Name: gas pressure in mixtures: partial pressures
Uploaded: 2020-09-03T13:38:26.000Z
Duration: 3 min 3 s
Channel: JoVE

K12 Standards

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NC K-12 Science Standard Course of Study

9-12

Chemistry

Energy

PS.Chm.7.3

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

הלחץ של גז טהור הוא הסכום של ההתנגשויות המולקולריות בין החלקיקים והמשטחים הסובבים. דוגמית גז עם פחות חלקיקים בנפח נתון מפעילה לחץ נמוך יותר לעומת דוגמית מרובת החלקיקים באותו נפח. אבל מהו הלחץ של תערובות של גזים שונים?בתערובת גז מרובת מרכיבים, הלחץ הוא סכום ההתנגשויות של כל מולקולת הגז. ההנחה היא שכל מרכיב בתערובת מפעיל לחץ משלו, שלא תלוי בגזים האחרים בתערובת. הלחץ מכל מרכיב נפרד נקרא לחץ חלקי.סך הלחץ של תערובת גזים אידיאליים שווה לסכום של הלחצים החלקיים של המרכיבים שלו. האבחנה הזו היא חוק דלטון ללחצים חלקייים. באמצעות החלת חוק הגז האידיאלי, על הלחץ החלקי של מרכיבי הגז הנפרדים, ניתן לתארם באמצעות גדלים מדידים.מכיוון שהגזים בתערובות חולקים את אותו נפח והם באותה טמפרטורה, ניתן לפשט את המשוואה. סכום המולים של המרכיבים הנפרדים שווה למספר המולים הכולל של כל מרכיבי הגז, n כולל. לפיכך, סך הלחץ של תערובת הגז שווה ל-n כולל כפול הקבוע RT חלקי V(נפח)מספר המולים של מרכיב חלקי סך כל המולים בתערובות הוא השבר המולי.סידור מחדש של השבר המולי מתוך סך המולים והצבת n כולל בחוק דלטון של לחץ חלקי יוצרים ביטויים של לחץ כולל. בסידור מחודש, הלחץ החלקי של גז בתערובת הוא המכפלה של השבר המולי שלו וסכום הלחץ הכולל של התערובות. אז בתערובת גז, הלחץ החלקי של כל מרכיב, i, שווה לשבר המולי של i כפול הלחץ הכולל.כדוגמה לחישוב, נניח שמכל מלא בשני גזים, הליום וארגון. 40%מהנפח הוא ארגון. המשמעות היא שהשבר המולי של ארגון הוא 0.4.אם הלחץ הכולל הוא 4 אטמוספרות, מהו הלחץ החלקי של הליום? מתוך המשוואה ללחץ חלקי של גז עולה כי הלחץ החלקי של ארגון שווה לשבר המולי שלו כפול הלחץ הכולל. לכן 0.4 כפול 4 אטמוספרות שווה ל-1.6 אטמסופרות, וזהו הלחץ החלקי של ארגון.מכיוון שהסכום של הלחצים החלקיים שווה ללחץ הכולל, המשוואה ניתנת לסידור מחדש כך שניתן לחסר את הלחץ החלקי של ארגון מהלחץ הכולל. מכאן שהלחץ החלקי של הליום הוא 2.4 אטמוספות.

תערובות גזים: חוק דלטון של לחצים חלקיים ושברי מולים

<div style="direction:rtl">

 אלא אם כן גזים בודדים מגיבים זה עם זה בצורה כימית, הגזים הנפרדים בתערובת של גזים אינם משפיעים זה על הלחץ של זה. כל גז בתערובת מפעיל את אותו לחץ שהיה מפעיל אילו היה קיים לבדו במיכל. הלחץ שמפעיל כל גז בודד בתערובת נקרא הלחץ החלקי שלו. 

