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15: Gases and Gas Laws

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• 15.1: Gas Pressure - a Result of Collisions Gases exert pressure, which is force per unit area. The pressure of a gas may be expressed in the SI unit of pascal or kilopascal, as well as in many other units including torr, atmosphere, and bar. Atmospheric pressure is measured using a barometer; other gas pressures can be measured using one of several types of manometers.
• 15.2: The Gas Laws The behavior of gases can be modeled with gas laws. Boyle's law relates a gas's pressure and volume at constant temperature and amount. Charles's law relates a gas's volume and temperature at constant pressure and amount. In gas laws, temperatures must always be expressed in kelvins.
• 15.3: Other Gas Relationships There are gas laws that relate any two physical properties of a gas. The combined gas law relates pressure, volume, and temperature of a gas.
• 15.4: Ideal Gases and The Ideal Gas Law
• 15.5.1: Vapor Pressure
• 15.6: Ideal Gases and Real Gases We imagine that the results of a large number of experiments are available for our analysis. Our characterization of these results has been that all gases obey the same equations—Boyle’s law, Charles’ law, and the ideal gas equation—and do so exactly. This is an oversimplification. In fact they are always approximations. They are approximately true for all gases under all “reasonable” conditions, but they are not exactly true for any real gas under any condition.
• 15.7: Gas Stoichiometry The ideal gas law relates the four independent physical properties of a gas at any time. The ideal gas law can be used in stoichiometry problems whose chemical reactions involve gases. Standard temperature and pressure (STP) are a useful set of benchmark conditions to compare other properties of gases. At STP, gases have a volume of 22.4 L per mole. The ideal gas law can be used to determine densities of gases.

Introduction to Temperature, Kinetic Theory, and the Gas Laws

Chapter outline.

Heat is something familiar to each of us. We feel the warmth of the summer Sun, the chill of a clear summer night, the heat of coffee after a winter stroll, and the cooling effect of our sweat. Manifestations of heat transfer —the movement of heat energy from one place or material to another—are apparent throughout the universe. Heat from beneath Earth’s surface is brought to the surface in flows of incandescent lava. The Sun warms Earth’s surface and is the source of much of the energy we find on it. Rising levels of atmospheric carbon dioxide threaten to trap more of the Sun’s energy, perhaps fundamentally altering the ecosphere. In space, supernovas explode, briefly radiating more heat than an entire galaxy does.

What is heat? How do we define it? How is it related to temperature? What are heat’s effects? How is it related to other forms of energy and to work? We will find that, in spite of the richness of the phenomena, there is a small set of underlying physical principles that unite the subjects and tie them to other fields.

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How is the Ideal Gas Law Explanatory?

Using the ideal gas law as a comparative example, this essay reviews contemporary research in philosophy of science concerning scientific explanation. It outlines the inferential, causal, unification, and erotetic conceptions of explanation and discusses an alternative project, the functional perspective. In each case, the aim is to highlight insights from these investigations that are salient for pedagogical concerns. Perhaps most importantly, this essay argues that science teachers should be mindful of the normative and prescriptive components of explanatory discourse both in the classroom and in science more generally. Giving attention to this dimension of explanation not only will do justice to the nature of explanatory activity in science but also will support the development of robust reasoning skills in science students while helping them understand an important respect in which science is more than a straightforward collection of empirical facts, and consequently, science education involves more than simply learning them.

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How is the Ideal Gas Law Explanatory?

• Published: 07 December 2011
• Volume 22 , pages 1563–1580, ( 2013 )

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• Andrea I. Woody 1  

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Using the ideal gas law as a comparative example, this essay reviews contemporary research in philosophy of science concerning scientific explanation. It outlines the inferential, causal, unification, and erotetic conceptions of explanation and discusses an alternative project, the functional perspective. In each case, the aim is to highlight insights from these investigations that are salient for pedagogical concerns. Perhaps most importantly, this essay argues that science teachers should be mindful of the normative and prescriptive components of explanatory discourse both in the classroom and in science more generally. Giving attention to this dimension of explanation not only will do justice to the nature of explanatory activity in science but also will support the development of robust reasoning skills in science students while helping them understand an important respect in which science is more than a straightforward collection of empirical facts, and consequently, science education involves more than simply learning them.

