Chemistry: Energy and Its Conservation

Chapter 3: Energy and Its Conservation

3.1 Types of Energy

• Energy: The ability to do work.
• Work ($w$): The displacement of an object against an opposing force.
  • Example: Backpackers do work by climbing against gravity.

Categories of Energy

1. Kinetic Energy

• Energy associated with the motion of an object.
• Formula: $E_{kinetic} = \frac{1}{2} mv^2$
  • $m$ = mass
  • $v$ = velocity
• SI Unit: Joule (J)
  • $1 \text{ joule} = 1\text{ J} = 1\text{ kg m}^2\text{ s}^{-2}$
• Kinetic Energy Calculation Example:
  • To calculate the kinetic energy of an electron moving at $4.55 \times 10^5 \text{ m/s}$, you would use the formula $\frac{1}{2} mv^2$.
• Conversion Factor (Revision):
  • $1 \text{ kilowatt-hour (kWh)} = 3.60 \times 10^6 \text{ J}$
  • Example: Converting $534 \text{ kWh}$ to Joules: $534 \text{ kWh} \times \frac{3.60 \times 10^6 \text{ J}}{1 \text{ kWh}} = 1.92 \times 10^9 \text{ J}$ (Units cancel out).

2. Potential Energy

• Stored energy an object has due to its position or configuration, typically from working against natural forces (gravity, elasticity, electrostatic forces).
• "Potential" signifies the ability to do something in the future.
• Types of Potential Energy:
  • a. Gravitational Energy:
    • Stored energy due to an object's height or position in a gravitational field.
    • Example: A rock teetering high on a ledge has gravitational energy, which converts to kinetic energy as it falls.
  • b. Electrical Energy:
    • Originates from the electrical forces between charged particles (protons in nuclei, negatively charged electrons).
    • The attractive force between opposite charges holds electrons and nuclei together in atoms and causes atoms to combine into molecules.
    • When opposite charges move closer, energy is released (system becomes more stable).
    • To separate opposite charges, energy must be supplied.
    • Example: Moving an electron farther from a nucleus increases its electrical potential energy, similar to lifting a backpack to a tabletop increasing its gravitational potential energy.
    • Formula for Electrical Energy between two ions: $E<em>{electrical} = k \frac{q</em>1 q_2}{r}$
      • $q<em>1$, $q</em>2$ = charges of two ions (in electrostatic units, ESU; $1 \text{ ESU} = 1.602 \times 10^{-19} \text{ coulombs})$
      • $r$ = distance between ions (in picometers, pm)
      • $k = 2.31 \times 10^{-16} \text{ J pm}$
    • Energy must be supplied to overcome this electrical energy to remove electrons from atoms or molecules.
  • c. Chemical Energy (Bond Energy):
    • A form of potential energy stored in the arrangement of atoms within molecules.
    • Arises from the electrical forces between negatively charged electrons and positively charged nuclei.
    • Atoms bond by sharing or transferring electrons, minimizing the system's electrical potential energy and making the molecule more stable.
    • Bond Breaking: Requires energy input to overcome attractive forces (endothermic).
    • Bond Formation: Releases energy as the system moves to a more stable, lower-energy arrangement (exothermic).
    • Example: Formation of H₂ and O₂ from free atoms releases energy. The reaction of H₂ and O₂ to form H₂O releases additional energy because H₂O molecules are even more stable.
  • d. Mass Energy: (Mentioned as a type, but not detailed in transcript)

Other Types of Energy

• Thermal Energy:
  • Energy an object has due to the movement of its particles.
  • In a monatomic gas (e.g., helium, argon), it's the total energy from continuous random translational motion of atoms.
  • Molecules possess additional thermal energy forms, like rotational and vibrational energy (e.g., a water molecule can rotate and vibrate).
• Radiant Energy:
  • The energy content of electromagnetic radiation, such as light or infrared radiation.

Energy Transfers and Transformations

• Energy Transfer: Energy can be moved from one object to another.
  • Example: When a hot object touches a cold one, thermal energy flows from hot to cold until temperatures equalize.
• Energy Transformation: Energy can change from one type to another.
  • Example: A falling rock transforms gravitational potential energy into kinetic energy.
• Energy Transformations in Chemical Reactions:
  • If a reaction releases energy, chemical energy is converted into other forms (thermal, kinetic, electrical potential) depending on conditions.
  • Example: An automobile engine converts the chemical energy of gasoline (via combustion) into thermal energy (heat) to power the car.

