Name: gas particle speed distributions and temperature
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 7 s
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Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

לכל חלקיקי הגז יש אנרגיה קינטית, שהיא פונקציה של מסת החלקיקים בקילוגרמים ומהירותם במטרים לשנייה. עם כל התנגשות, מהירותו של כל חלקיק משתנה. לכן, למצבור חלקיקי גז למעשה יש מנעד, או טווח של מהירויות ואנרגיות קינטיות.המשמעות היא שבכל רגע נתון יש מולקולות הנעות לאט יותר מאחרות. יחד עם זאת, האנרגיה הקינטית הממוצעת לא משתנה. האנרגיה הקינטית הממוצעת קשורה לממוצע הריבועים של המהירויות או המהירות הריבועית הממוצעת הנותרת קבועה עבור גז נתון בהינתן טמפרטורה קבועה.האנרגיה הקינטית הממוצעת של מול גז אחד מובעת באמצעות קבוע אבוגדרו, NA.מכפלת מסת החלקיק בקבוע אבוגדרו של חלקיקים למול שווה למסה המולרית של הגז בקילוגרמים למול. זכרו כי לפי התאוריה הקינטית של גזים, ממוצע האנרגיה הקינטית של מול גז אחד נמצא ביחס ישר לטמפרטורה. באמצעות חישובים מורכבים, קבוע היחס התגלה כ-3/2 R.בחיבור שתי המשוואות, סידור אברי השבר והוצאת השורש המרובע משני האגפים נחלץ את המהירות הריבועית הממוצעת הקרויה גם RMS, המסה המולית, והטמפרטורה המוחלטת של הגז.מהירות RMS נמצאת ביחס הפוך למסה המולית וביחס ישר לטמפרטורה. נניח ששני גזים, הליום וארגון הם באותה טמפרטורה. מאחר שלהליום יש מסה מולית קטנה יותר, המשוואה מראה שלהליום חייב להיות RMS גבוה יותר מארגון.נוכל לעמוד על אבחנה דומה אם נבחן גרף של חלוקת מהירויות החלקיקים של שלושה גזים:הליום, ארגון וכלור באותה טמפרטורה. שימו לב שלמרות שלכל הגזים יש אותה אנרגיה קינטית ממוצעת, לגז הקל ביותר, הליום, יש גם RMS הגבוה ביותר וגם טווח פיזור המהירויות גדול ביותר בהתאמה למנעד הרחב ביותר של המהירויות המולקולריות. גרף של טווח המהירויות לכל גז שהוא, לדוגמה, של ארגון, בטמפרטורות שונות, מראה כי חלה עלייה ב-RMS והרחבת מנעד המהירויות עם עליית הטמפרטורה.בקצרה, גזים נעים מהר יותר ככל שעולה הטמפרטורה. לדוגמה, חלקיקי הריח המופצים כגז ממאכלים חמים נעים מהר יותר מחלקיקי מזון קר. לכן אנחנו מזהים אוכל חם מהר יותר מאוכל קר.

תיאוריה מולקולרית קינטית: מהירויות מולקולריות, טמפרטורה ואנרגיה קינטית

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 התיאוריה המולקולרית הקינטית מסבירה באופן איכותי את ההתנהגויות המתוארות על ידי חוקי הגזים השונים. ניתן ליישם את ההנחות של תיאוריה זו בצורה כמותית יותר כדי לגזור חוקים בודדים אלה. 

 ביחד, למולקולות בדגימת גז יש אנרגיה קינטית ממוצעת ומהירות ממוצעת; אבל בנפרד, הם נעים במהירויות שונות. מולקולות עוברות לעיתים קרובות התנגשויות אלסטיות שבהן התנע נשמר. מכיוון שהמולקולות המתנגשות מוסטות במהירויות שונות, למולקולות בודדות יש מהירויות שונות מאוד. עם זאת, בגלל מספר העצום של מולקולות והתנגשויות המעורבות, התפלגות המהירות המולקולרית והמהירות הממוצעת קבועה. התפלגות מהירות מולקולרית זו ידועה בשם התפלגות מקסוול-בולצמן, והיא מתארת את המספר היחסי של מולקולות בדגימת גז בתפזורת שיש לה מהירות נתונה. 

