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Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425

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BuyFindarrow_forward

Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425
Textbook Problem
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hat does Charles’s law tell us about how the volume of a gas sample varies as the temperature of the sample is changed? How does this volume-temperature relationship differ from the volume-pressure relationship of Boyle’s law? Give two mathematical expressions that describe Charles’s law. For Charles’s law to hold true, why must the pressure and amount of gas remain the same? Sketch the general shape of a graph of volume versus temperature (at constant pressure) for an ideal gas.

Interpretation Introduction

Interpretation:

The validation of the fact that the volume of a gas varies as the temperature of the sample changed is to be stated on the basis of Charles’s law. The difference between volume-temperature relationship and the volume-pressure relationship of Boyle’s law is to be stated. The two mathematical expressions of Charles’s law are to be shown. The reason as to why the pressure and amount of gas remain the same in Charles’s law is to be stated. The sketch of the general shape of a graph of volume versus temperature (at constant pressure) for an ideal gas is to be drawn.

Concept Introduction:

Avogadro was the scientist who described the relationship between the number of moles of gas and volume of a gas. An ideal gas equation is derived from the combination of Charles’s law, Boyle’s law and Avogadro law.

The general expression for an ideal gas is shown below.

PV=nRT

This expression exhibits that an ideal gas law relies on the temperature, pressure, volume and moles of gas.

Explanation

According to Charles’s Law, the absolute zero temperature is 273°C or 0K. It is the lowest temperature. At this temperature, all molecular motions cease, and gases get liquefied. Liquid occupies less volume as compared to gas. It indicates that with the decrease in temperature, the volume of a gas decreases. Therefore, Charles law describes that volume and temperature are directly related.

The volume-temperature relationship given by Charles’s law is shown below.

VT

Where,

  • V is the volume of gas.
  • T is the temperature of gas.

The volume-pressure relationship given by Boyle’s law is shown below.

P1V

Where,

  • P is the pressure.
  • V is the volume.

Therefore, volume and temperature are directly related to each other, whereas volume and pressure are inversely proportional to each other.

The first mathematical expression for Charles’s law is shown below.

VT

The second mathematical expression for Charles’s law is shown below

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