Enthalpy of Reaction

Enthalpy of Reaction

Thermodynamics is the study of heat energy and other types of energy, such as work. The laws of thermodynamics are used across all known science fields and have applications ranging from biology to physics.

Three Laws of Thermodynamics

There are three principle laws of thermodynamics that describe the interactions occurring within the universe, regardless of scale.

The first is the law of conservation of energy, which describes that the total energy of an isolated system is constant. Energy can be transferred from one form of energy to another, but it can never be created or destroyed. For example, thermal energy can be transformed into work.

The second law of thermodynamics is the law of increased entropy. Entropy is a thermodynamic property that is related to the possible microscopic configurations of the system. Entropy describes the disorder of the thermodynamic system. The second law states that the sum of entropies in an isolated thermodynamic system must always increase because systems tend toward more disorder rather than less. Therefore, thermodynamic systems can never decrease in entropy, which would suggest a change from disordered to ordered, because that would violate this fundamental law of entropy.

Finally, the third law of thermodynamics is the law of absolute zero. This law states that the entropy of a system approaches a constant value as the system approaches the temperature of absolute zero. Absolute zero is a theoretical temperature where the motion of all matter stops, and it is defined as 0 degrees Kelvin.

Enthalpy

In physics and chemistry, there are two types of functions: state functions and path functions. Path functions depend on the transition a system undergoes from the initial state to the final state. The most common path functions are heat (Q) and work (W).

State functions are independent of the path and rely on the current equilibrium state of the system. State functions include pressure, temperature, volume, enthalpy, and entropy.

Enthalpy, H, is a thermodynamic property that describes the heat lost or gained in a system. The change in enthalpy, ΔH, is equal to the sum of the change in internal energy, ΔU, plus the product of the constant pressure, P, and the change in volume, ΔV.

ΔH = ΔU + PΔV

During a chemical reaction, energy is either gained or released. Since enthalpy is a state function, the change in enthalpy during a chemical reaction only depends on the difference between the final and initial enthalpies.

ΔH = H_final - H_initial

The initial enthalpy represents the enthalpy of the reactants, whereas the final enthalpy represents the enthalpy of the products. Thus, the enthalpy change of a reaction can be described by the following equation:

ΔH_rxn = H_products - H_reactants

When the enthalpy of the products is greater than the enthalpy of the reactants, ΔH is positive, indicating that the reaction absorbs heat and is endothermic. When the enthalpy of the reactants is greater than the enthalpy of the products, ΔH is negative, and the reaction releases heat and is exothermic. If the ΔH values are known for a reaction, the reverse reaction is the negative value of that ΔH. An exothermic forward reaction would become an endothermic reverse reaction, for example.

Some reactions occur in multiple steps, and each have their own enthalpy of reaction. According to Hess’s Law, we can determine the overall enthalpy of reaction by adding the enthalpy of reaction for each step.

For example, the formation of magnesium oxide from solid magnesium and oxygen gas can be divided into three individual reactions.

Mg_(s) + ½O_2(g) → MgO_(s) ΔH_rxn

Mg_(s) + 2H⁺_(aq) → Mg²⁺_(aq) + H_2(g) ΔH_rxn1

Mg²⁺_(aq) + H₂O_(l) → MgO_(s) + 2H⁺_(aq) ΔH_rxn2

½O_2(g) + H_2(g) → H₂O_(l) ΔH_rxn3

According to Hess’s law, the enthalpy of reaction for the overall reaction (ΔH_rxn) is equal to the sum of the individual enthalpies of reactions of each step.

ΔH_rxn = ΔH_{rxn1 +} ΔH_{rxn2 +} ΔH_rxn3

Calorimeter

A calorimeter is a device that measures the heat released or absorbed by a physical process or chemical reaction. A constant-pressure calorimeter consists of an insulated reaction chamber that is isolated from the surroundings. This minimizes the impact of any heat or work lost to the ambient environment. The calorimeter has a stirrer to mix the solution and a thermometer to measure temperature changes.