 האנרגיה הקינטית (KE) של חלקיק בעל מסה (m) ומהירות (u) ניתנת על ידי: 
 <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;"> 

 ביטוי המסה בקילוגרמים ומהירות במטרים לשנייה יניב ערכי אנרגיה ביחידות של ג'ול (J = kg·m2/s2). כדי להתמודד עם מספר רב של מולקולות גז, אנו משתמשים בממוצעים הן למהירות והן לאנרגיה קינטית. ב-KMT, מהירות הריבוע הממוצעת של השורש של חלקיק, urms, מוגדרת כשורש הריבועי של הממוצע של ריבועי המהירויות כאשר n = מספר החלקיקים: 
 <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;"> 

 האנרגיה הקינטית הממוצעת עבור מול של חלקיקים, KEavg, שווה אז ל: 
 <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;"> 

 כאשר M היא המסה המולרית מבוטאת ביחידות של ק"ג/מול. גם ה-KEavg של מולקולות גז העומדות ביחס ישר לטמפרטורת הגז וניתן לתאר אותה במשוואה: 
 <img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;"> 

 כאשר R הוא קבוע הגז ו-T הוא טמפרטורת הקלווין. בשימוש במשוואה זו, הצורה המתאימה של קבוע הגז היא 8.314 J/mol⋅K (8.314 kg·m2/s2·mol·K). ניתן לשלב ולארגן מחדש את שתי המשוואות הנפרדות הללו עבור KEavg כדי ליצור קשר בין מהירות מולקולרית לטמפרטורה:

 <img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-05.png" style="height: 40px;"> 
 <img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-06.png" style="height: 40px;"> 

 אם הטמפרטורה של גז עולה, ה-KEavg שלו עולה, ליותר מולקולות יש מהירויות גבוהות יותר ולפחות מולקולות יש מהירויות נמוכות יותר, וההפצה עוברת לעבר מהירויות גבוהות יותר בסך הכל, כלומר ימינה. אם הטמפרטורה יורדת, ה-KEavg יורד, ליותר מולקולות יש מהירויות נמוכות יותר ולפחות מולקולות יש מהירויות גבוהות יותר, וההתפלגות עוברת לעבר מהירויות נמוכות בסך הכל, כלומר שמאלה. 

 בטמפרטורה נתונה, לכל הגזים יש את אותו KEavg עבור המולקולות שלהם. המהירות המולקולרית של גז קשורה ישירות למסה המולקולרית. לגזים המורכבים ממולקולות קלות יותר יש יותר חלקיקים במהירות גבוהה ו-urms גבוה יותר, עם התפלגות המהירות שמגיעה לשיא במהירויות גבוהות יותר יחסית. לגזים המורכבים ממולקולות כבדות יותר יש יותר חלקיקים במהירות נמוכה, urms נמוך יותר והתפלגות המהירות שמגיעה לשיא במהירויות נמוכות יחסית.

 טקסט זה מותאם מ <a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory">Openstax, Chemistry 2e, Section 9.5: Kinetic-Molecular Theory.</a></div>

התיאוריה המולקולרית הקינטית מסבירה באופן איכותי את ההתנהגויות המתוארות על ידי חוקי הגזים השונים. הנחות היסוד של תיאוריה זו עשויות להיות מיושמות ב ...

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gas particle speed distributions and temperature

Gas particle speed distributions and temperature are key ideas in the kinetic molecular theory. This theory explains the gas laws by describing how gas molecules move, collide, and share energy.

Gas molecules do not all move at the same speed. A gas sample has an average speed and an average kinetic energy, but individual molecules move at different speeds. Their collisions are elastic, which means momentum is conserved. Because so many molecules collide, the overall speed distribution stays constant.

That distribution is called the Maxwell-Boltzmann distribution. It shows the relative number of molecules in a gas sample at each speed. Kinetic energy depends on both mass and speed, and it is measured in joules when mass is in kilograms and speed is in meters per second. For large numbers of molecules, chemists use averages for speed and kinetic energy.

The root mean square velocity, or u rms, is one way to describe average molecular speed. It is the square root of the average of the squared velocities. The average kinetic energy for one mole of gas also depends on molar mass, and it can be written in terms of the gas constant and the kelvin temperature. In this equation, the correct gas constant is 8.314 J/mol·K.

These relationships show how speed changes with temperature. When temperature increases, average kinetic energy increases. More molecules move at higher speeds, fewer move at lower speeds, and the distribution shifts to the right. When temperature decreases, average kinetic energy decreases, more molecules move slowly, and the distribution shifts to the left.

At the same temperature, gases have the same average kinetic energy, even if their molecules have different masses. Molecular mass still affects speed. Lighter gases have more high-speed particles and a higher u rms, while heavier gases have more low-speed particles and a lower u rms. Their speed distributions peak at different velocities, with lighter gases peaking at higher speeds and heavier gases peaking at lower speeds.

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

Through experiments, scientists established the mathematical relationships between pairs of variables, such as pressure and temperature, pressure and ...

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 ...

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.

Gas Particle Speed Distributions and Temperature

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