Chapter 13.1, Problem 5RQ

(a)

Interpretation Introduction

Interpretation:

The quantity which remains constant in Boyle’s law, Charles’s law and Avogadro’s law of the gas is to be written.

Concept Introduction:

Boyle’s law, Charles’s law and Avogadro’s law describe the relationship between two variables keeping one variable constant.

Answer to Problem 5RQ

In Boyle’s law, temperature remains constant.

In Charles’s law, Pressure remains constant.

In Avogadro’s law, Pressure and temperature remains constant.

Explanation of Solution

Boyle’s law: The pressure of a gas is inversely proportional to the volume of the gas at constant temperature.

The relationship between pressure and volume of a gas is expressed as-

  $\begin{array}{l}\mathrm{P}\propto \frac{1}{\mathrm{V}}\\ \mathrm{or},\mathrm{P}\mathrm{V}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T is constant.

Charles’s law: The volume of a given amount of gas is proportional to its temperature (in K) of the gas at constant pressure.

The relationship between volume of a gas and temperature is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{T}\\ \mathrm{or},\frac{\mathrm{V}}{\mathrm{T}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When P is constant.

Avogadro’s law: The volume of a given amount of gas is directly related to the number of moles at constant temperature and pressure.

The relationship between the volume of a gas and the number of moles present in the gas is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{n}\\ \mathrm{o}\mathrm{r},\frac{\mathrm{V}}{\mathrm{n}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T and P are constant.

So,

	Boyle’s law	Charles’s law	Avogadro’s law
Constants	Temperature	Pressure	Pressure and temperature

(b)

Interpretation Introduction

Interpretation:

The quantities which are variables in Boyle’s law, Charles’s law and Avogadro’s law of the gas is to be written.

Concept Introduction:

Boyle’s law, Charles’s law and Avogadro’s law describe the relationship between two variables keeping one variable constant.

Answer to Problem 5RQ

In Boyle’s law, Pressure and volume are variables.

In Charles’s law, Volume and temperature are variables.

In Avogadro’s law, Volume and number of moles are variables.

	Boyle’s law	Charles’s law	Avogadro’s law
Variables	Pressure and volume	Volume and temperature	Volume and number of moles

Explanation of Solution

Boyle’s law: The pressure of a gas is inversely proportional to the volume of the gas at constant temperature.

The relationship between pressure and volume of a gas is expressed as-

  $\begin{array}{l}\mathrm{P}\propto \frac{1}{\mathrm{V}}\\ \mathrm{or},\mathrm{P}\mathrm{V}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T is constant.

Charles’s law: The volume of a given amount of gas is proportional to its temperature (in K) of the gas at constant pressure.

The relationship between volume of a gas and temperature is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{T}\\ \mathrm{or},\frac{\mathrm{V}}{\mathrm{T}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When P is constant.

Avogadro’s law: The volume of a given amount of gas is directly related to the number of moles at constant temperature and pressure.

The relationship between the volume of a gas and the number of moles present in the gas is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{n}\\ \mathrm{o}\mathrm{r},\frac{\mathrm{V}}{\mathrm{n}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T and P are constant.

	Boyle’s law	Charles’s law	Avogadro’s law
Variables	Pressure and volume	Volume and temperature	Volume and number of moles

(c)

Interpretation Introduction

Interpretation:

The graph of Boyle’s law, Charles’s law and Avogadro’s law of the gas are to be drawn.

Concept Introduction:

Boyle’s law, Charles’s law and Avogadro’s law describe the relationship between two variables keeping one variable constant.

Answer to Problem 5RQ

  

Explanation of Solution

Boyle’s law: The pressure of a gas is inversely proportional to the volume of the gas at constant temperature.

The relationship between pressure and volume of a gas is expressed as-

  $\begin{array}{l}\mathrm{P}\propto \frac{1}{\mathrm{V}}\\ \mathrm{or},\mathrm{P}\mathrm{V}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T is constant.

  

Charles’s law: The volume of a given amount of gas is proportional to its temperature (in K) of the gas at constant pressure.

The relationship between volume of a gas and temperature is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{T}\\ \mathrm{or},\frac{\mathrm{V}}{\mathrm{T}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When P is constant.

  

Avogadro’s law: The volume of a given amount of gas is directly related to the number of moles at constant temperature and pressure.

The relationship between the volume of a gas and the number of moles present in the gas is expressed as-

  $\begin{array}{l}\mathrm{V}\propto \mathrm{n}\\ \mathrm{o}\mathrm{r},\frac{\mathrm{V}}{\mathrm{n}}\mathrm{}=\mathrm{}\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\end{array}$ When T and P are constant.

  

(d)

Interpretation Introduction

Interpretation:

Boyle’s law, Charles’s law and Avogadro’s law of the gas have to be compared.

Concept Introduction:

Boyle’s law, Charles’s law and Avogadro’s law describe the relationship between two variables keeping one variable constant.

Answer to Problem 5RQ

Volume of a gas is directly proportional to its temperature and the amount of gas.

Charles’s law showed that the volume of a gas is directly proportional to its temperature (in K) at constant pressure.

Avogadro’s law showed that the volume of a gas is directly proportional to the number of moles of gas present at constant pressure and temperature.

Explanation of Solution

Boyle’s law: $\mathrm{V}\propto \frac{1}{\mathrm{P}}$ When T is constant

Charles’s law: $\mathrm{V}\propto \mathrm{T}$ When P is constant

Avogadro’s law: $\mathrm{V}\propto \mathrm{n}$ When P and T are constant

So, volume of a gas is directly proportional to its temperature and the amount of gas. Charles’s law showed that the volume of a gas is directly proportional to its temperature (in K) at constant pressure and Avogadro’s law showed that the volume of a given amount of gas is directly related to the number of moles at constant temperature and pressure.