 151 kJ
Constant-Pressure Calorimetry: A coffee cup calorimeter may be used to measure the heat exchange for a variety of chemical reactions and physical processes at constant pressure, such as heat of neutralization, heat of ionization, heat of fusion, and heat of vaporization.
Concepts to consider for coffee cup calorimetry: qp = ΔH (coffee cup with liquid, lid, and vertical thermometer inserted through lid)
System: reactants and products (the reaction)
Surroundings: water in the calorimeter
For an exothermic reaction: the system loses heat and the surroundings gain or absorb heat
qsys = -msΔT (the minus sign is used to keep sign conventions consistent)
qsurr = msΔT
qsys = -qsurr
Constant-Volume Calorimetry: Constant volume calorimetry is carried out in a device known as a constant-volume bomb. A constant-volume calorimeter is an isolated system. Bomb calorimeters are typically used to determine heats of combustion.
qcal = -qrxn
To calculate qcal, the heat capacity of the calorimeter must be known.
qcal = CcalΔT
qrxn = -qcal
qrxn = -CcalΔT
Hess's law states that the change in enthalpy for a stepwise process is the sum of the enthalpy changes for each of the steps. Hess's law is consistent with the law of conservation of energy and the 1st law of thermodynamics.
CH4(g) + 2O2(g) => CO2(g) +2H2O(l) ΔH = -890.4 kJ/mol
2H2O(l) =>2H2O(g) ΔH = +88.0 kJ/mol
--------------------------------------------------------------------
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol (2H2O (l) on each side of the equations cancel out, leaving one 2H2O in the products)
When applying Hess's Law: (1) Manipulate thermochemical equations in a manner that gives the overall desired equation. (2) Remember the rules for manipulating thermochemical equations: Always specify the physical states of reactants and products because they help determine the actual enthalpy changes. When multiplying an equation by a factor (n), multiply the ΔH value by the same factor. Reversing an equation changes the sign but not the magnitude of ΔH. (3) Add the ΔH for each step after proper manipulation. (4) Process is useful for calculating enthalpies that cannot be found directly.
Standard Enthalpies of Formation: The standard enthalpy of formation (ΔH°f ) is defined as the heat change that results when one mole of a compound is formed from its constituent elements in their standard states.
C(graphite) + O2(g) ========> CO2(g) ΔH°f = -393.5 kJ/mol
(elements in standard states) (1 mole of product)
The superscripted degree sign denotes standard conditions: 1 atm pressure for gases and 1M concentration for solutions.
The "f" stands for formation
ΔH°f for an element in its most stable form is zero. ΔH°f for many substances are listed in table appendix form in chemistry textbooks or reference books.
The standard enthalpy of reaction (ΔH°rxn) is defined as the enthalpy of a reaction carried out under standard conditions.
aA + bB => cC + dD
ΔH°rxn = [cΔH°f (C) + dΔH°f (D)] - [aΔH°f (A) + bΔH°f (B)]
ΔH°rxn = ∑nΔH°f(products)-∑mΔH°f (reactants)
n and m are the stoichiometric coefficients for the reactants and products.
Bond Enthalpy and the Stability of Covalent Molecules: The bond enthalpy is the enthalpy change associated with breaking a bond in one mole of gaseous molecule.
H2(g) => H(g) + H(g) ΔH° = 436.4 kJ/mol
The enthalpy for a gas phase reaction is given by: ΔH° = ∑BE(reactants) - ∑BE(products)
ΔH° = total energy input (bonds broken)-total energy released (bonds formed)
Bond enthalpy change in an exothermic/endothermic reaction (listed in reference tables for various chemical bonds).
Therefore, to find the enthalpy of reaction, the enthalpies of reaction for each bond are multiplied by the number of bonds. Sum the all the reactant enthalpies. Then sum all the product enthalpies. Then subtract enthalpies of the reactants from the enthalpies products to find ΔH°, according to the equation ∑BE(reactants) - ∑BE(products).
Lattice Energy and the Stability of Ionic Compounds: A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured. Ionic and covalent compounds differ in their general physical properties because of the differences in the nature of their bonds.
The Born-Haber cycle calculation uses Hess's law to find the lattice enthalpy of an ionic compound by breaking down the formation process into a series of known steps.
