Name: how gas pressure, volume, and temperature change
Uploaded: 2020-09-03T13:38:26.000Z
Duration: 3 min 19 s
Channel: JoVE

K12 Standards

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NC K-12 Science Standard Course of Study

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Chemistry

Energy

PS.Chm.7.3

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Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

Le semplici leggi dei gas delineano le quattro proprietà interdipendenti del gas. Pressione, temperatura, volume e numero di mole. per derivare relazioni fra coppie di proprietà mantenendo costanti le altre.

Secondo la legge di Boyle, quando la temperatura e il numero di mole di un gas sono mantenuti costanti, la pressione e il volume mostrano una relazione inversa. Con il diminuire del volume, la pressione esercitata dal gas aumenta. Il prodotto di P e V, dunque, è uguale ad una costante.

In due diversi gruppi di condizioni, il prodotto della pressione e del volume iniziali e il prodotto della pressione e del volume finali sono uguali. Ora, se il volume e il numero di moli vengono mantenuti costanti, la pressione e la temperatura mostrano una relazione diretta. All'aumentare della temperatura, le particelle si muovono con maggiore velocità e hanno collisioni più frequenti ad alta energia, e la pressione aumenta.

Il rapporto fra P e T, dunque, è uguale ad una costante. Questa è la legge di Gay-Lussac, talvolta indicata come la legge di Amontons. In due diversi gruppi di condizioni, il rapporto tra pressione iniziale e temperatura e il rapporto tra pressione finale e temperatura sono uguali.

Quindi, si consideri un palloncino che viene gonfiato con un numero fisso di moli di gas. La pressione esterna dell'atmosfera è costante. Secondo la legge di Charles, se le moli e la pressione sono mantenute costanti, il volume di un gas e la sua temperatura, in Kelvin, mostrano una relazione diretta.

Con un aumento della temperatura, le particelle di gas si muovono più velocemente, provocando un maggior numero di collisioni e aumentando il volume del palloncino. Al contrario, abbassando la temperatura il palloncino si restringe e diminuisce di volume. Il rapporto tra V e T è uguale ad una costante.

In due diversi gruppi di condizioni, il rapporto tra volume e temperatura iniziali e il rapporto tra volume e temperatura finali sono uguali. Supponiamo ora che il palloncino venga gonfiato con più aria. Secondo la legge di Avogadro, quando la pressione e la temperatura sono mantenute costanti, il volume del gas e il numero di moli mostrano una relazione diretta.

L'aumento del numero di moli intensifica le particelle, determinando un maggior numero di collisioni. Questo costringe il palloncino ad espandere il suo volume per accogliere le particelle di gas. Il rapporto tra volume e numero di moli, quindi, è uguale ad una costante.

In due diversi gruppi di condizioni, il rapporto tra volume iniziale e numero di moli e il rapporto tra volume finale e numero di moli sono uguali. Combinando le espressioni di tre leggi dei gas e sostituendo il segno di proporzionalità incorporando la costante del gas ideale R, si ottiene la legge dei gas ideali. R ha lo stesso valore per tutti i gas ed è uguale a 8, 314 Joule per mole Kelvin o 0, 08206 litri atm per mole Kelvin.

leggi dei gas: legge di boyle, gay-lussac, di charles, di avogadro e dei gas ideali

Attraverso gli esperimenti, gli scienziati hanno stabilito le relazioni matematiche tra coppie di variabili, come pressione e temperatura, pressione e volume, volume e temperatura e volume e moli, che valgono per un gas ideale.

Pressione e Temperatura: Legge di Gay-Lussac (Legge di Amontons)

Immaginate di riempire di gas un contenitore rigido collegato ad un manometro e poi di sigillare il contenitore in modo che non possa fuoriuscire alcun gas. Se il contenitore viene raffreddato, anche il gas al suo interno diventa più freddo e si osserva una diminuzione della sua pressione. Poiché il contenitore è rigido e sigillato ermeticamente, sia il volume che il numero di moli di gas rimangono costanti. Se la sfera viene riscaldata, il gas al suo interno diventa più caldo e la pressione aumenta.

La temperatura e la pressione sono correlate in modo lineare e questa relazione si osserva per qualsiasi campione di gas confinato in un volume costante. Se la temperatura è sulla scala Kelvin, allora P e T sono direttamente proporzionali (di nuovo, quando volume e moli di gas sono mantenuti costanti); se la temperatura sulla scala Kelvin aumenta di un certo fattore, la pressione del gas aumenta dello stesso fattore.