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Social Learning Theory—Albert Bandura

Methodological Naturalism, Analyzed

Miles K. Donahue

Pragmatism—John Dewey

Some of these conceptions have several distinct variants.

The terminology of nomological subsumption simply refers to particular states of affairs (that is, descriptions of events or objects with specific properties) being subsumed under general laws in the sense that these states of affairs are seen to be instances of some lawlike generalizations.

By ‘phenomenological’ I mean a description of phenomena solely in terms of the detectable and measurable properties of macroscopic physical objects. Phenomenological descriptions, or models, of gases are composed of variables representing measurable quantities, including temperature, pressure, and volume, drawn from the framework of phenomenological thermodynamics (and without reference to the underlying micro-level constitution of gases).

The interested reader might want to consider what Woodward would say about the air mattress example offered by Salmon.

Friedman’s original article refers to Graham’s law of diffusion. As an anonymous referee helpfully pointed out, the kinetic theory of gases allows one to derive the law of effusion, but not the more complex law of diffusion.

More precisely, the unifying power of a theoretical structure varies directly with the size of the conclusion set regarding empirical phenomena generated from the associated argument patterns, inversely with the number of argument patterns, and directly with the stringency of the patterns (Kitcher 1989 : 435).

‘Erotetics’ or ‘erotetic logic’ is the area of study concerned with the logic and pragmatics of questions.

But what about the person who generates an explanatory question and answers it herself? This is certainly possible in principle, but as Salmon ( 1998 ) and Van Fraassen ( 1980 ) both discuss, explanatory demands would not arise for an omniscient being. Explanations arise from ignorance, or at the very least, uncertainty. Consequently, for an individual to pose a genuine explanation-seeking question, even to herself, in some respect she must not already know the answer and she will likely turn to some external source of information, one she considers authoritative, to find the answer. In doing so, she is engaged in an activity that is arguably social.

A rationale for the ordering can be distinct, of course, from the reasons why the ordering was originally established. That gases are an early topic in introductory textbooks is partially a legacy of the historical development of chemistry, in which gas experiments played a central role as the discipline was first emerging during the eighteenth century. Still, there is common ground between the historical explanation of why we start with gases and the current rationale for doing so. In each, the investigation of gas behavior has cultivated the development of atomic hypotheses; this fact is as clearly evidenced in the writings of Dalton ( 1808 ) as in any contemporary text.

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Acknowledgments

The author wishes to thank Jim Greisemer, Roberta Millstein, the audience for a Philosophy Department Colloquium at University of California at Davis in February 2011, two anonymous referees for this journal, and especially members of a graduate seminar at the University of Washington in winter 2011 for constructive feedback and insights regarding aspects of this project.

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Woody, A.I. How is the Ideal Gas Law Explanatory?. Sci & Educ 22 , 1563–1580 (2013). https://doi.org/10.1007/s11191-011-9424-6

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DOI : https://doi.org/10.1007/s11191-011-9424-6

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The Gas Laws

Introduction: what are the gas laws.

The gas laws are a group of laws that govern the behaviour of gases by providing relationships between the following:

• The volume occupied by the gas.
• The pressure exerted by a gas on the walls of its container.
• The absolute temperature of the gas.
• The amount of gaseous substance (or) the number of moles of gas.

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The gas laws were developed towards the end of the 18 th century by numerous scientists (after whom the individual laws are named). The five gas laws are listed below:

• Boyle’s Law: It provides a relationship between the pressure and the volume of a gas.
• Charles’s Law: It provides a relationship between the volume occupied by a gas and the absolute temperature.
• Gay-Lussac’s Law: It provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
• Avogadro’s Law: It provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
• The Combined Gas Law (or the Ideal Gas Law): It can be obtained by combining the four laws listed above.

Under standard conditions, all gasses exhibit similar behaviour. The variations in their behaviours arise when the physical parameters associated with the gas, such as temperature, pressure, and volume, are altered. The gas laws basically describe the behaviour of gases and have been named after the scientists who discovered them.

