Unit 5

# Internal energy

Internal energy is the sum of all heat and work contained in a system. A system can gain internal energy by exchanging heat, q, or work, w, with the surroundings.

Internal energy is the difference between the initial and final energies of the system:

$\Delta\text{E} = \Delta\text{E}_\text{final} - \Delta\text{E}_\text{initial}$

When energy is used by the system, internal energy increases (exothermic reaction). When energy is released from the system, internal energy decreases (endothermic reaction).

Any change in the energy of the system is accompanied by an opposite (proportional) change in the energy of the surroundings.

# Heat exchange with surroundings

The heat transferred in a reaction depends on the mass (m), specific heat (c), and temperature change (ΔT) of the reaction.

$q = m c \Delta T$

Usually, this is used when a reaction is done in water. The heat exchange for the water (using water's specific heat - 4.184J/g-K) can be calculated. Then, the amount of heat exchange for the reaction is the opposite of the heat exchange for the water.

# State changes

While a system is undergoing a state change, no temperature change occurs. This is because all energy is going towards breaking or creating bonds for the state change, and not towards changing the speed at which the molecules are moving.

When calculating the amount of energy needed for an energy change that passes through a state change, make sure to add the amount of energy needed for the state change.

Fusion is the state change between solid and liquid, and vaporization is the state change between gas and liquid.

# Enthalpy

The change in enthalpy, ΔH, is equal to the change in heat, q, at constant pressure. At constant volume, the change in enthalpy is equal to the change in internal energy, ΔE. However, the difference between ΔH and ΔE is usually very small.

Balanced chemical equations that show the associated enthalpy change in this way are called thermochemical equations.

## Guidelines for thermochemical equations:

1. Enthalpy is an extensive property, so it changes and is proportional to the amount of reactant in a reaction.
2. The enthalpy change for a reaction is equal in magnitude, but opposite in sign, to ΔH for the reverse reaction.
3. The enthalpy change for a reaction depends on the states of the reactants and products. Therefore, it is important to specify the states of the reactants and products in thermochemical equations.

# Calorimetry

Calorimetry is the measurement of heat flow accompanying a reaction at constant pressure (which equals ΔH). A device used to measure heat flow is a calorimeter.

## Coffee-cup calorimetry

A simple "coffee-cup" calorimeter is often used in general chemistry laboratories to illustrate the principles of calorimetry.

Two aqueous solutions are added to the coffee-cup calorimeter. If we assume that the calorimeter is perfectly insulated, any heat released or absorbed by the reaction will raise or lower the temperature of the water in the solution (the reactants and products are the system, the surroundings are just the water).

Therefore, we measure the temperature change of the solution and assume that any changes are due to heat transferred from the reaction to the water (for exothermic process) or transferred from the water to the reaction (endothermic).

The heat gained or lost by the solution is equal in magnitude but opposite in sign to the heat absorbed or released by the reaction. Therefore, it is possible to calculate the q change of the reaction using the temperature change of the solution (measured with the thermometer).

## Bomb calorimetry

Combustion reactions are most accurately studied using a bomb calorimeter. The substance is placed in a small cup within an insulated sealed vessel called a bomb. The reaction is then initiated from the outside.

The heat released when combustion occurs is absorbed by the water and the various components of the calorimeter (the surroundings). The change in water temperature is measured precisely.

To calculate the heat of combustion from the measured temperature increase, we must know the total heat capacity of the calorimeter.

$q_\text{rxn} = -C_\text{calorimeter} * \Delta T$

Reactions in the bomb calorimeter are carried out at constant volume, so the heat transferred corresponds to the change in internal energy (ΔE) rather than the change in enthalpy (ΔH). For most reactions, however, the difference between ΔE and ΔH is very small.

# Heat of formation

Sometimes, you're given the heat of formation for substances in an equation, and asked to calculate the overall enthalpy for the reaction.

The heat of formation provided is always negative, because energy is released when bonds are formed (the same amount of energy that is required to break those bonds).

To solve these types of problems, adjust the sign of each bond formation enthalpy provided as makes sense: If it's a reactant, then the reactant needs to be broken down, and therefore the enthalpy should be positive. If it's a product, then the substance will be formed, and the enthalpy should be negative.

# Spontaneous reactions

Entropy is a measure of randomness in a system. Both entropy and enthalpy play a role in determining whether a process is spontaneous.

A reaction is spontaneous if it increases the enthalpy of the universe. Therefore, there are some simple general guidelines to look for in a reaction when deciding whether it's spontaneous:

• State changes towards gas are usually spontaneous, since higher energy states vibrate more.
• Reactions that produce more elements (if they're the same state) are usually spontaneous.
• Reactions that produce larger molecules are usually spontaneous, since larger molecules have more ways that they can be turned and therefore more "ways" to be random.

## Gibbs free energy

Gibbs free energy is a way of calculating whether a process will be spontaneous. The equation to calculate this value (ΔG) is:

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

T is always in Kelvin for this equation.

If Gibbs free energy is negative, the process is spontaneous. If Gibbs free energy is positive, the reaction will be non-spontaneous, but spontaneous in the opposite direction. If gibbs free energy is 0, equilibrium has been reached.

There is a concept of a spontaneous reaction being enthalpy-driven or entropy-driven. This refers to which value, enthalpy or entropy, is making the equation more negative. For example, if enthalpy is making the reaction more negative (and spontaneous) than entropy, or the reaction is spontaneous despite the entropy value, the reaction would be enthalpy-driven.

## Solving Gibbs free energy problems

You may be asked at what temperatures a reaction is spontaneous, based on its enthalpy and entropy. To solve these problems, fill in what you know and think about what values of T would make the reaction negative.

For example, if ΔH and ΔS are both positive, then filling in the equation for ΔG above would make clear that the whole equation will only be negative if T is large.

To calculate the exact temperature above or below which the reaction is spontaneous, plug in 0 for ΔG and solve for T. Then, reason out whether the temperature needs to be above or below this value for the whole equation to be negative and the process to be negative.