# Chemistry Lab/Thermodynamics

Thermodynamics is a topic for Chemistry Lab for the 2017 and 2018 seasons. It was previously a topic in 2006.

Thermodynamics is a very broad topic, so a variety of problems may appear on tests for this topic. Although some tests may contain basic problems like enthalpy calculations, advanced topics such as Hess' Law, entropy and Gibbs Free Energy problems are more common. The lab section of the test is often based on coffee cup calorimeters, testing topics like specific heat or heat of reaction. However, some more advanced labs may contain other techniques.

The Thermodynamics event page may contain additional useful information. However, although it deals solely with thermodynamics, it is more oriented to the physical aspects of thermodynamics, with only limited overlap with the chemical aspects.

## Contents

## First Law of Thermodynamics

*Energy is conserved and can neither be created nor destroyed.*

This law is sometimes represented as [math]\Delta E(universe) = 0[/math].

In terms of chemistry, this means that energy is transferred by means of heat or work.

As such, the first law is traditionally represented as [math]\Delta E = q + W[/math].

## Second Law of Thermodynamics

*In an isolated system, a natural process is spontaneous if it leads to an increase in entropy*

Since the universe is considered to be an isolated system, the second law is sometimes stated as: entropy in the universe is always increasing over time.

The second law also states that the changes in entropy of the universe will never be negative. A good way to think about this is when time passes, change only occurs in one direction, such as ice melting at room temperature, or aging over time. Those functions only happen in one direction in that isolated system and environment.

From this law, the Gibbs Free Energy equation can be derived- that is a long drawn out process that for Science Olympiad, is not necessary.

The Second Law also applies to heat engines and inefficiency. Heat engines use heat [math]Q_h[/math] from a hot reservoir and use it to do work [math]W[/math]. A perfect heat engine is able to use all of its heat to do work but is stated as impossible because some amount of the heat [math]Q_h[/math] must be exhausted to a cold reservoir (losing heat to the environment) which forms an equation for the efficiency of a heat system. The equation is [math]\frac{W}{Q_H} = \frac{Q_h-Q_c}{Q_h}[/math]. An important reading for this is the Carnot Cycle and will be discussed below.

Also, it is not possible for heat to flow from a colder body to a warmer body without any work having to be done to accomplish this flow. Just like the previous inefficiency mentioned, this applies very similarly to refrigerators. This is the reason why refrigerators must be electrically powered to generate work as if not, they would have very brief lifetimes as seen before when people used iceboxes and had to replenish their supply constantly.

#### Carnot Cycle

Please check the Thermodynamics#Carnot_Cycle page for a detailed explanation; the Carnot Cycle is more likely to be in the scope of Thermodynamics than in Chem Lab.

## Third Law of Thermodynamics

*The entropy of a perfect crystal is zero when the temperature of the crystal is absolute zero.*

An imperfect crystal has inherent disorder, creating entropy.

Similarly, unless a crystal is at 0 K, there will be some thermal motion leading to disorder.

Enthalpy data is given in relative terms of enthalpy of formation, and has no absolute zero.

The third law is useful as it defines an absolute zero entropy.

## Gibbs Free Energy

#### Enthalpy

Enthalpy represents the heat content of a system, capturing both the internal energy and the energy due to pressure.

[math]H = E + PV[/math].

[math]\Delta H = \Delta E + \Delta PV[/math].

If pressure is kept constant such as in a coffee cup calorimeter, change in enthalpy equals q.

[math]\Delta H = \Delta E + P\Delta V = q - P\Delta V + P\Delta V = q[/math].

#### Entropy

Entropy measures the disorder in a system.

Entropy favors more probable solutions; for example, entropy is highest for gases equally spread out over all available volume, as that is the most statistically likely arrangement.

[math]\Delta S = \Sigma S(products) - \Sigma S(reactants)[/math]

Entropy of reaction calculations behave very similarly to enthalpy of reaction calculations.

At standard-state conditions, this equation yields the standard-state entropy of reaction.

Note that the standard-state conditions of thermodynamics are not equivalent to the STP of gases. Standard-state conditions are 298.15 K, where all gases are at 1 atm pressure, all liquids and gases are pure, and all solutions are 1 M. At standard-state conditions, the enthalpy of formation of a pure element can be assumed to be 0.

Entropy of reaction will be positive if the system becomes more disordered, and vice versa.