We will look at all the gas laws below and also understand a few underlying topics.

Boyle’s Law

• Charle’s Law

Gay-Lussac Law

Avogadro’s law, combined gas law.

• Gas Law Table
• Gas Law Problems
• Applications of Gas Law

Boyle’s law gives the relationship between the pressure of a gas and the volume of the gas at a constant temperature. Basically, the volume of a gas is inversely proportional to the pressure of a gas at a constant temperature.

Boyle’s law equation is written as:

Where V is the volume of the gas, P is the pressure of the gas, and K 1 is the constant.  Boyle’s Law can be used to determine the current pressure or volume of gas and can also be represented as,

P 1 V 1 = P 2 V 2

Problems Related to Boyle’s Law

An 18.10mL sample of gas is at 3.500 atm. What will be the volume if the pressure becomes 2.500 atm, with a fixed amount of gas and temperature?

By solving with the help of Boyle’s law equation

P 1 V 1 = P 2 V 2

V 2 = P 1 V 1 / P 2

V 2 = (18.10 * 3.500 atm)/2.500 atm

V 2 = 25.34 mL

Also Read: Behaviour of Gases

Charle’s Law

Charle’s law states that at constant pressure, the volume of a gas is directly proportional to the temperature (in Kelvin) in a closed system. Basically, this law describes the relationship between the temperature and volume of the gas.

Mathematically, Charle’s law can be expressed as,

Where, V = volume of gas, T = temperature of the gas in Kelvin. Another form of this equation can be written as,

V 1 / T 1 = V 2 / T 2

Problems Related to Charle’s Law

A sample of carbon dioxide in a pump has a volume of 21.5 mL, and it is at 50.0 °C. When the amount of gas and pressure remain constant, find the new volume of carbon dioxide in the pump if the temperature is increased to 75.0 °C.

V 2 = V 1 T 2 /T 1

V 2  = 7,485.225/ 323.15

V 2  = 23.16 mL

Gay-Lussac law gives the relationship between temperature and pressure at constant volume. The law states that at a constant volume, the pressure of the gas is directly proportional to the temperature of a given gas.

If  you  heat  up  a  gas,  the  molecules  will  be  given  more  energy;   they  move  faster.  If  you  cool  down  the  molecules,  they  slow  down, and  the  pressure  decreases. The change in temperature and pressure can be calculated using the Gay-Lussac law, and it is mathematically represented as,

P / T = k 1

P 1  / T 1 = P 2 / T 2

Where, P is the pressure of the gas, and T is the temperature of the gas in Kelvin.

Problems Related to Gay-Lussac Law

Determine the pressure change when a constant volume of gas at 2.00 atm is heated from 30.0 °C to 40.0 °C.

P 1 = 2.00 atm P 2 =? T 1 = (30 + 273) = 303 K T 2 = (40 + 273) = 313 K

According to the Gay-Lussac law, P ∝ T P/T = constant P 1 /T 1 = P 2 /T 2 P 2 =( P 1 T 2 ) / T 1 = (2 x 313) / 303 =2.06 atm

Avogadro’s law states that if the gas is an ideal gas, the same number of molecules exists in the system. The law also states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. This statement can be mathematically expressed as,

V / n = constant

V 1  / n 1 = V 2 / n 2

Where V is the volume of an ideal gas and n represents the number of gas molecules.

Problems Related to Avogadro’s Law

At constant temperature and pressure, 6.00 L of a gas is known to contain 0.975 mol. If the amount of gas is increased to 1.90 mol, what new volume will result?

V 1 = 6.00 L V 2 = ? n 1 = 0.975 n 2 = 1.90 mol

According to Avogadro’s law V ∝ n V/n = constant V 1 / n 1 = V 2 / n 2 V 2 = V 1 n 2 /n 1 V 2 = (6 x 1.90)/ 0.975 = 11.69 L

The combined gas law, also known as a general gas equation, is obtained by combining three gas laws which include Charle’s law, Boyle’s Law and Gay-Lussac law. The law shows the relationship between temperature, volume and pressure for a fixed quantity of gas.

