Question

You are given \(\Delta H\) for a process that occurs at constant pressure. What additional information do you need to determine \(\Delta E\) for the process?

Short answer

To determine the internal energy change (\(\Delta E\)) for the process, the additional information needed is the product of the constant pressure (\(P\)) and the change in volume of the system (\(\Delta V\)) during the process.

Step-by-step solution

Write down the relationship between enthalpy change, internal energy change and work done by the system

The relationship between \(\Delta H\), \(\Delta E\), and \(w\) is given by the equation: $$ \Delta H = \Delta E + P\Delta V $$ where \(\Delta H\) is the enthalpy change, \(\Delta E\) is the internal energy change, \(P\) is the constant pressure, and \(\Delta V\) is the change in volume during the process.

Identify the given information and the required information

The given information is \(\Delta H\). The additional information needed to determine \(\Delta E\) can be found by rearranging the equation above as: $$ \Delta E = \Delta H - P\Delta V $$ From this equation, it is clear that we need to find the value of \(P\Delta V\) to determine \(\Delta E\).

State the additional information needed to find \(\Delta E\)

To determine the internal energy change (\(\Delta E\)) for the process, the additional information needed is the product of the constant pressure (\(P\)) and the change in volume of the system (\(\Delta V\)) during the process.

Key concepts

Enthalpy Change (\(\text{\textDelta} H\))

Understanding the enthalpy change in a chemical or physical process is key for students tackling thermodynamics. Enthalpy, represented by \(\text{\textDelta} H\), is a measure of the total heat content in a system. It's important to remember that we can't measure this directly; we can only measure changes in enthalpy.

When a reaction or process occurs at constant pressure, the enthalpy change corresponds to the heat absorbed or released by the system. If \(\text{\textDelta} H\) has a positive value, it indicates that the system has absorbed heat from its surroundings, which is known as an endothermic process. Conversely, a negative value signifies heat release to the surroundings, defining an exothermic process.

To make this concept more relatable, let's consider melting ice cubes in a glass. The ice absorbs heat from the surroundings to melt, signifying a positive \(\text{\textDelta} H\) for the process.

Internal Energy Change (\(\text{\textDelta} E\))

Moving on to internal energy, labeled as \(\text{\textDelta} E\): this concept represents the sum total of kinetic and potential energies of the molecules within the system. It encompasses everything from the jiggling of atoms to the bonds between molecules. A change in internal energy is a sign that a substance has undergone some transformation, whether that be a chemical reaction or a change of state.

The internal energy can change either due to heat exchange with the surroundings or as work done by or on the system. Imagine blowing up a balloon. As the air molecules inside the balloon gain energy, they do work by pushing against the balloon walls, which is an example of work contributing to an increase in internal energy.

For students to make accurate predictions about the internal energy change, they'll often need two pieces of information: the enthalpy change and the pressure-volume work (which we'll explore next).

Pressure-Volume Work (\(P\text{\textDelta} V\))

Lastly, pressure-volume work, indicated by \(P\text{\textDelta} V\), ties with the concept of work done on or by the system during expansion or compression at constant pressure. The 'P' represents the constant external pressure, while \(\text{\textDelta} V\) denotes the change in volume.

In everyday terms, when a bicycle pump compresses air, work is done on the air molecules. If the volume of the pump's chamber decreases at a constant external pressure, we've performed pressure-volume work on the system. This work, along with heat absorbed or released, will contribute to the internal energy change.

It's worth highlighting that to comprehend \(\text{\textDelta} E\), a student indeed needs the value of \(P\text{\textDelta} V\), which is the additional information required in the given exercise solution. Clarifying what pressure-volume work involves will aid in cementing the understanding of the energy interactions during physical processes or chemical reactions.