 המשמעות היא שבתערובת המכילה שלושה גזים שונים A, B ו-C, אם PA הוא הלחץ החלקי של גז A; PB הוא הלחץ החלקי של גז B; PC הוא הלחץ החלקי של גז C; אז הלחץ הכולל ניתן על ידי משוואה 1: 
 <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-01.png" style="height: 40px;"> 

 זהו חוק הלחצים החלקיים של דלתון: הלחץ הכולל של תערובת של גזים אידיאליים שווה לסכום הלחצים החלקיים של הגזים המרכיבים. 

 תנו ל-nA, nB ו-nC להיות מספר המולים של כל אחד מהגזים בתערובת. אם כל גז מציית למשוואת הגז האידיאלי, ניתן לכתוב את הלחץ החלקי כך:
 <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-02.png" style="height: 40px;"> 

 מכיוון שכל הגזים נמצאים באותה טמפרטורה ותופסים אותו נפח, החלפה למשוואה 1 נותנת: 
 <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-03.png" style="height: 40px;"> 

 המשוואה מצביעה על כך שבטמפרטורה קבועה ובנפח קבוע, הלחץ הכולל של דגימת גז נקבע על פי המספר הכולל של מול הגז הנמצא. 

 עבור תערובות גזים, נוח להכניס כמות הנקראת שבר המול, χ, המוגדר כמספר המולות של חומר מסוים בתערובת חלקי המספר הכולל של מולות של כל החומרים הקיימים. מבחינה מתמטית, שבר המול של חומר A בתערובת עם B ו-C מבוטא כ 
 <img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-04.png" style="height: 40px;"> 

 באופן דומה, חלק המול של B ו-C הם; 
 <img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-05.png" style="height: 40px;"> 
 <img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-06.png" style="height: 40px;"> 

 שילוב המשוואה עבור שבר המול של A והמשוואה עבור הלחץ החלקי נותן: 
 <img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-07.png" style="height: 40px;"> 

 הלחץ החלקי של גז A קשור ללחץ הכולל של תערובת הגז דרך חלק המול שלו. 

 במילים אחרות, הלחץ של גז בתערובת גזים הוא התוצר של שבר המול שלו והלחץ הכולל של התערובת. 

 טקסט זה מותאם מ <a href="https://openstax.org/books/chemistry-2e/pages/9-3-stoichiometry-of-gaseous-substances-mixtures-and-reactions">Openstax, Chemistry 2e, Section 9.3: Stoichiometry of Gaseous Substances, Mixtures, and Reactions.</a></div>

אלא אם כן גזים בודדים מגיבים כימית זה עם זה, הגזים הבודדים בתערובת של גזים אינם משפיעים זה על הלחץ של זה. כל גז ...

Education

JoVE Core

כימיה

אחד

Gases

גזים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

gas pressure in mixtures: partial pressures

Gas pressure in mixtures is described by partial pressure and mole fraction. When gases do not chemically react, each gas in the mixture acts as if it were alone in the container. The pressure from one gas is called its partial pressure.

For a mixture of three gases, A, B, and C, the total pressure equals the sum of their partial pressures: PA, PB, and PC. This is Dalton's law of partial pressures. It states that the total pressure of a mixture of ideal gases is the sum of the pressures from each gas.

If each gas follows the ideal-gas equation, its partial pressure can be written in terms of moles, temperature, and volume. Because every gas in the mixture has the same temperature and takes up the same volume, these terms can be combined. At constant temperature and constant volume, the total pressure depends on the total number of moles of gas present.

For gas mixtures, chemists also use mole fraction, x. Mole fraction is the number of moles of one substance divided by the total number of moles in the mixture. For gas A in a mixture with B and C, the mole fractions of A, B, and C are found in this way.

Mole fraction also links directly to partial pressure. The partial pressure of gas A equals its mole fraction times the total pressure of the mixture. In other words, a gas's pressure in a mixture is its share of the total pressure.