The standard enthalpy of formation is the sum of the enthalpy changes for each step in the cycle.
ΔH°f = ΔHsub (enthalpy of sublimation) + IE (ionization energy) + 1/2ΔHdiss (dissociation energy) +EA(electron affinity) + ΔH°latt (lattice energy)
To calculate, arrange the enthalpy changes for each step in a cycle and apply Hess's law to find the unknown value. The equation is generally rearranged to isolate the lattice enthalpy and can be written as:
ΔH°latt = ΔH°f - ΔHsub - IE - 1/2 ΔHdiss - EA
The system is a part of the universe that is of specific interest. The surroundings constitute the rest of the universe outside the system. The system is usually defined as the substances involved in chemical and physical changes. Universe = System + Surroundings.
Thermochemistry is the study of heat (the transfer of thermal energy) in chemical reactions. Heat is the transfer of thermal energy. Heat is either absorbed or released during a process.
The SI energy unit is a Joule, (J). The joule is the modern, standard international (SI) unit for all forms of energy, including heat and work. Often calories are used as a unit of energy and one (1) calorie is the amount of heat required to raise 1 gram of water by 1 degree Celsius. [1 calorie (cal) = 4.184 Joules (J)]
The heat calorie is not the same as a nutritional Calorie (Cal). (1 Cal = 1000 cal). Therefore the heat calorie is usually denoted with a lowercase "c" and the nutritional calorie is usually denoted by an uppercase C. A nutritional calorie is the amount of energy needed to raise the temperature of 1 kilogram of water by 1 degree Celsius ( So 1 Calorie = 1000 calories).
Exothermal processes occur when heat is transferred from the system to the surroundings. Such as: 2H2(g) + O2(g) => 2H2O(l) + energy.
Endothermal processes occur when heat is transferred from the surroundings to the system. Such as: energy + 2HgO(s) => 2Hg(l) + O2(g)
Thermodynamics is the study of the interconversion of heat and other kinds of energy. In thermodynamics, there are three types of systems.
Open systems can exchange mass and energy with the surroundings. Closed systems allow the transfer of energy but not mass. Isolated systems do not exchange either mass or energy with its surroundings.
State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. The magnitude of the change depends only on the initial and final states of the system. Energy, Pressure, Volume, Temperature.
The First Law of Thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed.
ΔUsys + ΔUsurr = 0
ΔU is the change in the internal energy. Symbols (sys) and (surr) refer to the system and surroundings. (ΔU = Uf-Ui) is the difference in the energies of the initial and final states.
(ΔUsys = -ΔUsurr)
Work and Heat: The overall change in the system's internal energy is ΔU = q + w
q (heat) is positive for an endothermic process (head absorbed by the system)
q is negative for an exothermic process (heat released by the system)
w (work) is positive for work done ON the system
w is negative for work done BY the system
ΔU = q + w
Sign conventions for Heat (q) and Work (w)
Heat absorbed by the system (endothermic process) = (q is positive)
Heat released by the system (exothermic process) = (q is negative)
Work done ON the system BY the surroundings (such as a volume decrease) = (w is positive)
Work done BY the system ON the surroundings (such as a volume increase) = (w is negative)
Enthalpy: Reactions Carried Out at Constant Volume or at Constant Pressure
Sodium azide reacts to give a large quantity of nitrogen gas: 2NaN3(s) => 2Na(s) + 3N2(g)
Under constant volume conditions, pressure increases.
Pressure-volume, or PV work, is done when there is a volume change under constant pressure.
w = -PΔV
P is the external opposing pressure. ΔV is the change in the volume of the container.
w = -PΔV
ΔU = q + w (substitute -PΔV for w)
ΔU = q-PΔV
When a change occurs at constant volume, ΔV = 0 and no work is done.
qv = ΔU
Under conditions of constant pressure:
ΔU = q + w
ΔU = q-PΔV
qp = ΔU + PΔV
The thermodynamic function of a system called enthalpy (H) is defined by the equation H = U + PV
SI Units: Pressure: pascal: 1Pa = 1 kg/(m*s^2)
Volume: cubic meters, m^3
PV: 1 kg/(m*s^2) x m^3 = 1(kg*m^2)/(s^2) = 1J
Enthalpy: joules
U, P, V, and H are all state functions.