3.2 Thermodynamics

• Thermodynamics: The study of energy transfers and transformations, focusing on "how much energy goes where."

Key Terms

• System: The specific part of the universe we are studying.
• Surroundings: Everything else outside the system.
• Boundary: The separation between the system and its surroundings.

Conservation of Energy (First Law of Thermodynamics)

• Statement: Energy is neither created nor destroyed in any process. It can be transferred from one body to another or transformed from one form into another.
• Restatement: Energy may be transferred as work or heat, but no energy can be lost, nor can heat or work be obtained from nothing.
• This implies that if energy flows out of the system, it must flow into the surroundings, and vice-versa ($\Delta U{sys} = -\Delta U{surr}$). The total energy of the universe is constant.

Heat ($q$) and Temperature Change ($\Delta T$)

• A system can exchange thermal energy with its surroundings, known as heat ($q$), measured in Joules (J).

• Chemical reactions often involve heat flows:

  • Exothermic reactions: Release energy, transferring heat from the system to the surroundings. The sign of $q$ is negative.
  • Endothermic reactions: Absorb energy, drawing heat from the surroundings into the system. The sign of $q$ is positive.

• Temperature Change ($\Delta T$): $\Delta T = T<em>{final} - T</em>{initial}$

• The magnitude of $\Delta T$ depends on four factors:

  1. Amount of heat transferred ($q$): More heat produces a larger temperature change ($50 \text{ J}$ causes twice the $\Delta T$ of $25 \text{ J}$).
  2. Direction of heat flow:
     • If heat is absorbed, $\Delta T$ is positive (temperature rises).
     • If heat is released, $\Delta T$ is negative (temperature falls).
  3. Amount of material ($n$ (moles) or $m$ (mass)):
     • Temperature change is inversely related to the quantity of the substance. For example, $50 \text{ J}$ raises the temperature of $1 \text{ mole}$ twice as much as it raises $2 \text{ moles}$.
  4. Identity of the material (Molar Heat Capacity, $C<em>m$ or Specific Heat Capacity, $C</em>s$):
     • Different substances respond differently to the same heat input. Example: $50 \text{ J}$ heats $1 \text{ mole}$ of silver more than $1 \text{ mole}$ of water.
     • Molar Heat Capacity ($C_m$): The amount of heat needed to raise the temperature of $1 \text{ mole}$ of a substance by $1^\circ\text{C}$.
       • Units: \text{J mol}^{-1} ^\circ\text{C}^{-1}.
     • Specific Heat Capacity ($C_s$): The amount of heat required to raise the temperature of $1 \text{ gram}$ of a substance by $1^\circ\text{C}$.
       • Units: \text{J g}^{-1} ^\circ\text{C}^{-1}.

• Equations for Temperature Change and Heat Transfer:

  • Using molar heat capacity: $\Delta T = \frac{q}{nC<em>m}$ or $q = nC</em>m \Delta T$
  • Using specific heat capacity: $q = mC_s \Delta T$

• Important Note on Temperature Scales:

  • The difference in temperature ($\Delta T$) is the same for the Celsius and Kelvin scales (e.g., an increase of $10^\circ\text{C}$ is an increase of $10 \text{ K}$).

• Thermal Energy Transfer between Objects:

  • When heat flows from a hotter object (system) to a cooler object (surroundings), the heat ($q$) is negative for the hot object and positive for the cool object.
  • The magnitude of heat flow is the same for both objects.
  • $q<em>{water} = -q</em>{metal}$ or $q<em>{surroundings} = -q</em>{system}$ (Law of Conservation of Energy).
  • $(m<em>{surr} \times C</em>{s,surr} \times \Delta T<em>{surr}) = -(m</em>{sys} \times C<em>{s,sys} \times \Delta T</em>{sys})$

Work ($w$)

• Work is a flow of energy between objects or between a chemical system and its surroundings.
• Sign Convention for Work:
  • When a system does work on the surroundings, $w$ is negative (system loses energy).
  • When the surroundings do work on the system, $w$ is positive (system gains energy).
• The amount of work is the same for the system and surroundings: $w<em>{surroundings} = -w</em>{system}$

Internal Energy ($U$)

• Internal Energy ($U$): The sum of the kinetic and potential energies of all particles that compose a system.
• Internal Energy Change ($\Delta U$): The sum of heat transferred ($q$) and work done ($w$).
  • $\Delta U = q + w$
  • Think of energy as something an object possesses; heat and work are ways objects exchange energy.
• Can increase or decrease through heat transfer ($q$) or work ($w$).
• $\Delta U<em>{sys} = -\Delta U</em>{surr}$ (Restatement of the First Law of Thermodynamics).