Gas Pressure in Mixtures: Partial Pressures

gas-pressure-in-mixtures-partial-pressures

definition and measurement of pressure: atmospheric pressure, barometer, and manometer

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Pressure Units and Tools for Gas Measurement

Pressure is the force applied to a given area, and gas pressure comes from gas molecules colliding with surfaces. Each collision is tiny, but many collisions over a small area can create high pressure. Pressure increases when force increases or when the area gets smaller. It decreases when force drops or when the area gets larger. Pressure is measured in pascals, or Pa, in the SI system. One pascal equals 1 newton per square meter, and a newton is a unit of force equal to 1 kg·m/s2. A pascal...

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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...

applications of the ideal gas law: molar mass, density, and volume

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Ideal Gas Law at STP and Gas Density

The ideal gas law links pressure, volume, number of moles, and temperature. It helps explain how gas volume changes when pressure or temperature changes. At standard temperature and pressure, or STP, the values are 273.15 K and 1 atm. At STP, one mole of an ideal gas occupies about 22.4 L. This is called the standard molar volume. The gas can be hydrogen, oxygen, argon, or carbon dioxide, and the volume is still about 22.4 liters. Half a mole occupies 11.2 L, and 2 moles occupy 44.8 L. The...

mixtures of gases: dalton's law of partial pressures and mole fractions

Gas pressure in mixtures is described by partial pressure and mole fraction. When gases do not chemically react, each gas in the mixture acts as if it were alone in the container. The pressure from one gas is called its partial pressure. For a mixture of three gases, A, B, and C, the total pressure equals the sum of their partial pressures: PA, PB, and PC. This is Dalton's law of partial pressures. It states that the total pressure of a mixture of ideal gases is the sum of the pressures from...

chemical stoichiometry and gases: using ideal gas law to determine moles

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Stoichiometry of Gases with the Ideal Gas Law

Chemical stoichiometry links the amounts of reactants and products in a chemical reaction. For gases, those amounts can also be measured by volume. If a gas’s volume, pressure, and temperature are known, the ideal gas equation can be used to find the number of moles present. The same idea works in reverse. If the moles of a gas are known, its volume can be found at any temperature and pressure. The transcript gives an example using 8.88 g of gallium reacting with excess hydrochloric acid.

basic postulates of kinetic molecular theory: particle size, energy, and collision

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Kinetic Molecular Theory and Gas Behavior

Kinetic molecular theory explains gas behavior at the particle level. It gives a microscopic model for what happens when pressure or temperature changes. Gas laws describe how macroscopic properties change, but they do not explain why those changes happen. The theory was put into a complete form by Rudolf Clausius in 1857. It was built from hundreds of experimental observations about gases. Those observations helped explain the different gas laws through a few basic postulates. One key idea...

kinetic molecular theory and gas laws explain properties of gas molecules

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Gas Pressure Patterns in Kinetic Molecular Theory

Kinetic molecular theory explains gas pressure by linking it to the motion of gas molecules. Gas pressure comes from rapidly moving molecules hitting the walls of a container. It depends on how many molecules strike a unit area in a given time. The theory also helps explain the main gas laws. In Gay-Lussac’s law, also called Amontons’s law, raising temperature increases the average speed and kinetic energy of gas molecules. If volume stays constant, the molecules collide with the walls more...

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Real Gases: When the Ideal Gas Law Breaks Down

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key terms and concepts

Learn how partial pressure and mole fraction describe gas mixtures, and how Dalton's law connects each gas to the total pressure.

Gas Pressure in Mixtures: Partial Pressures | JoVE K12

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Ohio’s Learning Standards and Model Curriculum

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Virginia  Standards of Learning

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CH.6

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CHEM.10

CHEM.10.B

CHEM.10.C

Alabama Course of Study Science

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PS.Chm.7.1

Energy Basics

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PS.Chm.7.2

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Gas Pressure in Mixtures: Partial Pressures

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