Questa relazione pressione-temperatura per i gas è nota come legge di Gay-Lussac. La legge afferma che la pressione di una data quantità di gas è direttamente proporzionale alla sua temperatura sulla scala Kelvin quando il volume è mantenuto costante. Matematicamente, questo può essere scritto come:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-01.png" style="height: 40px;" />

dove k è una costante di proporzionalità che dipende dall'identità, dalla quantità e dal volume del gas. Per un volume di gas confinato e costante, il rapporto P/T è quindi costante (cioè P/T = k). Se il gas è inizialmente nella â&#128;&#156;Condizione 1â&#128;? (con P = P_1 e T = T_1) e passa alla â&#128;&#156;Condizione 2â&#128;? (con P = P_2 e T = T_2), allora

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-02.png" style="height: 40px;" />

Perciò,

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-03.png" style="height: 40px;" />

Si noti che per qualsiasi calcolo della legge dei gas, le temperature devono essere sulla scala Kelvin.

Volume e temperatura: legge di Charles

Se un palloncino è riempito d'aria e sigillato, contiene una quantità specifica di aria a pressione atmosferica (1 atm). Se il palloncino viene messo in un frigorifero, il gas al suo interno si raffredda e il palloncino si restringe (anche se sia la quantità di gas che la sua pressione rimangono costanti). Se il palloncino viene raffreddato molto, si restringerà notevolmente. Una volta riscaldato, il palloncino si espanderà nuovamente.

Questo è un esempio dell'effetto della temperatura sul volume di una data quantità di gas confinato a pressione costante. Il volume aumenta all'aumentare della temperatura e diminuisce al diminuire della temperatura.

La relazione tra il volume e la temperatura di una determinata quantità di gas a pressione costante è nota come legge di Charles. La legge afferma che il volume di una determinata quantità di gas è direttamente proporzionale alla sua temperatura sulla scala Kelvin quando la pressione è mantenuta costante.

Matematicamente, questo può essere scritto come:

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-04.png" style="height: 40px;" />

dove k è una costante di proporzionalità che dipende dalla quantità e dalla pressione del gas. Per un gas confinato a pressione costante, il rapporto V/T è costante.

Volume e pressione: legge di Boyle

Se una siringa ermetica è parzialmente riempita d'aria, allora la siringa conterrà una quantità specifica di aria a una temperatura costante, ad esempio 25 Â°C. Se lo stantuffo viene premuto lentamente mentre la temperatura rimane costante, il gas nella siringa viene compresso in un volume più piccolo e la sua pressione aumenta. Se si estrae lo stantuffo il volume del gas aumenta e la pressione diminuisce.

Diminuendo il volume di un gas contenuto ne aumenterà la pressione, mentre aumentandone il volume ne diminuirà la pressione. Se il volume aumenta di un certo fattore, la pressione diminuisce dello stesso fattore e viceversa. Pertanto, pressione e volume presentano una proporzionalità inversa: proporzionalità: aumentare la pressione comporta una diminuzione del volume del gas. Matematicamente si può scrivere:

<img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-05.png" style="height: 40px;" />

dove k è una costante. Un grafico di P rispetto a V mostra un'iperbole. I grafici con linee curve sono difficili da leggere con precisione a valori bassi o alti delle variabili e sono più difficili da utilizzare per adattare equazioni e parametri teorici ai dati sperimentali. Per questi motivi, gli scienziati spesso cercano di trovare un modo per â&#128;&#156;linearizzareâ&#128;? i propri dati. Graficamente, la relazione tra pressione e volume viene mostrata tracciando l'inverso della pressione rispetto al volume, o l'inverso del volume rispetto alla pressione.

La relazione tra il volume e la pressione di una data quantità di gas a temperatura costante è data dalla legge di Boyle: il volume di una data quantità di gas mantenuta a temperatura costante è inversamente proporzionale alla pressione alla quale viene misurato.

Mole di gas e volume: legge di Avogadro

Nel 1811 lo scienziato italiano Amedeo Avogadro avanzò un'ipotesi per spiegare il comportamento dei gas, affermando che volumi uguali di tutti i gas, misurati nelle stesse condizioni di temperatura e pressione, contengono lo stesso numero di molecole. Nel corso del tempo, in queste relazioni Lâ&#128;&#153;ipotesi era supportata da molte osservazioni sperimentali espresse dalla legge di Avogadro: per un gas confinato, il volume (V) e il numero di moli (n) sono direttamente proporzionali se la pressione e la temperatura rimangono entrambe costanti.

In forma di equazione, questo è scritto come:

<img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-06.png" style="height: 40px;" />

Le relazioni matematiche possono essere determinate anche per le altre coppie di variabili, come P rispetto a n e n rispetto a T.

La legge dei gas ideali

La combinazione di queste quattro leggi produce la legge dei gas ideali, una relazione tra pressione, volume, temperatura e numero di moli di un gas:

<img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-07.png" style="height: 40px;" />

Qui, R è una costante chiamata costante dei gas ideali o costante dei gas universale. Le unità utilizzate per esprimere pressione, volume e temperatura determinano la forma corretta della costante dei gas come richiesto dall'analisi dimensionale. I valori di R più comunemente riscontrati sono 0,08206 L⋅atm mol^–1⋅K^–1 e 8,314 kPa⋅L mol^–1⋅K^–1.

