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Chapter 9: Problem 81

What is an ideal gas?

Short Answer

Expert verified
An ideal gas is a theoretical gas composed of many particles in constant, random motion. These particles have perfectly elastic collisions, they don't exert intermolecular forces on each other, and they are assumed to be far apart. It follows the ideal gas law, which is P*V = n*R*T.

Step by step solution

01

Define Ideal Gas

An ideal gas is a theoretical gas composed of numerous randomly moving point particles whose only interaction is perfectly elastic collisions.
02

Discuss the properties of Ideal Gas

Ideal gases are assumed to obey several specific conditions (or assumptions). These include: 1. The gas particles are in constant and random motion. 2. The gas particles are far apart from each other. 3. The gas particles have perfectly elastic collisions (i.e., there is no loss of kinetic energy during collision). 4. The gas particles do not exert any intermolecular forces on each other.
03

Connect with the Ideal Gas Law

Ideal gases obey the ideal gas law, a simplified equation of state. The ideal gas law is usually stated as: P*V = n*R*T. Where: P represents pressure, V represents volume, n is the number of moles, R is the universal gas constant, and T is the temperature.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Properties of an Ideal Gas
The simplicity of an ideal gas lies in its hypothetical nature which doesn't completely exist in the real world. Despite this, studying ideal gases provides valuable insights into how real gases behave under various conditions. An ideal gas has certain distinct properties that simplify the clues to understanding gas behavior on a basic level.
  • The gas comprises numerous tiny particles in ceaseless, haphazard motion.
  • These particles are considered to be point-like, meaning they have no volume and are far apart relative to their size.
  • When these particles collide with one another or the walls of their container, the collisions are perfectly elastic, ensuring no kinetic energy is lost in the process.
  • There are no intermolecular forces acting between the particles of an ideal gas; they are independent players in their high-speed molecular ballet.
Acknowledging these properties helps in comprehending why ideal gases are modeled the way they are, paving the path for an easier grasp of related concepts.
Ideal Gas Law
The ideal gas law represents a cornerstone in the study of thermodynamics and is critical in linking the properties of an ideal gas with its behavior. The equation ties together four state variables: pressure (P), volume (V), temperature (T), and the amount of gas measured in moles (n), with a proportionality constant R, known as the universal gas constant.
The law is encapsulated by the equation: \( P \cdot V = n \cdot R \cdot T \). Each variable in the equation has a role to play:
  • \(P\): Pressure is the force exerted by gas particles against the walls of their container.
  • \(V\): Volume is the space the gas particles are confined in.
  • \(n\): Number of moles, representing the amount of substance.
  • \(R\): The universal gas constant, which melds the physical constants into a single value.
  • \(T\): Temperature, measured on an absolute scale (Kelvin), is directly proportional to the average kinetic energy of the gas particles.
Understanding this law allows students to predict how a gas will respond when any of the variables are altered; a crucial skill in chemistry and physics.
Kinetic Theory of Gases
The kinetic theory provides a molecular-level explanation for the macroscopic properties of gases. It provides a framework for understanding how the motion and speed of gas particles relate to the observable quantities, like temperature and pressure. According to this theory:
  • Gas particles are always in motion, and this motion is random and isotropic, meaning it is the same in all directions.
  • The temperature of a gas is directly proportional to the average kinetic energy of its particles. Thus, as a gas heats up, its particles move faster.
  • When gas particles collide, either with each other or with the walls of their container, no kinetic energy is lost. These are perfectly elastic collisions.
  • The volume that the particles occupy is negligible compared to the volume of the container, reinforcing the point particle assumption from our ideal gas properties.
With the kinetic theory, students gain a more nuanced understanding of why gas pressure increases with temperature or why expanding a gas's volume can cause it to cool鈥攑henomena that are ultimately rooted in the energy and motion of molecules.

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Most popular questions from this chapter

How does the density of warm air differ from the density of cooler air?

Plot the velocity of sound at \(25^{\circ} \mathrm{C}\) as a function of the density of the liquid medium through which it is passing. Is there a relationship between these variables? What is the value of the velocity for a liquid with a density of \(0.92 \mathrm{~g} / \mathrm{mL}\) ? $$ \begin{array}{|l|c|c|} \hline \text { Liquid } & \begin{array}{l} \text { Velocity of } \\ \text { Sound }(\mathrm{m} / \mathrm{s}) \end{array} & \text { Density }(\mathrm{g} / \mathrm{mL}) \\ \hline \text { ethyl ether } & 985 & 0.713 \\ \hline \text { acetone } & 1174 & 0.79 \\ \hline \text { ethanol } & 1207 & 0.79 \\ \hline \text { methanol } & 1103 & 0.791 \\ \hline \text { kerosene } & 1324 & 0.81 \\ \hline \text { benzene } & 1295 & 0.870 \\ \hline \text { turpentine } & 1255 & 0.88 \\ \hline \text { castor oil } & 1477 & 0.969 \\ \hline \text { distilled water } & 1497 & 0.998 \\ \hline \text { seawater } & 1531 & 1.025 \\ \hline \text { ethylene glycol } & 1658 & 1.113 \\ \hline \text { glycerol } & 1904 & 1.26 \\ \hline \end{array} $$

Why do gases expand when they are heated?

What is the relationship between the volume of a gaseous reactant and the volume of a gaseous product when temperature and pressure are constant?

Given a fixed quantity of a gas at constant temperature, calculate the new volume the gas would occupy if the pressure were changed as shown in the following table. $$ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Initial } \\ \text { Volume } \end{array} & \begin{array}{c} \text { Initial } \\ \text { Pressure } \end{array} & \begin{array}{c} \text { Final } \\ \text { Pressure } \end{array} & \begin{array}{c} \text { Final } \\ \text { Volume } \end{array} \\ \hline 6.00 \mathrm{~L} & 3.00 \mathrm{~atm} & 5.00 \mathrm{~atm} & ? \\ \hline 40.0 \mathrm{~mL} & 60.0 \text { torr } & 90.0 \text { torr } & ? \\ \hline 2.50 \mathrm{~mL} & 40.0 \text { torr } & 255 \text { torr } & ? \\ \hline \end{array} $$
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