First Law of Thermodynamics (Energy Conservation)

• $\Delta E$ or $\Delta U = q + w$

• A profound statement meaning energy is neither created nor destroyed.

• State Function vs. Path Function:

  • Internal energy ($U$) is a state function: Its value depends only on the current state of the system (initial and final conditions), not on how that state was reached (the path taken).
    • Example: A climber's change in height (state function) is the same regardless of the path taken between two points.
  • Heat ($q$) and Work ($w$) are path functions: Their values depend on the specific path or process taken.
    • Example: The distance a climber travels (path function) differs depending on the route.

• The energy change ($\Delta U$) in a chemical reaction is independent of the manner in which the reaction takes place; it depends only on the strengths of chemical bonds formed and broken.

3.3 Energy Changes in Chemical Reactions

Origins of Energy Changes

• Chemical reactions involve the rearrangement of atoms: some chemical bonds break, and others form.
• Bond breakage: Always requires an input of energy (endothermic process).
• Bond formation: Always results in a release of energy (exothermic process).
• The net energy change for a reaction is the sum of these energies.
  • Net energy released: Energy released by bond formation > energy consumed by bond breakage (Exothermic, \Delta U < 0).
  • Net energy absorbed: Energy released by bond formation < energy consumed by bond breakage (Endothermic, $\Delta U > 0$).

Features of Reaction Energies

• If the chemical reaction is reversed, the direction of energy flow is also reversed (e.g., if a reaction releases energy in one direction, it must absorb it in the opposite direction).

  • Reversing a reaction changes the sign of the energy change but not its magnitude.

• When a reaction releases energy, $\Delta U$ has a negative sign (\Delta U < 0).

• When a reaction absorbs energy, $\Delta U$ has a positive sign (\Delta U > 0).

  • $q<em>{sys} = -q</em>{surr}$ (Law of conservation of energy).

• If the bonds of the products are more stable than the bonds of the reactants, energy is released.

• If the bonds of the products are less stable than the bonds of the reactants, energy is absorbed.

• The amount of energy released or absorbed is proportional to the amounts of chemicals that react.

• Molar energy change: Overall energy change divided by the stoichiometric coefficient of the specific reagent.

• Bond Energy (BE):

  • The energy required to break a specific bond, always positive.
  • Usually expressed in $\text{kJ/mol}$.
  • Example: $\text{H}<em>2\text{(g)} \rightarrow \text{H(g)} + \text{H(g)}$ $\Delta E</em>{bond breaking} = +435 \text{ kJ/mol}$ (Bond Energy of H-H).
  • The reverse process (bond formation): $\text{H(g)} + \text{H(g)} \rightarrow \text{H}<em>2\text{(g)}$ $\Delta E</em>{bond making} = -435 \text{ kJ/mol}$.
  • Bond energies depend on the types of atoms bonded and, for polyatomic molecules, on the molecular structure (average values are often used).

• Using Average Bond Energies to Estimate Enthalpy Changes for Reactions:

  • The energy change for a reaction ($\Delta E_{rxn}$) can be estimated as:
    • $\Delta E<em>{rxn} = \sum\text{BE}</em>{bonds broken} - \sum\text{BE}_{bonds formed}$ (Sum of energies required to break bonds minus sum of energies released when forming bonds).

• Example Calculations:

  • Combustion of Methane (Simplified): If breaking C-H and O=O bonds requires $2650 \text{ kJ}$ and forming C=O and H-O bonds releases $3440 \text{ kJ}$, the net energy change is $2650 \text{ kJ} + (-3440 \text{ kJ}) = -790 \text{ kJ}$.
  • Formation of Vinyl Chloride (Example 3-4): Involves breaking C=C, H-Cl, and O=O bonds and forming C-H, C=C, C-Cl, and O-H bonds. The calculation predicts release of energy (exothermic).

3.4 Measuring Energy Changes: Calorimetry

• Calorimeter: A device used to measure the heat flows ($q_r$) that accompany chemical reactions.

