   Chapter 13, Problem 11ALQ ### Introductory Chemistry: A Foundati...

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

#### Solutions

Chapter
Section ### Introductory Chemistry: A Foundati...

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

# Show how Boyle‘s law and Charles‘s law are special cases of the ideal gas law.

Interpretation Introduction

Interpretation:

How the Boyle’s law and Charle’s law are special cases of the ideal gas law should be explained.

Concept introduction:

An ideal gas can be categorized by three variables state: absolute pressure (P), absolute temperature (T) and volume (V), and the relationship between them are expressed in terms of ideal gas law.

Ideal gas law is a hypothetical law and is mathematically expressed as:

PV = nRT

Where,

P is the pressure of gas

V is the volume of the gas

T is the absolute temperature of the gas

R is the gas constant and

n is the number of moles of the gas molecules

Boyle’s law determines the relation between pressure and volume at a constant temperature for a fixed amount of gas. Boyle’s law is expressed as:

P1V

That is pressure is inversely proportional to the volume for a fixed amount of gas at a particular temperature.

Charle’s law determines the relation between volume and the temperature (kelvin) for a fixed amount of gas when the pressure is held constant. The law is expressed as:

VT

That is volume is directly proportional to the temperature (kelvin) for a fixed amount of gas when at a particular pressure.

Explanation

Both Boyle’s law and Charle’s law are special case of ideal gas law and can be derived from the ideal gas law as follows:

The ideal gas laws

PV = nRT

Now when T and n is constant, the ideal gas equation become

PV = Constant

P1V (Boyle’s law)

Similarly, when P and n is constant, the ideal gas equati

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