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

جميع جزيئات الغاز لها طاقة حركية،وهي دالة على كتلة الجسيم،بالكيلوغرامات،والسرعة،أو مقدار سرعتها،بالأمتار في الثانية. مع كل اصطدام فإنّالسرعات الفردية لجزيئات الغاز تتغير. لذلك،مجموعة من جزيئات الغاز،في الواقع،لها توزيع أو نطاق للسرعة و طاقة حركية.هذا يعني أنه في أي لحظة،بعض الجزيئات تتحرك أبطأ من غيرها. ومع ذلك،متوسط الطاقة الحركية يبقى كما هو. يرتبط متوسط الطاقة الحركية بمتوسط مربعات السرعات،أو متوسط تربيع السرعة-كلاهما يظل ثابتًا عند درجة حرارة معينة للغاز.الآن،متوسط الطاقة الحركية لمول واحد من الغاز يتم التعبير عنه من خلال إدخال ثابت أفوجادرو،NA. حاصل ضرب الكتلة لكل جسيم،وثابت أفوجادرو للجسيمات لكل مول،يساوي الكتلة المولية للغاز بالكيلوجرام لكل مول. نتذكر من النظرية الجزيئية الحركية أن متوسط الطاقة الحركية للمول الغازي تتناسب طرديا مع درجة الحرارة.من خلال الاشتقاقات المعقدة،لثابت التناسب تم العثور على 3/2 R.بالجمع بين المعادلتين وإعادة ترتيب المصطلحات،وأخذ الجذر التربيعي على كلا الجانبين يربط بين الجذر التربيعي لمتوسط السرعة التربيعية ويسمى أيضًا جذر-المتوسط-التربيعي،أو RMS،و بين السرعة الكتلة المولية ودرجة الحرارة المطلقة للغاز. سرعة RMS متناسبة عكسيًا مع الكتلة المولية وتتناسب طرديا مع درجة الحرارة. لنفترض أن غازين الهيليوم والأرجون موجودان في نفس درجة الحرارة.بما أن الهيليوم له الكتلة المولية الأقل،تشير المعادلة إلى أن الهليوم يجب أن يحتوي على RMS أعلى سرعة من الأرجون. يتم إجراء ملاحظة مماثلة في جزء من توزيع السرعات الجزيئية لثلاثة غازات الهيليوم والأرجون والكلور بنفس درجة الحرارة. نلاحظ أنه على الرغم من احتواء جميع الغازات على نفس متوسط الطاقة الحركية،أخف غاز،الهيليوم،لديه أعلى سرعة RMS وأوسع سرعة توزيع،بالاشارة الى أوسع نطاق من السرعات الجزيئية.جزء من توزيع السرعة لأي غاز لنقل الأرجون في درجات حرارة مختلفة،يظهر زيادة في سرعة RMS،وتوسيع توزيع السرعة،عند أعلى درجات الحرارة. باختصار،تتحرك الغازات بشكل أسرع في درجات الحرارة المرتفعة. على سبيل المثال،جزيئات الغاز المسببة للرائحة من الطعام الساخن تتحرك أسرع من الجزيئات من الطعام البارد.وبالتالي،يتم اكتشاف الطعام الساخن بشكل أسرع من الطعام البارد.

