Problem 28 - Chemistry: An Atoms-Focused Approach

Question

Calculate \(\Delta E\) for a chemical reaction that releases \(90.7 \mathrm{kJ}\) of heat to its surroundings but does no work on them.

Step-by-Step Solution

Answer

Answer: The change in internal energy for the chemical reaction is -90.7 kJ.

Step 1: Write the first law of thermodynamics equation

The first law of thermodynamics equation for the change in internal energy (\(\Delta E\)) is: $$\Delta E = q - w$$

Step 2: Identify known values

According to the exercise, the chemical reaction releases \(90.7 \mathrm{kJ}\) of heat to its surroundings. This means that \(q = -90.7 \mathrm{kJ}\) (since heat is released, it has a negative sign). We are also told that no work is done by the system, so \(w = 0\).

Step 3: Calculate the change in internal energy

Now we can plug the known values into the first law of thermodynamics equation: $$\Delta E = (-90.7 \mathrm{kJ}) - (0)$$

Step 4: Simplify the equation

Simplifying the equation, we get the change in internal energy: $$\Delta E = -90.7 \mathrm{kJ}$$ So, the change in internal energy for the chemical reaction is \(-90.7 \mathrm{kJ}\).

Key Concepts

Understanding Internal Energy

Internal energy is an essential concept in thermodynamics. It's the total energy that is present within a system. This includes kinetic energy, which is due to the motion of particles, and potential energy, which is due to the positions of particles.
The change in internal energy, represented by \( \Delta E \), is crucial for understanding how energy is transferred or transformed in a system.

• When a system absorbs energy, its internal energy increases.
• Conversely, when it loses energy, its internal energy decreases.

In the context of the first law of thermodynamics, the internal energy change is given by \( \Delta E = q - w \), where \( q \) is heat, and \( w \) is work.
In our exercise, the chemical reaction releases heat, which decreases its internal energy, leading to the negative value of \( \Delta E \). Understanding this helps explain how reactions can transfer energy to their surroundings.

Heat Transfer Basics

Heat transfer is a process of energy exchange between systems or surroundings. It plays a fundamental role in thermodynamics when it comes to understanding how systems interact.
There are three modes of heat transfer: conduction, convection, and radiation.

• Conduction occurs when heat is transferred through direct contact.
• Convection happens in fluids where warmer parts move, carrying energy with them.
• Radiation is the transfer of energy through electromagnetic waves.

In this context, when we say a chemical reaction releases heat, we mean it transfers energy from the system (like a reaction inside a beaker) to the surroundings (like the air around the beaker).
In the problem exercise, we see that \( q = -90.7 \mathrm{kJ} \), indicating an exothermic process. Heat transfer results in the release of stored internal energy, which you can quantify using the first law of thermodynamics equation.

Role of Chemical Reactions

Chemical reactions involve the breaking and forming of chemical bonds, which leads to changes in energy. These energy changes often manifest as heat.
Every chemical reaction has an associated energy change, characterized by its enthalpy.

• Exothermic reactions release energy into surroundings, often as heat, resulting in negative enthalpy and internal energy changes.
• Endothermic reactions absorb energy, leading to positive changes.

In thermodynamics, this is relevant because the change in chemical energy can directly affect the internal energy \( \Delta E \) of the system.
For our exercise, where no work is done on the surroundings, all the released heat is the only change in energy that affects the system's internal energy. Recognizing the impact of a chemical reaction on internal energy helps paint a clearer picture of the energy dynamics within a system.