Types of Calorimetry

1. Bomb Calorimetry (Constant-Volume Calorimetry)

• Purpose: Measures the change in internal energy ($\Delta U$) for chemical reactions.
• Principle: If a reaction occurs at constant volume ($\Delta V = 0$), then the work done by expansion ($w = -P\Delta V$) is zero. In this case, $\Delta U = q + w = q - P\Delta V = q<em>V$. Thus, the measured heat ($q</em>V$) is equal to the change in internal energy ($\Delta U$).
• Setup: A sample is burned in excess oxygen inside a sealed steel container (the bomb), placed in an insulated water bath.
• Measurement: All heat released by the chemicals is absorbed by the calorimeter. The temperature change ($\Delta T$) of the calorimeter, combined with its total heat capacity ($C<em>{cal}$), gives the amount of heat released ($q</em>{calorimeter} = C_{cal}\Delta T$).
• Relationship: $q<em>{calorimeter} = -q</em>r$ (heat released by reaction) $\Rightarrow \Delta U<em>{reaction} = -C</em>{cal}\Delta T$
• Molar Energy Changes: Energy change is an extensive quantity, dependent on the amount of substance. $\Delta E_{molar} = \frac{\Delta E}{n}$.
• Calorimeter Calibration (Example 3-5):
  • To determine $C<em>{cal}$, a known amount of electrical energy ($q</em>{electrical}$) is added to the calorimeter, and the resulting temperature change ($\Delta T$) is measured.
  • $q<em>{calorimeter} = C</em>{cal}\Delta T \Rightarrow C<em>{cal} = \frac{q</em>{electrical}}{\Delta T}$.
  • Example: $2.02 \times 10^3 \text{ J}$ electrical energy, $\Delta T = 4.0 ^\circ\text{C}$, so $C_{cal} = 5.1 \times 10^2 \text{ J/}^\circ\text{C}$.

2. Coffee-Cup Calorimetry (Constant-Pressure Calorimetry)

• Purpose: Measures the change in enthalpy ($\Delta H$) for chemical reactions, particularly convenient for reactions in liquid solutions.
• Principle: The reaction takes place at constant pressure. Under these conditions, the measured heat ($q_P$) is equal to the enthalpy change ($\Delta H$).
• Setup: An insulated container (like a Styrofoam cup) where the pressure of the system is fixed (usually atmospheric pressure).
• Approximation: If no specific information is given, the heat capacity of the calorimeter is often approximated as the heat capacity of its water content.
• Measurement: Heat exchanged with the solution ($q_{soln}$) is measured.
  • $q<em>{soln} = m</em>{soln} \times C_{s,soln} \times \Delta T$
  • The heat of reaction ($q<em>r$) is the negative of the heat absorbed by the solution: $q</em>r = -q_{soln}$.
• Relationship: $q<em>r = q</em>P = \Delta_r H$
• Key Distinction: Bomb calorimeters measure $\Delta U$ (constant volume), while coffee-cup calorimeters measure $\Delta H$ (constant pressure).

3.5 Enthalpy

Expansion Work

• When a chemical process occurs at constant pressure, the volume can change, especially with gases.
• Work done by the system ($w_{sys}$) against a constant external pressure:
  • $w<em>{sys} = -P</em>{external} \times \Delta V$

Definition of Enthalpy ($H$)

• From the First Law ($\Delta U = q + w$), and for constant pressure work ($w_P = -P\Delta V$):
  • $\Delta U = q_P - P\Delta V$
  • Rearranging, the heat at constant pressure is: $q_P = \Delta U + P\Delta V$
• Enthalpy ($H$) is a thermodynamic state function defined as: $H = U + PV$
  • Since $U$, $P$, and $V$ are all state functions, $H$ is also a state function. This means the change in enthalpy ($\Delta H$) depends only on the initial and final states, not the path.
• Enthalpy of the system ($\Delta H$): The heat given off or absorbed during a chemical reaction at constant pressure ($\Delta H = q_P$).