السرعات الجزيئية والطاقة الحركية

تشرح النظرية الجزيئية الحركية نوعيّاً السلوكيات الموصوفة في قوانين الغاز المختلفة. ويمكن تطبيق افتراضات هذه النظرية بطريقة أكثر كمّية لاشتقاق هذه القوانين الفردية. بشكل جماعي، فإن الجزيئات في عينة من الغاز لها متوسط طاقة حركية وسرعة متوسطة؛ ولكنها تتحرك بشكل فردي بسرعات مختلفة. غالباً ما تتعرض الجزيئات لتصادمات مرنة يتم فيها الحفاظ على قوة الدفع. ونظراً لأن الجزيئات المتصادمة تنحرف عن بعضها بسرعات مختلفة، فإن الجزيئات الفردية لها سرعات متفاوتة على نطاق واسع. ومع ذلك، نظراً للعدد الهائل من الجزيئات والتصادمات، فإن توزيع السرعة الجزيئية ومتوسط السرعة ثابتان. ويُعرف توزيع السرعة الجزيئية هذا بتوزيع ماكسويل-بولتزمان، وهو يصف الأعداد النسبية للجزيئات في عينة كبيرة من الغاز التي تمتلك سرعة معينة.  يتم إعطاء الطاقة الحركية (KE) لجسيم كتلته (m) وسرعته (u) عن طريق: <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />سينتج عن التعبير عن الكتلة بالكيلوغرام والسرعة بالمتر في الثانية قيماً للطاقة بوحدات الجول (J = kg·m2/s2). للتعامل مع عدد كبير من جزيئات الغاز، نستخدم المتوسطات لكل من السرعة والطاقة الحركية. في KMT، يُعرَّف جذر متوسط السرعة التربيعي لجسيم urms بأنه الجذر التربيعي لمتوسط مربّعات السرعات مع n = عدد الجسيمات: <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />يساوي متوسط الطاقة الحركية لمول من الجسيمات، KEavg، إذاً: <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />حيث M تمثّل الكتلة المولية التي تعبر عنها وحدات الكيلوغرام/مول. كماأن KEavg لمول من جزيئات الغاز يتناسب طرديّاً مع درجة حرارة الغاز ويمكن وصفه بالمعادلة: <img alt="Eq4" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />حيث أن R هو ثابت الغاز و T هو درجة حرارة بالكلفين. عند استخدامه في هذه المعادلة، يكون الشكل المناسب لثابت الغاز هو 8.314 J/mol⋅K (8.314 kg·m2/s2·mol·K). هاتين المعادلتين المنفصلتين لـ KEavg يمكن فصلهما وإعادة ترتيبهما لتحقيق علاقة بين السرعة الجزيئية ودرجة الحرارة: <img alt="Eq5" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-05.png" style="height: 40px;" /><img alt="Eq6" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-06.png" style="height: 40px;" />كلّما زادت درجة حرارة الغاز،فإن KEavg يزداد، ويزاد عدد الجزيئات ذات السرعة العالية ويقلّ عدد الجزيئات ذات السرعة المنخفضة، ويتحول التوزيع إلى سرعات أعلى بشكل عام، أي إلى اليمين. إذا انخفضت درجة الحرارة، فإن KEavg ينخفض، وويزاد عدد الجزيئات ذات السرعة المنخفضة ويقلّ عدد الجزيئات ذات السرعة العالية، ويتحول التوزيع إلى سرعات أقل بشكل عام، أي إلى اليسار.  عند درجة حرارة معينة، تكون جميع الغازات لها نفسKEavg لجزيئاتها. ترتبط السرعة الجزيئية للغاز بشكل مباشر بالكتلة الجزيئية. تحتوي الغازات المكونة من جزيئات أخف وزناً على عدد أكبر من الجسيمات الأكثر سرعة والأعلى urms، وسرعة توزيع تصل لذروتها عند سرعات مرتفعة نسبياً. تحتوي الغازات التي تتكون من جزيئات أثقل وزناً على عدد أكبر من الجسيمات الأقل سرعة، والأقل urms، وسرعة توزيع تصل لذروتها عند سرعات منخفضة نسبياً.  تم اقتباس هذا النص من <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>

تشرح النظرية الجزيئية الحركية نوعيا السلوكيات الموصوفة بقوانين الغاز المختلفة. يمكن تطبيق افتراضات هذه النظرية في ...

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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.

Gas Particle Speed Distributions and Temperature

gas-particle-speed-distributions-and-temperature

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

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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...

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...

kinetic molecular theory: molecular velocities, temperature, and kinetic energy

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...

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Gas Particle Motion, Diffusion, and Effusion

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Real Gases: When the Ideal Gas Law Breaks Down

Real gases are gases that do not always follow the ideal gas law, PV = nRT, especially when pressure is high or temperature is low. The ideal gas model assumes gas particles have no attractive or repulsive forces and take up negligible space compared with the container. At room temperature and 1 atm or less, many gases behave close to ideally. When conditions change, the measured relationships between pressure, volume, and temperature can drift away from the ideal prediction. One way to see...

key terms and concepts

Explore how gas particle speeds, Maxwell-Boltzmann distributions, temperature, and kinetic energy are linked in kinetic molecular theory for high school chemistry.

Gas Particle Speed Distributions and Temperature | JoVE K12

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Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
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Physical and Chemical Properties of Matter

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Physical Properties of Matter

A physical property is ...

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Molecular Comparison of Gases, Liquids, and Solids

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Intermolecular vs Intramolecular Forces

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Intermolecular Forces

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Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

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Surface Tension, Capillary Action, and Viscosity

Surface Tension
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States of Matter and Phase Changes

The internal energy of a substance&#8212;the total kinetic energy of all its molecules and the potential energy of their associated forces&#8212;depends ...

Phase Transitions

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Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally ...

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

Phase Transitions: Melting and Freezing

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Phase Transitions: Sublimation and Deposition

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Heating and Cooling Curves

When a substance&#8212;isolated from its environment&#8212;is subjected to heat changes, corresponding changes in temperature and phase of the substance ...

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. ...

Use models to explain how changes in energy affect the arrangement and movement of the particles in solids, liquids, and gases, as well as the relative strengths of their intermolecular forces.

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Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

First Law of Thermodynamics

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Internal Energy

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Quantifying Heat

Thermal Energy&#160;

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Quantifying Work

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Enthalpy

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Thermochemical Equations

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Constant Pressure Calorimetry

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Constant Volume Calorimetry

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Using Differential Scanning Calorimetry to Measure Changes in Enthalpy

Source: Laboratory of Dr. Terry Tritt &#8212; Clemson University
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Hess's Law

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Standard Enthalpy of Formation

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Enthalpies of Reaction

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Use mathematics and computational thinking to execute simple calorimetric calculations based on the Law of Conservation of Energy.

PS.Chm.7.2

Definition and Measurement of Pressure: Atmospheric Pressure, Barometer, and Manometer

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

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

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

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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
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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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