# Energy Changes in Chemical Reactions

An isolated system is one where there is no exchange of heat, work, or matter with the surroundings while a closed system is one where there is an exchange of heat and work, but not matter with the surroundings. An open system is one where all three are exchanged with the surroundings. A state function is path-independent and depends only on the initial and final states. State functions include ΔH (enthalpy), ΔS (entropy), ΔG (free energy change) and ΔU (internal energy change). A state function is also called a state quantity or function of state. Zeroth law (concept of temperature) of thermodynamics states that heat flows from hot objects to cold objects to achieve thermal equilibrium. Mathematically, if TA = TB, and TB = TC, then TA = TC, where T is the temperature. The first law states that:

ΔE = q + w                        conservation of energy

The first law of thermodynamics is based on the principle of conservation of energy and it states that the change in total internal energy of a system is equal to the contributions from heat and work. ΔE is the same thing as ΔU, which is the change in internal energy and Q is the contribution from heat. Q is positive when heat is absorbed into the system (ie. heating it) while Q is negative when heat leaks out of the system (ie. cooling it). W refers to the contribution from work, which is positive when work is done on the system (ie. compression) and negative when work is done by the system (ie. expansion). Energy is measured in Joules. Whether it is potential energy, kinetic energy or any energy, it has the unit Joules. Energy is equivalent even if they are in different forms. For example, 1 Joule of mechanical energy can be converted into 1 Joule of electrical energy (ignoring heat loss). PV diagrams depict thermodynamic processes by plotting pressure against volume. Adiabatic process refers to no heat exchange, where:

q = 0. ΔE = W

Isothermal process is when there is no change in temperature (ΔT = 0)

Isobaric process is one where pressure is constant and:

W = PΔV

Isovolumetric (isochoric) process is when volume is constant and:

W = 0. ΔE = q

Work done is the area under or enclosed by the curve.

The second law of thermodynamics states that things like to be in a state of higher entropy and disorder. Entropy is a measure of disorder and is found by the equation:

energy / temperature = J / K

It can also be expressed as molar entropy in J / mol·K. The entropy of gas is greater than that of a liquid, which is greater than the entropy of crystal states.  An isolated system will increase in entropy over time and an open system can decrease in entropy, but only at the expense of a greater increase in entropy of its surroundings. The universe as a whole is increasing in entropy.

ΔS ≥ q / T

Where q is the heat transferred and T is the temperature in Kelvin.

For reversible processes, ΔS = q / T and for irreversible processes ΔS > q / T.

Real processes that occur in the world are never reversible, so entropy change is always greater than the heat transfer over temperature. Due to the irreversibility nature of real processes, as long as anything occurs, the entropy of the universe increases. At room temperature, the gas molecules are flying around but the table in front of you is just sitting there. So, gases have more disorder. Reactions that produces more moles of gas have a greater increase in entropy. The total energy of an isolated system remains constant while the total energy of a closed or open system plus the total energy of its surroundings is constant. Total energy is neither gained nor lost, it is merely transferred between the system and its surroundings. Endothermic refers to when energy is taken up by the reaction in the form of heat and ΔH is positive. Exothermic refers to when energy is released by the reaction in the form of heat and ΔH is negative.

Heat absorbed / heat input is given by the formula:

q = mcΔT

Where m is mass, c is specific heat and ΔT is change in temperature.

This formula only works if no phase change is involved. Different phases have different specific heats and a phase change requires extra energy such as heat of fusion and heat of vaporization, which is why the above formula does not work across different phases. To work problems that involve a phase change, the calorimetry equation is used individually for the different phases, then the heat of fusion or vaporization is taken into account.

For example, to calculate how much energy it takes to heat ice from -20 °C to water at 37 °C, there are 3 components to this question:

For the ice phase from -20 °C to 0 °C, use:

q = mciceΔT        where ΔT is 20.

For the phase transition, use heat of fusion:

q = (ΔHfus) x (# of moles of ice/water),                 where ΔHfus is in energy per mol.

If the heat of fusion is given in energy per mass, then it should be multiplied by the mass to get energy.

For the water phase from 0 °C to 37 °C, use:

q = mcwaterΔT,                   where ΔT is 37.

Heat capacity is the amount of heat required to raise the temperature of something by 1 °C. The molar heat capacity is the heat capacity per mol = J / mol·°C. The specific heat capacity is the heat capacity per mass = J / g·°C. Celsius can be replaced by Kelvin here because a change in 1 °C is the same as a change in 1 K. It takes 4.2 J of heat energy to raise the temperature of 1 gram of water by 1 °C. Some useful conversion factors are:

1 calorie = 4.2 J; 1 Calorie (with capital C) = 1000 calorie = 4200 J.

For water, 1 gram = 1 cubic centimeter = 1 mL

Heat transfer occurs via three ways: conduction, convection, radiation. Conduction is the transfer of heat by direct contact. It requires things to be in contact. Convection is heat transfer by flowing current and it needs the physical flow of matter. Radiation refers to heat transfer by electromagnetic radiation, commonly in the infra-red frequency range. It does not need the physical flow of matter and it can occur through a vacuum.