Relationship Between Enthalpy Change ($\Delta H$) and Internal Energy Change ($\Delta U$)

• Generally, $\Delta H = \Delta U + \Delta(PV)$.
• For solids and liquids: Volume changes are typically small enough to be neglected. Therefore, $\Delta(PV) \approx 0$.
  • Thus, $\Delta H \approx \Delta U$ for processes involving only condensed phases.
  • Example: Dissolving $\text{NH}<em>4\text{NO}</em>3\text{(s)}$ in water. Since no gases are involved, $\Delta U<em>{molar} \approx \Delta H</em>{molar}$ (e.g., $21.1 \text{ kJ/mol}$ for this process).
• For reactions involving gases: Both pressure and volume may change significantly.
  • We use the ideal gas equation, $PV = nRT$, to relate the change in the pressure-volume product to the change in the number of moles of gas:
    • $\Delta(PV)<em>{gases} = \Delta(nRT)</em>{gases}$
  • Assuming constant temperature ($T$) and a constant gas constant ($R$): $\Delta(PV)<em>{gases} = RT\Delta n</em>{gases}$
  • Key Relationship: $\Delta H<em>{reaction} = \Delta U</em>{reaction} + RT\Delta n_{gases}$ (at constant T)
    • $\Delta n<em>{gases} = n</em>{gas \ products} - n_{gas \ reactants}$ (the difference in the mole amounts of gaseous products and gaseous reactants in the balanced chemical equation).
    • Values of gas constant ($R$): $8.314 \text{ J K}^{-1} \text{mol}^{-1}$ or $0.0821 \text{ L atm K}^{-1} \text{mol}^{-1}$.
    • Example: For the combustion of octane ($\text{C}<em>8\text{H}</em>{18}(\text{l}) + \frac{25}{2} \text{O}<em>2(\text{g}) \rightarrow 8 \text{ CO}</em>2(\text{g}) + 9 \text{ H}_2\text{O}(\text{l})$ at $298 \text{ K}$),
      • $\Delta n_{gases} = 8 - \frac{25}{2} = -\frac{9}{2} \text{ mol}$.
      • $\Delta H - \Delta U = RT\Delta n_{gases} = (8.314 \text{ J mol}^{-1}\text{ K}^{-1}) (298 \text{ K}) (-\frac{9}{2} \text{ mol}) = -1.11 \times 10^4 \text{ J/mol octane} = -11.1 \text{ kJ/mol octane}$.

Energy and Enthalpy of Vaporization/Sublimation

• These are two processes where $\Delta H$ and $\Delta U$ differ significantly.
• When a substance changes from a condensed phase (liquid or solid) to the gas phase:
  1. $\Delta n_{gas} = 1 \text{ mol}$.
  2. The change in volume is almost equal to the volume of the resulting gas (volume of condensed phase is negligible).
• Therefore, $\Delta H \approx \Delta U + RT$ for vaporization or sublimation of $1 \text{ mole}$ of substance (at a given temperature).

Enthalpies of Formation

• Formation Reaction: A reaction that produces $1 \text{ mole}$ of a chemical substance from the elements in their most stable forms.
  • It has a single product with a stoichiometric coefficient of $1$.
  • All starting materials are elements in their most stable forms.
  • Pressures must be specified for gases, and concentrations for species in solution.
• Standard Enthalpy of Formation ($\Delta H_f^\circ$): The enthalpy change in a formation reaction when conditions are standard.
  • Standard State: The most stable form of a substance at a specific temperature ($25 ^\circ\text{C}$), pressure ($1 \text{ bar}$ for gases), and concentration ($1 \text{ M}$ for solutions).
  • The superscript "$\circ$" indicates standard conditions.
  • By definition, the standard enthalpy of formation for any element in its most stable standard state is zero (e.g., $\Delta H<em>f^\circ(\text{O}</em>2(\text{g})) = 0$).

Determining Enthalpies of Reaction ($\Delta H<em>r^\circ$) from Standard Enthalpies of Formation ($\Delta H</em>f^\circ$)

