Enthalpy

In thermodynamics, Enthalpy is a measure of the total energy of a system, including both the internal energy and the energy required to create space for the system by displacing its surroundings (pressure-volume work). During chemical reactions, energy is either absorbed or released, changing the system's enthalpy. This change in enthalpy is denoted as ΔH, and it helps in understanding the heat flow in reactions at constant pressure.

1.0Standard Conditions for Measuring Enthalpy

• Pressure: The standard pressure for measuring enthalpy changes is 1 bar (100 kP_a). This pressure is close to atmospheric pressure, making it a convenient reference.
• Temperature: Although reactions can be conducted at various temperatures, the standard temperature commonly used is 298 K (25°C). This temperature is chosen because it is close to room temperature and is a convenient reference for most chemical processes.
• Substance in Pure Form: Each substance participating in the reaction must be in its pure form at standard pressure. For example, a gas's standard state is its pure form at 1 bar, and for a liquid or solid, the standard state is the pure substance at 1 bar.

2.0Enthalpy and its Relationship with Internal Energy

In thermodynamics, chemical reactions often take place at constant pressure (typically atmospheric pressure). To better understand energy changes in such systems, scientists introduced the concept of enthalpy (H). This is particularly useful when dealing with heat transfer and reactions in an open system.

Definition of Enthalpy (H):

Enthalpy is defined as:

H = U + PV

Where:

• H = Enthalpy
• U = Internal energy of the system
• P = Pressure of the system
• V = Volume of the system

Internal energy (U) represents the total energy (kinetic + potential) stored within a system. The term PV represents the work done by the system to push against the external pressure.

At constant pressure, the change in enthalpy (ΔH) is related to the change in internal energy (ΔU) and the work done due to volume change (PΔV):

                                                      ΔH = ΔU + PΔV

This equation allows us to relate heat absorbed or released during a reaction to the system’s internal energy and volume change.

3.0Relationship with the First Law of Thermodynamics

The first law of thermodynamics states that the change in internal energy (ΔU) is equal to the heat added to the system (q) plus the work done by the system (W):

                                                    ΔU = q−W

At constant pressure, the heat absorbed or released, denoted as qₚ, is equal to the change in enthalpy (ΔH):

                                                     ΔH = qp

This shows that at constant pressure, the change in enthalpy represents the total heat absorbed or released by the system.

4.0Relationship Between ΔH and ΔU

The difference between ΔH (change in enthalpy) and ΔU (change in internal energy) becomes noticeable when gases are involved because gases undergo significant volume changes. For solids and liquids, this difference is typically negligible.

In general:

ΔH = ΔU + Δ(PV)

If a substance is not undergoing a chemical reaction or phase change, the equation simplifies to:

ΔH = ΔU + nRΔT

Where:

• n = Number of moles of gas
• R = Universal gas constant
• ΔT = Change in temperature

For Chemical Reactions Involving Gases:

When a chemical reaction involves gases, the difference between ΔH and ΔU depends on the change in the number of moles of gas. This relationship can be expressed as:

ΔH = ΔU + (Δn_g)RT

Where:

• Δn_g = Change in the number of moles of gas (products - reactants)
• R = Gas constant
• T = Temperature in Kelvin

Understanding Δn_g:

• If Δ_g = 0 (i.e., no change in the number of moles of gas), then ΔH = ΔU. 

Example:H₂(g) + I₂(g) → 2HI(g)

• Here, the number of moles of gas on both sides is the same, so Δn_g = 0.

If Δn_g > 0 (i.e., there is an increase in the number of moles of gas), 

then ΔH > ΔU. 

Example:PCl₅(g) → PCl₃(g) + Cl₂(g)

In this case, the number of gas molecules increases, making Δn_g positive.

• If Δn_g < 0 (i.e., there is a decrease in the number of moles of gas), then ΔH < ΔU. 

Example:N₂(g) + 3H₂(g) → 2NH₃(g)

The total number of gas molecules decreases, making Δn_g negative.

5.0Heat Transfer at Constant Volume and Pressure

Heat at constant volume (qᵥ):When heat is transferred at constant volume, it leads to a change in the internal energy (ΔU) of the system. The formula is: Uqᵥ = ΔU

Heat at constant pressure (qₚ):When heat is transferred at constant pressure, it causes a change in the enthalpy (ΔH) of the system. The formula is: qₚ = ΔH 

Golden Key Points to Remember:

If Δn_g = 0 (no change in moles of gas):  ΔH = ΔU

Example: H₂(g) + I₂(g) → 2HI(g)

If Δn_g > 0 (increase in moles of gas): ΔH > ΔU

Example: PCl₅(g) → PCl₃(g)+Cl₂

If Δn_g < 0 (decrease in moles of gas): ΔH < ΔU

Example: N₂(g) + 3H₂ (g) → 2NH₃(g)