CHEM 1411 Concept Reviews: Thermochemistry

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Energy:  the capacity to do work or transfer heat

Work: energy that causes an object to change its motion (i.e- a force is applied across a distance)

Heat:  the energy used to cause the temperature of an object to increase

Types of Energy

Kinetic Energy:  the energy of motion                   Equation:  $E_k=\frac{1}{2}mv^2$ (m is mass, v is velocity)

Potential Energy:  any type of energy that is in a “stored” form, which includes gravitational potential energy, electrostatic potential energy, chemical potential energy, and more.

Chemical Potential Energy:  the energy stored in the structure of atoms and molecules.

Joule:  the SI unit of energy which is defined as $\frac{kg\cdot m^2}{s^2}$.              4.184 J = 1 calorie (cal). 

 

 

Applications of the First Law of Thermodynamics

The First Law of Thermodynamics:  Energy is neither created nor destroyed, but merely converted from one form to another or transferred from one place to another.

One way to apply this law is to look at the universe in two parts:  a closed portion that we single out for study called the system and everything else which is referred to as the surroundings.  If energy is lost by the system, it MUST be gained by the surroundings.  In equation form, this can be written as follows:

$\Delta E_{system}=-\Delta E_{surroundings}$

 

The change in the internal energy of a system is represented as the difference between its final and initial states.

$\Delta E=\Delta E_{final}-\Delta E_{initial}$

This change in energy can only be directly measured in reference to the system and comes in the form of either heat transferred to or from the system and/or work done on or by the system.  This relationship is shown in the following equation:

$\Delta E=q+w$

 

Thermodynamic Identity	If the Sign is…	Meaning
∆E	+	Energy is gained by the system.
∆E	-	Energy is lost by the system.
q	+	Heat is absorbed by the system from the surroundings.
q	-	Heat is released by the system to the surroundings.
w	+	Work is done on the system by the surroundings.
w	-	Work is done by the system on the surroundings.

 

State Function:  a property of a system that is determined by specifying the system’s condition, or state.  The value of a state function depends solely on the present state of the system, not on the path it took to get there.

 

In the chemical systems we deal with, the most common kind of work we will see is pressure-volume work, in which an applied pressure causes a change in volume.  The equation is as follows:

 $w=-P\Delta V$      (where $\Delta V=V_{final}-V_{initial}$)

 

 

 

Enthalpy is a state function that combines internal energy, pressure, and volume.  The equation is as follows:

$H=E+PV$

At constant pressure, the $\Delta H=q$, which makes it extremely useful for comparing heat (energy) flow in chemical reactions since many reactions take place at constant or nearly constant pressure.  It is important to note that while ∆H is a state function, q and w are not.

 

 

 

When an Enthalpy of Reaction is specified, it refers to the heat transfer that occurs when the stoichiometric number of moles of reactants reacts to form the stoichiometric number of moles of products. 

For example:                                   $2H_2\left(g\right)+O_2\left(g\right)\longrightarrow2H_2O\left(g\right)$                         $\Delta H=-483.6\:kJ$

The above equation tells us that 2 mol H₂ reacting with 1 mol O₂ to form 2 mol H₂O releases -483.6 kJ of heat.  These relationships can be used as conversion factors to convert between heat released by a reaction and moles:

$\left(\frac{2\:mol\:H_2}{-483.6\:kJ}\right)\:\:or\:\:\left(\frac{-483.6\:kJ}{1\:mol\:O_2}\right)$

When ∆H is positive, a reaction absorbs heat energy and is called endothermic.

When ∆H is negative, a reaction releases heat energy and is called exothermic.

The reverse reaction has an enthalpy of equal magnitude but OPPOSITE sign compared to its forward reaction.

 

 

 

Calorimetry

Calorimetry is the measurement of heat flow.  Devices used to measure heat flow are called calorimeters.  To measure heat flow effectively, it is necessary to determine the heat capacity of the substances and/or the calorimeter used.  Heat capacity is the amount of energy required to raise the temperature of an object 1˚C.  For pure substances, it is useful to determine their molar heat capacity, C_m, (the amount of energy required to raise 1 mole of a substance 1˚C) or specific heat capacity, C_s (the amount of energy required to raise 1 gram of a substance 1˚C).  The following equations are used for calorimetry experiments:

$q=m\times C_s\times\Delta T$  (for use when specific heat is given)

Where q is heat transferred, m is mass, C_s is specific heat, and ∆T is change in temperature). 

 

$q=m\times C_m\times\Delta T$  (for use when molar heat capacity is given)

Where q is heat energy transferred, n is moles, C_m is molar heat capacity, and ∆T is change in temperature

 

$q_{cal}=C_{cal}\times\Delta T$  (for use when heat capacity of the calorimeter is given)

Where q_cal is heat energy transferred to (+) or from (-) the calorimeter, C_cal is the heat capacity of the calorimeter, and ∆T is change in temperature

 

When the above equations are used to find the q_rxn, one must remember that   q_solution = -q_rxn      or    q_cal = -q_rxn

 

 

 

Enthalpies of Formation

Enthalpy of Formation (∆H_f):  The enthalpy change accompanying the formation of EXACTLY 1 mole of a substance from its constituent elements in their natural states. (Also called the heat of formation)

Standard Enthalpy Change (∆H˚):  the enthalpy change at standard conditions of 1 atm and 25˚C (298K)

 

Applying Hess’ Law, we can use standard enthalpies of formation to determine the enthalpy of reaction as follows:

$\Delta H^\circ_{rxn}=\sum n\Delta H^\circ_{f\:}\left(products\right)-\sum m\Delta H^\circ_{f\:}\left(reactants\right)$

 

Thus, for any reaction “$aA+bB\longrightarrow cC+dD$” where lowercase letters indicate coefficients and uppercase letters indicate chemical symbols, the ∆H_rxn can be given by the following equation:

$\Delta H^\circ_{rxn}=\left[c\left(\Delta H^\circ_{f\:of\:C}\right)+d\left(\Delta H^\circ_{f\:of\:D}\right)\right]-\left[a\left(\Delta H^\circ_{f\:of\:A}\right)+b\left(\Delta H^\circ_{f\:of\:B}\right)\right]$