To measure heat using a calorimeter, reactants are placed inside of the reaction chamber and mixed. As the reaction occurs, the temperature changes are recorded as ΔT. Since the calorimeter is insulated and isolated from the surroundings, any temperature change is due to heat gained or lost during the chemical reaction.

The calorimeter can be used to determine the enthalpy of a reaction by determining the thermodynamic value of heat, Q, using the change in temperature. When Q is positive, heat is absorbed by the system, whereas a negative Q indicates heat released by the system.

Heat is related to the change in temperature during a reaction, ΔT, by the mass of the substance, m, and its specific heat capacity, c_s. The specific heat capacity represents the amount of energy needed, in the form of heat, to raise the temperature of one unit of mass of a pure substance by one unit and is written in units of J/kg·K.

Q = mc_sΔT

The subscript p indicates that the reaction is performed under constant pressure.

Q = mc_pΔT

Since each component of the reaction and calorimeter absorbs or loses heat, all components must be taken into account when calculating the thermodynamic heat of the reaction, Q_rxn. Therefore, the total heat of the reaction is equal to the heat gained or lost by the solution plus the heat gained or lost by the calorimeter.

Q_rxn = - (Q_soln + Q_calorimeter)

Q_rxn = - (m_solnc_solnΔT + C_calorimeterΔT)

The thermodynamic heat of the reaction, Q_rxn, measured in the calorimeter is equal to the heat of the reaction, ΔH_rxn.

References

1. Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). Chemistry and Chemical Reactivity. Belmont, CA: Brooks/Cole, Cengage Learning.
2. Silderberg, M.S. (2009). Chemistry: The Molecular Nature of Matter and Change. Boston, MA: McGraw Hill.

Thermodynamics is the study of heat and its relation to energy and work. One of the most important thermodynamic properties is enthalpy, which indicates the heat energy transferred by a process at constant pressure. Enthalpy is used to describe chemical reactions, where the enthalpy change, ΔH, tells us how much heat is absorbed or released during a chemical reaction.

Enthalpy is a state function, meaning that the change is independent of the path and only takes into account the initial and final state. Thus, the ΔH of a reaction is calculated by subtracting the sum of the enthalpies of the reactants from the sum of the enthalpies of the products.

If ΔH is positive, the reaction is endothermic and absorbs heat from the surroundings. If ΔH is negative, the reaction is exothermic and releases heat to the surroundings.

We can measure the enthalpy change of a reaction using an isolated system like a calorimeter. A simplified calorimeter, like the one we have here, consists of an insulated sample cell with a stirrer and a thermometer. As the reaction proceeds inside of the insulated cell, the temperature changes and we are able to measure ΔT.

We can assume that no energy is transferred into or out of the sample cell because it is insulated. So, we can then assume that the temperature change is due to the heat change in the reaction.

So, how do we use ΔT to calculate ΔH? At constant pressure, ΔH is equal to the heat flow, Q. Q is equal to the mass of the substance times its specific heat capacity and the change in temperature. The specific heat capacity, c_s, is a measure of how much heat is required to increase the temperature of 1 g of a material by 1 °C.

A material with a higher specific heat capacity requires more energy to raise its temperature and vice versa. Specific heat capacity values for common substances can be found in the literature. Thus, we can use the specific heat capacity, along with the mass of the substance and the temperature change, to calculate ΔH for the reaction.

In your experiment, we will measure the change in enthalpy for the formation of magnesium oxide from magnesium and oxygen. Using our simple calorimeter requires us to measure the heat of reaction indirectly with a series of separate reaction steps. So, we will run each reaction separately and measure ΔT and, by extension, ΔH for each reaction. Then, according to Hess's Law, the enthalpy of the overall reaction is equal to the sum of each of the enthalpies of reaction for each reaction step.

In this lab, you will construct a simple calorimeter using polystyrene cups and then experimentally determine the enthalpy of formation of magnesium oxide.