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Chapter 11: Problem 73

According to the ideal gas model, why does the chemical identity of a gas not matter when it comes to producing pressure?

Short Answer

Expert verified
In the ideal gas model, the chemical identity of a gas does not matter when it comes to producing pressure because the pressure of an ideal gas is determined solely by the number of particles (n), the volume (V), and the temperature (T), as shown by the ideal gas law \(PV = nRT\). Gas particles interact only through elastic collisions, and thus, their chemical properties do not contribute to pressure production. As long as the ideal gas assumptions hold for a gas, its chemical identity is not relevant to pressure generation.

Step by step solution

01

Understanding the Ideal Gas Model: #

The ideal gas model assumes that a gas is made up of a large number of particles in constant, random motion. These particles interact only through elastic collisions, meaning that the total kinetic energy of the system remains constant. The ideal gas model also assumes that the particles have no volume and do not have any attractive or repulsive forces between them. These assumptions allow us to simplify the behavior of gases and derive the ideal gas law, which relates pressure (P), temperature (T), and volume (V) to the number of particles (n) in the gas: \( PV = nRT \), where R is the ideal gas constant.
02

Factors Affecting Gas Pressure in the Ideal Gas Model #

According to the ideal gas model, the pressure of an ideal gas depends on the following factors: 1. Number of particles (n): The more particles there are, the more collisions there will be with the container walls, leading to higher pressure. 2. Volume (V): A smaller volume results in a higher concentration of gas particles, which increases the frequency of collisions with the container walls, leading to higher pressure. 3. Temperature (T): As the temperature increases, the average kinetic energy of the gas particles also increases. This results in stronger and more frequent collisions with the container walls, which leads to higher pressure.
03

Why Chemical Identity Does Not Matter for Pressure Production #

The chemical identity of a gas does not affect its pressure production in the ideal gas model. This is because the pressure is determined solely by the number of particles, the volume, and the temperature, as shown by the ideal gas law \(PV = nRT\). The ideal gas model assumes that gas particles interact only through elastic collisions, which means that the chemical properties of the gas particles, such as their size, mass, and chemical composition, do not play a role in pressure production. As long as the ideal gas assumptions are valid for a given gas, its chemical identity will not matter when considering its pressure generation.

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Most popular questions from this chapter

Given some mass \(m\) of a known pure substance, what is the quickest way to determine the number of moles \(n\) you have of the substance?

A 7.24-g sample of gas is contained in a 4.00-L flask. Its pressure is \(765.0 \mathrm{~mm} \mathrm{Hg}\), and its temperature is \(25.0^{\circ} \mathrm{C}\). What is the molar mass of this gas?

A balloon of methane gas, \(\mathrm{CH}_{4}\), has a temperature of \(-2.0^{\circ} \mathrm{C}\) and contains \(2.35 \mathrm{~g}\) of the gas. What is the temperature of the gas in Kelvin? How many moles of the gas does the balloon contain?

A balloon filled with He gas and another balloon filled with \(\mathrm{H}_{2}\) gas have the same values for \(P\) and \(\bar{T}\). (a) The density of the He gas is greater than the density of the \(\mathrm{H}_{2}\) gas. How can you prove this using the ideal gas law? (b) How much more dense than the \(\mathrm{H}_{2}\) gas is the He gas?

Perform the following conversions: (a) \(30.2\) in. \(\mathrm{Hg}\) to millimeters of mercury (b) \(890.0 \mathrm{~mm} \mathrm{Hg}\) to atmospheres (c) \(300.0 \mathrm{lb} / \mathrm{in} .^{2}\) to atmospheres
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