Enthalpy or H is the heat content of a reaction. ΔH is the change in the heat content of a reaction. When it is positive it means heat is taken up and when it is negative it means heat is released. The standard heat of reaction, ΔHrxn, is the change in heat content for any reaction. The standard heat of formation, ΔHf, is the change in heat content of a formation reaction. A formation reaction is where a compound or molecule in its standard state is formed from its elemental components in their standard states. The standard state is where things are in their natural, lowest energy, state. For example, oxygen is O2 (diatomic gas) and carbon is C (solid graphite). The unit for enthalpy is in energy (J), or it can be expressed as energy per mol (J/mol).

Hess’ law of heat summation:

ΔHrxn = Δ(ΔHf) = sum of ΔHf (products) – sum of ΔHf (reactants)

ΔHrxn is the bond dissociation energy of all the bonds in reactants minus the bond dissociation energy of all the bonds in products.

ΔHrxn is the enthalpy of formation of all the bonds in products minus the enthalpy of formation of all the bonds in reactants.

Bond dissociation is the energy required to break bonds and it is positive because energy input is required to break bonds.4 The enthalpy of formation of bonds is negative because energy is released when bonds form.

Free energy is the energy available that can be converted to do work and is given by the formula:

ΔG = ΔH – TΔS       ,T is temperature in Kelvin.

Spontaneous reactions are reactions that can occur all by itself and they have a negative ΔG. We should not assume that an exothermic reaction is spontaneous, because a large, negative ΔS can cause it to become nonspontaneous. We must also not assume that an endothermic reaction is nonspontaneous, because a large, positive ΔS can make it spontaneous. It is not wise to assume that spontaneous reactions will occur quickly, because it may take a million years for it to happen, depending on its kinetics.

Heat of fusion, ΔHfus, is the energy input needed to melt something from the solid to the liquid at constant temperature. Heat of fusion is also called latent heat of fusion or enthalpy of fusion. Heat of vaporization, ΔHvap, is the energy input needed to vaporize something from the liquid to the gas at constant temperature. Heat of vaporization is also called latent heat of vaporization or enthalpy of vaporization. Latent heats can be expressed as molar values such as J / mol. The energy it takes to melt a solid is:

(ΔHfus) x (# of moles of that solid)

The energy it takes to vaporize a liquid is:

(ΔHvap) x (# of moles of that liquid)

Latent heats can also be expressed as J / mass, where energy can be obtained by multiplying the latent heats by the mass of the substance. Energy is released when either a gas condenses into a liquid, or when a liquid freezes into a solid. The energy released is the same as the energy of their reverse processes (see formula above).

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. A typical phase diagram has pressure on the y-axis and temperature on the x-axis. As we cross the lines or curves on the phase diagram, a phase change occurs. In addition, two states of the substance coexist in equilibrium on the lines or curves. A phase transition is the transition from one state of matter to another. There are three states of matter: liquid, solid, and gas. A liquid is a state of matter that consists of loose, free moving particles which form the shape set by the boundaries of the container in which the liquid is in. One may notice that some liquids flow readily whereas some liquids flow slowly. A liquid’s relative resistance to flow is viscosity. A solid is a state of matter with tightly packed particles which do not change the shape or volume of the container that it is in. However, this does not mean that the volume of a solid is a constant. Solids can expand and contract when temperatures change. Solids have strong intermolecular forces that keep particles in close proximity to one another. All true solids have crystalline structures. This means that their particles are arranged in a three-dimensional, orderly pattern.  Solids will undergo phase changes when they come across energy changes. A gas is a state of matter where particles are spread out with no definite shape or volume. The particles of a gas will take the shape and fill the volume of the container that it is placed in. In a gas, there are no intermolecular forces holding the particles of a gas together since each particle travels at its own speed in its own direction. Phase diagrams illustrate the variations between the states of matter of elements or compounds as they relate to pressure and temperatures. The following is an example of a phase diagram for a generic single-component system: Triple point is the point on a phase diagram at which the three states of matter co-exist. The critical point is the point on a phase diagram at which the substance is indistinguishable between liquid and gaseous states. Fusion(melting) or freezing curve is the curve on a phase diagram which represents the transition between liquid and solid states. Vaporization (or condensation) curve is the curve on a phase diagram which represents the transition between gaseous and liquid states. Sublimation (or deposition) curve is the curve on a phase diagram which represents the transition between gaseous and solid states. With most substances, the temperature and pressure related to the triple point lie below standard temperature and pressure and the pressure for the critical point lies above standard pressure. Therefore at standard pressure as temperature increases, most substances change from solid to liquid to gas, and at standard temperature as pressure increases, most substances change from gas to liquid to solid.

References

1) Cermak, N. (2009, March 12). Fundamentals of Enzyme Kinetics: Michaelis-Menten and Deviations. Retrieved from http://cermak.scripts.mit.edu/papers/383final_cermak_enzymekinetics_20090312.pdf

3) Miles, B. (2003, January 17). Biological Redox Reactions. Retrieved from Texas A&M University: https://www.tamu.edu/faculty/bmiles/lectures/Biological%20Redox%20Reactions.pdf

4) Stephen J. Blanksby, G. B. (2002, August 6). Bond Dissociation Energies of Organic Molecules. Retrieved from Michigan State University: http://www2.chemistry.msu.edu/courses/cem850/handouts/Ellison_BDEs.pdf

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