The general equation of combined gas law is given as,

If we want to compare the same gas in different cases, the law can be represented as,

P 1 V 1  / T 1 = P 2 V 2 / T 2 

Also Read: Kinetic Theory of Gas 

Ideal Gas Law

Much like the combined gas law, the ideal gas law is also an amalgamation of four different gas laws. Here,  Avogadro’s law is added, and the combined gas law is converted into the ideal gas law. This law relates four different variables, which are pressure, volume, number of moles or molecules and temperature. Basically, the ideal gas law gives the relationship between these four different variables.

Recommended Videos

Boyle’s law – video lesson.

Ideal Gas Equation

Mathematically Ideal gas law is expressed as,

V = volume of gas

T = temperature of the gas

P = pressure of the gas

R = universal gas constant

And n denotes the number of moles

We can also use the equivalent equation given below.

Where, k = Boltzmann constant and N = number of gas molecules.

Ideal gases are also known as perfect gas. It establishes a relationship among the four different gas variables such as pressure (P), Volume (V), Temperature (T) and amount of gas (n).

Ideal Gas Properties and Characteristics

• The motion of ideal gas in a straight line is constant and random.
• The gas occupies a very small space because the particle in the gas is minimal.
• There is no force present between the particle of the gas. Particles only collide elastically with the walls of the container and with each other.
• The average kinetic energy of the gas particle is directly proportional to the absolute temperature.
• The gases are made up of many of the same particles (atoms or molecules), which are perfectly hard spheres and also very small.
• The actual volume of the gas molecule is considered negligible as compared to the space between them, and because of this reason, they are considered as the point masses.

Gas Law Formula Table

The following table consists of all the formulas of Gas Law:

Problems Related to Gas Law

(1) A sealed jar whose volume is exactly 1 L, which contains 1 mole of air at a temperature of 20 degrees Celcius, assuming that the air behaves as an ideal gas. So, what is the pressure inside the jar in Pa?

By solving with the help of the ideal gas equation,

(1) By rearranging the equation, we can get,

(2) Write down all the values which are known in the SI unit.

R= 8.314J/K/mol

T= 20degree celcius=(20+273.15)K=293.15K

V=1L=0.001m 3

(3) Put all the values in the equation

P=(1*8.314*293.15)/0.001

P= 2,437,249

P=2.437*10^6 Pa

The pressure is almost 24atm.

Application of Gas-law

During summer, when the temperature is high, and pressure is also high, a tire is at risk of bursting because it is inflated with air. Or when you start climbing a mountain, you feel problems related to inhaling. Why does it happen?

When the physical condition changes with changes in the environment, the behaviour of gases particle also deviates from their normal behaviour. These changes in gas behaviour can be studied by studying various laws known as gas laws.

Gas laws have been around for quite some time now, and they significantly assist scientists in finding amounts, pressure, volume, and temperature related to matters of gas.

Besides, the gas law, along with modern forms, are used in many practical applications that concern gas. For example, respiratory gas measurements of tidal volume and vital capacity etc., are done at ambient temperature while these exchanges actually take place in the body at 37 degrees Celsius. The law is used often in thermodynamics as well as in fluid dynamics. Also, it can be used in weather forecast systems.

Frequently Asked Questions on Gas Laws

What is an ideal gas.

Gases are puzzling. They are packed with a large number of very energetic gas molecules that can collide and interact. Because it’s difficult to precisely characterise a real gas, the concept of an ideal gas was developed as an approximation to help us model and understand the behaviour of real gases.

What are the rules followed by ideal gas?

Ideal gas molecules are neither attracted nor repellent to one another. An elastic collision is the only interaction between ideal gas molecules when they collide with each other or with the container’s walls.

The volume of ideal gas molecules is zero. The ideal gas molecules are considered as point particles with no volume in and of themselves.

What is the expression for ideal gas law?

PV = nRT P is the pressure of the ideal gas. V is the volume of the ideal gas. T is the temperature of the ideal gas. R is the gas constant. n is the number of moles.

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