• Hess's Law: The enthalpy change for any overall process is equal to the sum of the enthalpy changes for any set of steps that leads from the starting materials to the products.
  • This is possible because enthalpy ($H$) is a state function.
• Calculating Total Enthalpy Change for a Reaction ($\Delta H_{reaction}^\circ$):
  • $\Delta H<em>{reaction}^\circ = \sum\nu</em>p \Delta H<em>{f,p}^\circ - \sum\nu</em>r \Delta H_{f,r}^\circ$
    • $\sum\nu<em>p \Delta H</em>{f,p}^\circ$ = sum of standard enthalpies of formation of products, each multiplied by its stoichiometric coefficient ($\nu_p$).
    • $\sum\nu<em>r \Delta H</em>{f,r}^\circ$ = sum of standard enthalpies of formation of reactants, each multiplied by its stoichiometric coefficient ($\nu_r$).
• Rules Derived from Hess's Law:
  1. If a chemical equation is multiplied by some factor, then $\Delta H_r$ is also multiplied by the same factor.
  2. If a chemical equation is reversed, then $\Delta H_r$ changes its sign.
  3. If a chemical equation can be expressed as the sum of a series of steps, then $\Delta H<em>r$ for the overall equation is the sum of the $\Delta H</em>r$'s for each step.
• Example (Hess's Law): Calculating $\Delta H$ for $2 \text{ NO}<em>2(\text{g}) \rightarrow \text{N}</em>2\text{O}_4(\text{g})$ using formation enthalpies.
  • $\Delta H<em>{reaction}^\circ = (1 \text{ mol N}</em>2\text{O}<em>4)(11.1 \text{ kJ/mol}) - (2 \text{ mol NO}</em>2)(33.2 \text{ kJ/mol}) = -55.3 \text{ kJ}$ (This implies that the formation of $\text{N}<em>2\text{O}</em>4$ from $\text{NO}_2$ spontaneously leads to lower energy).

Enthalpy Changes Under Nonstandard Conditions

• Energies and enthalpy change as temperature, concentration, and pressure change. Therefore, $\Delta H$ also depends on these variables.

3.6 Energy Sources

• Energy and Civilization: Advances in civilization are largely attributed to increasing the availability of energy.

Ultimate Energy Sources

• Solar Energy: The vast majority of our energy sources originate from the sun.
  • Photosynthesis: Converts solar energy into more concentrated forms (e.g., glucose).
    • $6 \text{ CO}<em>2\text{(g)} + 6 \text{ H}</em>2\text{O}(\text{l}) + 2880 \text{ kJ} \rightarrow \text{C}<em>6\text{H}</em>{12}\text{O}<em>6\text{(s)} + 6 \text{ O}</em>2\text{(g)}$
• Nonsolar Sources:
  • Nuclear energy.
  • Geothermal energy: From the Earth's hot interior.

Future Resources

• Economically desirable sources: High intensity, readily extracted and transported.
• Environmentally desirable sources: Renewable and environmentally benign.

Summary of Key Formulas

• Kinetic Energy: $E_{kinetic} = \frac{1}{2} mv^2$
• Electrical Energy: $E<em>{electrical} = k \frac{q</em>1 q_2}{r}$
• Heat Transfer (moles): $q = nC_m \Delta T$
• Heat Transfer (mass): $q = mC_s \Delta T$
• Thermal Energy Transfer between objects: $-(m<em>{sys} \times C</em>{s,sys} \times \Delta T<em>{sys}) = (m</em>{surr} \times C<em>{s,surr} \times \Delta T</em>{surr})$
• Work: $w<em>{surroundings} = -w</em>{system}$
• Internal Energy Change: $\Delta U = q + w$
• Expansion Work: $w<em>{sys} = -P</em>{external} \times \Delta V$
• Internal Energy Change (constant volume): $\Delta U = q_V$ (Bomb calorimetry)
• Enthalpy Definition: $H = U + PV$
• Enthalpy Change (constant pressure): $\Delta H = q_P$ (Coffee-cup calorimetry)
• Relationship between $\Delta H$ and $\Delta U$ (for gases): $\Delta H<em>{reaction} = \Delta U</em>{reaction} + RT \Delta n_{gases}$
• Reaction Energy from Bond Energies: $\Delta E<em>{rxn} = \sum\text{BE}</em>{bonds broken} - \sum\text{BE}_{bonds formed}$
• Molar Energy: $\Delta E_{molar} = \frac{\Delta E}{n}$
• Enthalpy of Reaction from Standard Enthalpies of Formation (Hess's Law): $\Delta H<em>{reaction}^\circ = \sum\nu</em>p \Delta H<em>{f,p}^\circ - \sum\nu</em>r \Delta H_{f,r}^\circ$

Summarizing Energy Flow

• If the reactants have a higher internal energy than the products:
  • $\Delta U_{sys}$ is negative.
  • Energy flows out of the system into the surroundings.
• If the reactants have a lower internal energy than the products:
  • $\Delta U_{sys}$ is positive.
  • Energy flows into the system from the surroundings.