Question

Consider what happens when a sample of the explosive TNT (Section 8.8: "Chemistry Put to Work: Explosives and Alfred Nobel") is detonated under atmospheric pressure. (a) Is the detonation a spontaneous process? (b) What is the sign of \(q\) for this process? (c) Can you determine whether \(w\) is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of \(\Delta E\) for the process? Explain.

Short answer

(a) Yes, the detonation of TNT is a spontaneous process. (b) The sign of \(q\) is negative, indicating heat transfer from the system to the surroundings. (c) The work (\(w\)) is negative, as the system does work on the surroundings. (d) The sign of \(\Delta E\) is negative, as energy is transferred out of the system in the form of heat and work done on the surroundings.

Step-by-step solution

Understand the process of detonation

To begin, detonation is a chemical reaction that involves the rapid decomposition of a material by the action of heat or a shock wave. It is a highly exothermic process, which means a lot of energy is being released. When a sample of TNT explodes under atmospheric pressure, it produces gaseous products along with energy.

Determine the spontaneity of the process

Spontanity of a process depends on the change in Gibbs Free Energy (∆G). A process happens spontaneously if ∆G is negative. Since the detonation of TNT is a rapid and exothermic process that results in a decrease in Gibbs Free Energy, it is indeed a spontaneous process. Therefore, the answer to (a) is "Yes, the detonation of TNT is a spontaneous process."

Find the sign of heat transfer (\(q\))

During the detonation of TNT, a large amount of heat is generated due to the exothermic chemical reaction that occurs. The system releases energy and heats the surroundings, meaning that the heat transfer occurs from the system to the surroundings. Hence, the sign of \(q\) for the process is negative, as energy is being lost by the system. The answer to (b) is "The sign of \(q\) is negative."

Identify the sign of work (\(w\))

Since the detonation of TNT results in an explosion, it primarily does work on its surroundings, causing expansion and pushing the surrounding molecules away. This indicates that the system is doing work on the surroundings. In this context, the work done by the system (\(w\)) is negative. The answer to (c) is "The work (\(w\)) is negative as the system does work on the surroundings."

Determine the sign of the change in internal energy (\(\Delta E\))

According to the first law of thermodynamics, the change in internal energy is equal to the sum of heat transferred and work done: \(\Delta E = q + w\). Since both the heat transfer (\(q\)) and the work done (\(w\)) are negative, as discussed in Steps 3 and 4, the sign of \(\Delta E\) will also be negative. Therefore, the internal energy of the system decreases as energy is transferred out in the form of heat and work done on the surroundings. The answer to (d) is "The sign of \(\Delta E\) is negative, as energy is transferred out of the system."

Key concepts

Spontaneous Process

A spontaneous process is a fascinating phenomenon in the world of chemistry and physics. It refers to a change that occurs without the need for continuous energy input from an external source.

In the case of TNT detonation, this process is spontaneous. Here's why: the transformation of TNT into gaseous products and energy does not require an external push once initiated. Like a boulder rolling downhill, once TNT is ignited, it continues its explosive reaction without further prompting.

It's important to note that 'spontaneous' doesn't necessarily mean 'instantaneous'. Spontaneous processes can be rapid, like a TNT explosion, or slow, like the rusting of iron.

Thermodynamics

Thermodynamics is the science that studies energy transformations in physical and chemical processes. It is grounded in a set of laws that describe how energy moves and changes form.

One key aspect of thermodynamics is that it helps us predict whether a process will occur spontaneously. For TNT detonation, thermodynamics explains how the energy stored in TNT's chemical bonds is converted into the explosive energy we witness. This conversion adheres to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed.

Understanding thermodynamics is critical in explaining not just why explosions occur, but also how we can harness such reactions for work, such as in engines or even rocket propulsion.

Gibbs Free Energy

Gibbs Free Energy, often denoted as \( G \), is a thermodynamic quantity that measures the amount of usable energy in a system that can perform work at a constant temperature and pressure. This value is especially crucial when predicting the spontaneity of a process.

If the change in Gibbs Free Energy \( \Delta G \) is negative, we are dealing with a spontaneous process. For an explosive reaction like TNT detonation, \( \Delta G \) is indeed negative, indicating that the reaction will proceed spontaneously under the right conditions.

Moreover, the relationship \( \Delta G = \Delta H - T\Delta S \)—where \( H \) is enthalpy, \( T \) is temperature, and \( S \) is entropy—reveals how energy and disorder play roles in driving the process forward.

Exothermic Reaction

An exothermic reaction is a chemical process in which energy is released to the surroundings, typically in the form of heat. This release of energy is what makes a reaction exothermic.

The detonation of TNT exemplifies an exothermic reaction—energy stored in chemical bonds is liberated swiftly and with great intensity, resulting in an explosion. This process generates heat \( (q) \), reflected by the negative sign in the thermodynamic calculations.

Real-World Applications

In addition to explosions, exothermic reactions are fundamental to various applications, ranging from everyday conveniences like hand warmers to critical industrial processes like steel manufacturing. Understanding these reactions not only aids in explaining phenomena like explosions but also in designing systems and materials that safely utilize the energy released.