Due to the regular structure of solids, solids are more ordered than either liquids or gases; gases are more disordered than liquids due to their state of constant and random motion.

As temperature and average kinetic energy increase, entropy increases. Abrupt entropy changes occur during melting and boiling.

Also, any process or reaction that increases the number of particles increases the amount of disorder.

Remember that as part of the definition of an isolated system, no heat or work can be exchanged between such a system and its surroundings. Therefore, no net enthalpy change can occur in an isolated system, and entropy is the only driving force.

In an isolated system, entropy of reaction will be positive if a process is spontaneous, and negative if a process is nonspontaneous.

#### Spontaneity

As described above, entropy drives all processes in an isolated system. However, most processes occur in the "real world", where enthalpy serves as another critical driving force.

Gibbs free energy is used to determine if a reaction is spontaneous based on both enthalpy and entropy.

[math]G = H - TS[/math]

[math]\Delta G = \Delta H - T\Delta S[/math]

Using standard-state conditions results in the standard-state free energy change of reaction.

The free energy change directly determines spontaneity - if free energy change is positive, the reaction is non-spontaneous, while if free energy change is negative, the reaction is spontaneous.

If enthalpy is negative and entropy is positive, the reaction is spontaneous at all temperatures. Meanwhile, if enthalpy is positive and entropy is negative, the reaction will be non-spontanous at any temperature. If both driving factors are negative, the reaction will become less favorable as temperature increases, as the negative entropy becomes more dominant. Finally, if both are positive, the reaction will become more favorable as temperature increases, as the positive entropy dominates the equation.

#### Reversibility

A reversible process is a process which can be reversed in direction without increasing entropy. In other words, a reversible process can be reversed to its initial state with no changes. Perfectly reversible processes are impossible for a number of reasons, but some processes are more reversible than others.

A free energy of reaction close to zero signifies a highly reversible reaction, while a massive free energy of reaction would signify a more irreversible process.

Reversible processes define the efficiency of heat engines; a heat engine utilizing only perfectly reversible processes would be perfectly efficient with no heat loss.

## Thermochemistry

#### Internal Energy

Thermodynamics often divides the universe into two regions - a system and its surroundings.

*Internal energy*, or E, is a property of any system. E is the sum of all potential and kinetic energies in the system.

Unlike in engineering, chemistry views energy change from the perspective of a system. That is, increased internal energy represents a positive change in energy.

Work is equal to the product of pressure and change in volume. However, since expansion requires the system to expend energy, a negative term is required to reflect the internal energy of the system.

[math]W = -P\Delta V[/math], or [math]\Delta E = q - P\Delta V[/math].

Exothermic reactions require a decrease in internal energy, or a negative q, while endothermic reactions mean an increase in internal energy and a positive q.

#### Calorimetry

Heat flow can be measured using a device known as a calorimeter. Calorimeters are designed to hold heat while a chemical reaction is taking place. The reaction occurs in a solution, typically water, such that the change in temperature of the water can be used to calculate the heat flow between the chemical system and the water surrounding it. The most easily attainable calorimeter consists of two nested coffee cups; this provides good heat insulation and a constant pressure.

This equation is used to calculate the heat flow in a reaction: [math]q = m\cdot \Delta T\cdot C_p[/math]. C(p) represents the specific heat of the solution, or the amount of energy required to raise the temperature of a gram of a substance by 1 degree Celsius.

The equation is slightly altered for the calorimeter itself: [math]q = C\cdot \Delta T[/math]. In this case, C represents the heat capacity of the entire calorimeter, or the heat lost due to inefficiency.

The entire heat flow of the reaction is calculated by adding these two sums: [math]q = m\cdot \Delta T\cdot C_p + C\cdot \Delta T[/math].

However, remember that the an endothermic reaction for the calorimeter represents an endothermic reaction for the chemicals themselves.

[math]q(rxn) = -q(cal)[/math].

#### Hess' Law

*Hess' Law* is used to calculate enthalpy change simply from the enthalpies of formation or bond enthalpies.

[math]\Delta H = \Sigma \Delta H_f(products) - \Sigma \Delta H_f(reactants)[/math].

[math]\Delta H = \Sigma \Delta H_b(reactants) - \Sigma \Delta H_b(products)[/math]. The bond energies of the reactants represent the influx of energy from breaking bonds, while the bond energies of the products represent the outflow of energy from forming them.