State functions

State functions are properties of a system that depend on the current state of a particular system.

What is temperature?

Temperature is the property that describes the transfer of energy which travels from areas of higher temperature to areas of lower temperature. Higher temperature reflects increased vibration and kinetic movement of atoms in a system. There are many units to measure temperature but familiarity with Celsius, Kelvin and Fahrenheit degrees should be plenty:

$Kelvin \longrightarrow Celsius$
$K - 273 = ^{o}C$

$Celsius \longrightarrow Fahrenheit$

$^{o}C = (5/9) (^{o}F- 32)$

What is pressure?

Pressure is how hard one thing pushes on another and reflects the forces within a system. Pressure can be calculated by dividing the exerted force over a defined area:

$$P = \frac{F}{A}$$ (38.1)

Pascals ($Pa$), atmospheres ($atm$), and millimeters of mercury ($mmHg$) are common units of pressure, but conversions should be supplied by the MCAT passage. Be sure to understand that the smaller the area for a given force the higher the pressure - remember the classic physics example of someone standing you on your hand wearing a tennis shoe vs. wearing stilettos.

What is entropy?

Entropy, $S$, is the measure of disorder in a system with the greater the disorder the greater the $S$.

A more advanced interpretation of entropy shows that entropy can be calculated from heat capacity. Although this is beyond the scope of the MCAT, it does point out how inter-related thermodynamic concepts are.

What is the relationship between entropy and various states of matter?

Table 37.2: Relationship between states of matter and entropy.

Gas	Highest entropy
Liquid	``Medium'' entropy
Crystal/solids	Lowest entropy

If this is unclear, think about which one takes more energy to create. To get from crystal to liquid or liquid to gas you need to add energy, which makes the system more disorderd.

What is $\Delta S$ at equilibrium?

Zero.

What is enthalpy?

Enthalpy, $H$, is the measure of internal energy in a system.

What are three ways energy^38.1 can be transferred?

1. Conduction
   • No matter exchange.
   • Transfer of heat is accomplished by direct contact, e.g. a stove heating a tea kettle.
2. Convection
   • Matter exhange.
   • Transfer of heat when a hotter (lower density) substance rises to take the place of a colder (higher density) substance, e.g. hot air coming off of asphalt on a road in the desert.
3. Radiation
   • Release of energy from a hot object in the form of electromagnetic radiation, e.g. the heat you feel from a light bulb

What is Gibbs free energy?

Gibbs free energy is a very important function:

$$\Delta G = \Delta H - T\Delta S$$ (38.2)

Note: Temperature is in Kelvins, and is therefore always a positive value.

This function will be revisited in more detail below, but briefly:

$\Delta G > 0$	Non-spontaneous reaction (+ $\Delta G$)
$\Delta G = 0$	Reaction at equilibrium
$\Delta G < 0$	Spontaneous reaction ($- \Delta G$)

What is the role of $\Delta H$, $T$ and $\Delta S$ in determining the outcome of a reaction?

$\Delta G = \Delta H - T\Delta S$

Table 37.3: Role of $\Delta H$, $T$ and $\Delta S$ in reaction outcomes.

$\Delta H$	$T*$	$\Delta S$
-	+	+	Spontaneous at all temperatures
-	+	-	Spontaneous at low temperatures
+	+	+	Spontaneous at high temperatures
+	+	-	Non-spontaneous at all temperatures

What is the relationship between the standard free energy of a system ($\Delta$ G$^{o}$) and the equilibrium constant ($K_{eq}$)?

$\Delta G^{o}$ is the likelihood that a reaction will proceed spontaneously (or not) at standard conditions (298.15 K and 1 atm of pressure). The magnitude of $\Delta G^{o}$ indicates how far the system is from equilibrium because when $\Delta G^{o} = 0$, equilibrium is achieved.

Therefore, the relationship between $\Delta G^{o}$ and $K_{eq}$ is directly related because they both reflect, in their own manner, how far the reaction is from equilibrium.