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Chapter 12: Problem 81

How is the phenomenon of temperature explained on the basis of the kinetic molecular theory? What microscopic property of gas molecules is reflected in the temperature measured?

Short Answer

Expert verified
Based on the Kinetic Molecular Theory, temperature is a measure of the average kinetic energy of gas particles. This microscopic property of gas molecules is reflected in the temperature measured. As temperature increases, the average kinetic energy of the gas molecules increases, resulting in particles moving faster on average. Conversely, as temperature decreases, particles move slower on average due to a lower average kinetic energy.

Step by step solution

01

Introduce Kinetic Molecular Theory

The Kinetic Molecular Theory (KMT) is a model used to describe the behavior of matter, particularly gases, on a microscopic level. The KMT attempts to provide a qualitative and quantitative understanding of the gas properties by making several postulates about the microscopic behavior of the gas molecules.
02

Discuss the postulates of KMT

The main postulates of the Kinetic Molecular Theory are: 1. Gases consist of a large number of tiny particles (atoms or molecules) that are in constant random motion. 2. Gas particles are so small compared to the distances between them that the particles have a negligible volume. 3. The gas particles are in constant collision with one another, as well as the walls of their container. Collisions are perfectly elastic (no loss of energy). 4. Gas particles don't interact with each other through attractive or repulsive forces. The only forces acting are the ones during collisions. 5. The average kinetic energy of gas particles is directly proportional to the absolute temperature of the gas.
03

Explain the concept of temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. In other words, it is a macroscopic property that indicates how fast or slow the particles of a substance are moving on average. For gases, the temperature is directly related to the average kinetic energy of the gas molecules, as stated in the fifth postulate of KMT.
04

Connect the microscopic property to temperature

Based on the Kinetic Molecular Theory, the microscopic property of gas molecules that is reflected in the temperature measured is their average kinetic energy. Higher temperature corresponds to a higher average kinetic energy of the gas molecules, implying that the gas particles move faster on average. Similarly, when the temperature is lower, the average kinetic energy of the gas molecules is lower, and the particles move slower on average.
05

Relating temperature and molecular speed

The temperature of a gas is directly related to the average speed of its particles. When the temperature of a gas is increased, the gas molecules gain kinetic energy, and their speed increases. Conversely, when the temperature decreases, the gas molecules lose kinetic energy, and their speed decreases.

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Most popular questions from this chapter

If a gaseous mixture is made of \(2.41 \mathrm{g}\) of \(\mathrm{He}\) and 2.79 g of Ne in an evacuated 1.04-L container at \(25^{\circ} \mathrm{C},\) what will be the partial pressure of each gas and the total pressure in the container?

At what temperature does \(100 .\) mL of \(\mathrm{N}_{2}\) at \(300 . \mathrm{K}\) and 1.13 atm occupy a volume of \(500 .\) mL at a pressure of 1.89 atm?

A tank contains a mixture of 3.0 mol of \(\mathrm{N}_{2}, 2.0 \mathrm{mol}\) of \(\mathrm{O}_{2},\) and \(1.0 \mathrm{mol}\) of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and a total pressure of 10.0 atm. Calculate the partial pressure (in torr) of each gas in the mixture.

When sodium bicarbonate, \(\mathrm{NaHCO}_{3}(s),\) is heated, sodium carbonate is produced, with the evolution of water vapor and carbon dioxide gas. $$ 2 \mathrm{NaHCO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g) $$ What total volume of gas, measured at \(29^{\circ} \mathrm{C}\) and 769 torr, is produced when \(1.00 \mathrm{g}\) of \(\mathrm{NaHCO}_{3}(s)\) is completely converted to \(\mathrm{Na}_{2} \mathrm{CO}_{3}(s) ?\)

What conditions are considered "standard temperature and pressure" (STP) for gases? Suggest a reason why these particular conditions might have been chosen for STP.
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