Question

The air bags that provide protection in autos in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of \(q\) and \(w\) in this process?

Short answer

In the airbag inflation process due to the rapid chemical decomposition of sodium azide, we expect the sign of \(q\) to be negative \(q < 0\), as the exothermic reaction releases heat and loses thermal energy. We also expect the sign of \(w\) to be positive \(w > 0\), as the expanding nitrogen gas does work on the surroundings.

Step-by-step solution

Analyze the chemical reaction for airbags inflation

To determine the signs of q and w, we first need to understand the chemical reaction that causes airbags to inflate. The reaction used for inflating airbags is the decomposition of sodium azide (NaN₃). When activated, sodium azide breaks down rapidly into sodium metal and nitrogen gas. This reaction is highly exothermic, meaning it releases a large amount of heat. The reaction can be written as: \[2 NaN_3(s) \rightarrow 2 Na(s) + 3 N_2(g) + \text{heat}\]

Determine the sign of q

Since the reaction is exothermic, it releases heat. This means that thermal energy is transferred from the system (the chemical reactants) to the surroundings. Thus, the sign of q is negative. q < 0

Determine the sign of w

Due to the rapid production of nitrogen gas, the airbags expand quickly, exerting pressure on their surroundings (the car and its occupants). This means that the system is doing work on the surroundings. Therefore, the sign of w is positive. w > 0

Summarize the results

In the process of airbags expanding due to a rapid chemical reaction, we expect the signs of q and w to be as follows: - q < 0: The system loses thermal energy as it releases heat to the surroundings. - w > 0: The system does work on its surroundings, as the expanding gas exerts pressure on the surroundings. These results highlight that the chemical reactants in the process lose thermal energy while doing work on the surroundings (inflating the airbags) to provide protection during an accident.

Key concepts

Exothermic Reaction

When we consider the term 'exothermic', we are talking about a process that releases energy in the form of heat. The chemical reaction that inflates airbags is a perfect example of this. Imagine the rapid decomposition of sodium azide within the airbag's mechanism.

This safety feature relies on a precise chemical formula: \[2 NaN_3(s) \rightarrow 2 Na(s) + 3 N_2(g) + \text{heat}\].

Whenever a sodium azide molecule breaks apart, it releases heat energy into the surrounding area. This heat is not just a byproduct; it is a fundamental aspect of how the airbag works, propelling the inflation process and ultimately cushioning the car's occupants more effectively. This is what makes it an exothermic reaction – it is an essential component that contributes to the swift reaction that airbag deployment requires.

Enthalpy Change

The concept of enthalpy change is essentially a way of expressing the heat change at constant pressure within a chemical system. In the case of the airbag inflation, we see this in action as the enthalpy changes when sodium azide decomposes.

Enthalpy, symbolized as H, changes as exothermic reactions release heat, leading to a drop in the system's enthalpy. Mathematically, this is shown by a negative sign for the change in enthalpy (\( \Delta H < 0 \)). This means in the context of airbags, the energetic output is a significant factor, and it's measured as part of the chemical thermodynamics of the reaction.

Chemical Thermodynamics

Delving further into chemical thermodynamics, we understand that it pertains to the transfer of heat and work in chemical processes. The activation of an airbag showcases the interplay between various forms of energy during a chemical reaction.

As highlighted by the signs of \(q\) (heat) and \(w\) (work), chemical thermodynamics involves understanding how energy is moved or transformed. In an airbag, the initial chemical potential energy stored in the sodium azide is suddenly released as kinetic energy of nitrogen gas molecules and thermal energy (heat), showcasing an exothermic thermodynamic process.

Gas Expansion

Gas expansion in the context of airbags refers to the rapid increase in volume as a result of chemical reactions producing gas. Specifically, the nitrogen gas produced during the decomposition of sodium azide fills the airbag, expanding it almost instantaneously.

The production of gas is a physical manifestation of work (\(w\)) being done, where the force of the expanding gases pushes against the confines of the airbag and also on the surrounding environment. The rapidness of this expansion is crucial for protection during a collision, and it underscores the vital relationship between chemical reactions and physical outcomes in practical applications like vehicle safety.