For any process, the change in enthalpy is: ΔH = ΔU + Δ(PV) (equation 1)
If pressure is constant: ΔH = ΔU + PΔV (equation 2)
Rearrange to solve for ΔU: ΔU = ΔH - PΔV (equation 3)
Remember, qp: qp = ΔU + PΔV (equation 4)
Substitute equation (3) into equation (4) and solve: qp = (ΔH - PΔV) + PΔV (equation 5)
qp = ΔH for a constant-pressure process.
Enthalpy of reaction (ΔH) is the difference between the enthalpies of the products and the enthalpies of the reactants.
ΔH = H(products) - H(reactants)
Assumes reactions in the lab occur at constant pressure.
ΔH > 0 (positive) endothermic process
ΔH < 0 (negative) exothermic process
Thermochemical Equations:
H2O(s) => H2O (l)
ΔH = +6.01 kJ/mol Heat absorbed by the system from the surroundings. Enthalpy increasing.
Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH > 0 endothermic
CH4(g) + 2O2(g) => CO2 (g) + 2H2O(l) ΔH = -890.4 kJ/mol Heat is given off by the system to the surroundings.
-890.4 kJ/1 mol CH4
-890.4 kJ/2 mol O2
-890.4 kJ/1 mol CO2
-890.4 kJ/2 mol H2O
Concepts to consider: Is this a constant pressure process? What is the system? What are the surroundings? ΔH < 0 exothermic
Enthalpy is an extensive property. Extensive properties are dependent on the amount of matter involved.
H2O(l) => H2O(g) ΔH = +44 kJ/mol
Double the amount of matter, Double the enthalpy
2H2O(l) => 2H2O(g) ΔH = +88 kJ/mol
Regarding thermochemical equations: (1) Always specify the physical states of reactants and products because they help determine the actual enthalpy changes (such as (g) or (l)). Different states of matter have different enthalpy values. (2) When multiplying an equation by a factor (n), multiply the ΔH value by the same factor.
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol
2CH4(g) + 4O2(g) => 2CO2(g) + 4H2O(g) ΔH = -1604.8 kJ/mol
(3) Reversing an equation changes the sign but not the magnitude of ΔH
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol
CO2(g) + 2H2O(g) =>CH4(g) + 2O2(g) ΔH = +802.4 kJ/mol
---------------------------------------------------------------------------------
Calorimetry is the measurement of heat changes. Heat changes are measured in a device called a Calorimeter. The Specific Heat of a substance is the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius. Different substances, element, and compounds have different specific heat values.
Specific Heat and Heat Capacity: The heat capacity (C) is the amount of heat required to raise the temperature of an object by 1 degree Celsius. The object may be a given quantity of a particular substance.
The heat capacity of 1 kg of water = 4.184 J/1g*degrees Celsius (specific heat capacity of water) x 1000g = 4184 J/degrees Celsius (heat capacity of 1 kg of water).
Specific heat capacity has units of J/(g*degrees C). Heat capacity has units of J/degrees Celsius.
The heat associated with a temperature change may be calculated by: (q = smΔT ) and (q = CΔT)
m=mass
s=specific heat
ΔT=change in temperature (ΔT = Tfinal -Tinitial)
C= heat capacity
Ex. What is q of 1.o1 kg water from 0.05degC to 35.81degC? q = 1.o1 kg(1000g/1kg)(4.184 J/g*degC)(35.81degC-0.05degC) = 151000 J = 151 kJ
Constant-Pressure Calorimetry: A coffee cup calorimeter may be used to measure the heat exchange for a variety of chemical reactions and physical processes at constant pressure, such as heat of neutralization, heat of ionization, heat of fusion, and heat of vaporization.