Si dice che i gas le cui proprietà P, V e T sono accuratamente descritte dalla legge dei gas ideali (o dalle altre leggi dei gas) mostrino un comportamento ideale o si avvicinino alle caratteristiche di un gas ideale. Un gas ideale è un costrutto ipotetico che è ragionevole solo per i gas in condizioni di pressione relativamente bassa e temperatura elevata.

L'equazione dei gas ideali contiene cinque termini, la costante dei gas R e le proprietà variabili P, V, n e T. Specificare quattro di questi termini consentirà di utilizzare la legge dei gas ideali per calcolare il quinto termine.

Se il numero di moli di un gas ideale viene mantenuto costante in due diversi insiemi di condizioni, si ottiene un'utile relazione matematica chiamata legge dei gas combinati (utilizzando unità atm, L e K):

<img alt="Eq8" src="https://www.jove.com/files/core/CDNSource/lessons/1036/1036_Equations-08.png" style="height: 40px;" />

Entrambi gli insiemi di condizioni sono uguali al prodotto di n Ã&#151; R (dove n = il numero di moli del gas e R è la costante della legge dei gas ideali).

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law">Openstax, Chemistry 2e, Section 9.2: Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law.</a>

Leggi dei gas: legge di Boyle, Gay-Lussac, di Charles, di Avogadro e dei gas ideali

Attraverso esperimenti, gli scienziati hanno stabilito le relazioni matematiche tra coppie di variabili, come pressione e temperatura, pressione e ...

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how gas pressure, volume, and temperature change

Gas pressure, volume, temperature, and amount are linked by several gas laws. Scientists found these relationships by studying how a confined gas changes when one variable is held constant and another changes. These patterns apply to an ideal gas, which is a useful model for gases under low pressure and high temperature.

Gay-Lussac’s law, also called Amontons’s law, connects pressure and temperature. If gas is trapped in a rigid container, the volume and number of moles stay constant. When the gas is cooled, its pressure drops. When it is heated, its pressure rises. On the kelvin scale, pressure and temperature are directly proportional, so the ratio P/T stays constant.

Charles’s law describes the link between volume and temperature at constant pressure. A sealed balloon in a refrigerator shrinks because the gas inside gets colder. When the balloon warms, it expands again. In this case, the amount of gas and the pressure stay constant, while volume changes with temperature. On the kelvin scale, volume and temperature are directly proportional, so V/T remains constant.

Boyle’s law explains the relationship between pressure and volume at constant temperature. An airtight syringe shows this effect clearly. Pressing the plunger compresses the gas into a smaller volume and raises the pressure. Pulling the plunger out lets the gas expand and lowers the pressure. This is an inverse relationship, so a larger volume means a lower pressure. A graph of P versus V is a hyperbola, which is hard to read at very high or low values. Scientists often linearize the data by plotting inverse pressure or inverse volume instead.

Avogadro’s law connects volume and the number of moles of gas. Amedeo Avogadro proposed in 1811 that equal volumes of gases, measured at the same temperature and pressure, contain the same number of molecules. For a confined gas, volume and moles are directly proportional when pressure and temperature stay constant. Other pairs of variables, such as pressure versus moles and moles versus temperature, can also be related.

The ideal gas law combines these relationships into one equation that links pressure, volume, temperature, and moles. It uses the gas constant R, which has different values depending on the units, such as 0.08206 L·atm mol−1·K−1 or 8.314 kPa·L mol−1·K−1. Gases that closely follow this model show ideal behavior. The ideal gas law uses five terms, so knowing any four lets you solve for the fifth. If the number of moles stays the same, the combined gas law is also useful for comparing two sets of gas conditions.

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How Gas Pressure, Volume, and Temperature Change | JoVE K12

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Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

The volume occupied by one mole of a substance is its molar volume. The ideal gas law, PV = nRT, &nbsp;suggests that the volume of a given quantity of gas ...

Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other&rsquo;s pressure. Each gas ...

Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities ...

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ...

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws ...

Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a ...

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many ...

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and ...

Ideal Gas Law

Source: Laboratory of Dr. Andreas Z&#252;ttel - Swiss Federal Laboratories for Materials Science and Technology
The ideal gas law describes the behavior ...

Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between their ...

Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation for 10 students ...

Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Determining the Mass of the Unknown LiquidExpand
	According to the ideal gas law for a given ...

Use mathematics and computational thinking to explain the relationships among pressure, temperature, volume, and quantity of gas, both qualitatively and quantitatively.

Understand the relationship among pressure, temperature, volume, and phase.

How Gas Pressure, Volume, and Temperature Change

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