Concepts to consider for coffee cup calorimetry: qp = ΔH (coffee cup with liquid, lid, and vertical thermometer inserted through lid)
System: reactants and products (the reaction)
Surroundings: water in the calorimeter
For an exothermic reaction: the system loses heat and the surroundings gain or absorb heat
qsys = -msΔT (the minus sign is used to keep sign conventions consistent)
qsurr = msΔT
qsys = -qsurr
Constant-Volume Calorimetry: Constant volume calorimetry is carried out in a device known as a constant-volume bomb. A constant-volume calorimeter is an isolated system. Bomb calorimeters are typically used to determine heats of combustion.
qcal = -qrxn
To calculate qcal, the heat capacity of the calorimeter must be known.
qcal = CcalΔT
qrxn = -qcal
qrxn = -CcalΔT
Hess's law states that the change in enthalpy for a stepwise process is the sum of the enthalpy changes for each of the steps. Hess's law is consistent with the law of conservation of energy and the 1st law of thermodynamics.
CH4(g) + 2O2(g) => CO2(g) +2H2O(l) ΔH = -890.4 kJ/mol
2H2O(l) =>2H2O(g) ΔH = +88.0 kJ/mol
--------------------------------------------------------------------
CH4(g) + 2O2(g) => CO2(g) + 2H2O(g) ΔH = -802.4 kJ/mol (2H2O (l) on each side of the equations cancel out, leaving one 2H2O in the products)
When applying Hess's Law: (1) Manipulate thermochemical equations in a manner that gives the overall desired equation. (2) Remember the rules for manipulating thermochemical equations: Always specify the physical states of reactants and products because they help determine the actual enthalpy changes. When multiplying an equation by a factor (n), multiply the ΔH value by the same factor. Reversing an equation changes the sign but not the magnitude of ΔH. (3) Add the ΔH for each step after proper manipulation. (4) Process is useful for calculating enthalpies that cannot be found directly.
Standard Enthalpies of Formation: The standard enthalpy of formation (ΔH°f ) is defined as the heat change that results when one mole of a compound is formed from its constituent elements in their standard states.
C(graphite) + O2(g) ========> CO2(g) ΔH°f = -393.5 kJ/mol
(elements in standard states) (1 mole of product)
The superscripted degree sign denotes standard conditions: 1 atm pressure for gases and 1M concentration for solutions.
The "f" stands for formation
ΔH°f for an element in its most stable form is zero. ΔH°f for many substances are listed in table appendix form in chemistry textbooks or reference books.
The standard enthalpy of reaction (ΔH°rxn) is defined as the enthalpy of a reaction carried out under standard conditions.
aA + bB => cC + dD
ΔH°rxn = [cΔH°f (C) + dΔH°f (D)] - [aΔH°f (A) + bΔH°f (B)]
ΔH°rxn = ∑nΔH°f(products)-∑mΔH°f (reactants)
n and m are the stoichiometric coefficients for the reactants and products.
Bond Enthalpy and the Stability of Covalent Molecules: The bond enthalpy is the enthalpy change associated with breaking a bond in one mole of gaseous molecule.
H2(g) => H(g) + H(g) ΔH° = 436.4 kJ/mol
The enthalpy for a gas phase reaction is given by: ΔH° = ∑BE(reactants) - ∑BE(products)
ΔH° = total energy input (bonds broken)-total energy released (bonds formed)
Bond enthalpy change in an exothermic/endothermic reaction (listed in reference tables for various chemical bonds).
Therefore, to find the enthalpy of reaction, the enthalpies of reaction for each bond are multiplied by the number of bonds. Sum the all the reactant enthalpies. Then sum all the product enthalpies. Then subtract enthalpies of the reactants from the enthalpies products to find ΔH°, according to the equation ∑BE(reactants) - ∑BE(products).
Lattice Energy and the Stability of Ionic Compounds: A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured. Ionic and covalent compounds differ in their general physical properties because of the differences in the nature of their bonds.
The Born-Haber cycle calculation uses Hess's law to find the lattice enthalpy of an ionic compound by breaking down the formation process into a series of known steps.
The standard enthalpy of formation is the sum of the enthalpy changes for each step in the cycle.
ΔH°f = ΔHsub (enthalpy of sublimation) + IE (ionization energy) + 1/2ΔHdiss (dissociation energy) +EA(electron affinity) + ΔH°latt (lattice energy)
To calculate, arrange the enthalpy changes for each step in a cycle and apply Hess's law to find the unknown value. The equation is generally rearranged to isolate the lattice enthalpy and can be written as:
ΔH°latt = ΔH°f - ΔHsub - IE - 1/2 ΔHdiss - EA