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

Tüm gaz parçacıkları, parçacığın kilogram cinsinden kütlesinin ve saniyede metre cinsinden hızın bir fonksiyonu olan kinetik enerjiye sahiptir. Her çarpışmada, ayrı ayrı gaz parçacıklarının hızları değişir. Bu nedenle, bir gaz parçacıkları topluluğunda aslında hızlar ve kinetik enerjiler bir aralıkta dağılım gösterir.Bu, herhangi bir anda bazı moleküllerin diğerlerinden daha yavaş hareket ettiği anlamına gelir;ancak ortalama kinetik enerji aynı kalır. Ortalama kinetik enerji, her ikisi de belirli bir gaz için belirli bir sıcaklıkta sabit kalan hızların karelerinin ortalamasıyla veya ortalama hızın karesiyle orantılıdır. Dolayısı ile, bir mol gazın ortalama kinetik enerjisi, Avogadro sabiti NA eklenerek ifade edilir.Parçacık başına kütlenin çarpımı ve mol başına Avogadro parçacık sabiti, mol başına kilogram cinsinden gazın molar kütlesine eşittir. Kinetik moleküler teoriden bir mol gazın ortalama kinetik enerjisinin sıcaklıkla doğru orantılı olduğunu hatırlayın. Karmaşık türevler yoluyla, orantılılık sabiti 3/2 R olarak bulunur.İki denklemi birleştirilip, terimler yeniden düzenlendiğinde, ve her iki tarafta kare kök alındığında hızın ortalama karesinin kare kökü ortalama karekök veya RMS hız olarak da adlandırılır molar kütle ve gazın mutlak sıcaklığı arasındaki ilişki görülür. RMS hızı molar kütle ile ters orantılıdır ve sıcaklıkla doğru orantılıdır. İki gazın helyum ve argon aynı sıcaklıkta olduğunu varsayalım.Helyum daha düşük molar kütleye sahip olduğundan, denklem helyumun argondan daha yüksek bir RMS hızına sahip olması gerektiğini gösterir. Benzer bir gözlem, aynı sıcaklıkta üç gaz için moleküler hızların dağılımı grafiğinde yapılabilir. Tüm gazlar aynı ortalama kinetik enerjiye sahip olsa da, en hafif gaz olan helyumun hem en yüksek RMS hızına hem de en geniş moleküler hız aralığına karşılık gelen en geniş hız dağılımına sahip olduğuna dikkat edin.Farklı sıcaklıklarda herhangi bir gazın hız dağılımının bir grafiği, RMS hızında bir artış ve daha yüksek sıcaklıklarda hız dağılımının genişlemesini gösterir. Kısacası, gazlar daha yüksek sıcaklıklarda daha hızlı hareket eder. Örneğin, sıcak yiyeceklerden gelen aroma oluşturan gaz parçacıkları, soğuk yiyecektekileden daha hızlı hareket eder.Bu nedenle sıcak yemeğin kokusu, soğuk yemeğe göre daha hızlı algılanır.

moleküler hız ve kinetik enerji

Kinetik moleküler teori, çeşitli gaz yasaları tarafından tanımlanan davranışları niteliksel olarak açıklar. Bu teorinin varsayımları, bu bireysel yasaları türetmek için daha nicel bir şekilde uygulanabilir.
 
 Toplu olarak, bir gaz örneğinde moleküllerin ortalama kinetik enerjisi ve ortalama bir hızları vardır fakat bireysel olarak farklı hızlarda hareket ederler. Moleküller genellikle momentumun korunduğu elastik çarpışmalara maruz kalırlar. Çarpışan moleküller farklı hızlarda saptırıldığından, bireysel moleküller çok farklı hızlara sahiptir. Bununla birlikte, çok sayıda molekül ve çarpışma nedeniyle, moleküler hız dağılımı ve ortalama hız sabittir. Bu moleküler hız dağılımı, Maxwell-Boltzmann dağılımı olarak bilinir ve belirli bir hıza sahip olan toplu bir gaz örneğindeki moleküllerin nispi sayılarını gösterir. 
 
 (m) kütleli ve (u) hızına sahip bir partikülün kinetik enerjisi (KE) şu şekilde hesaplanır:
 
 <img alt=""Eq1"" src=""https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-01.png"" style=""height: 40px;"" />
 
 Kütlenin kilogram cinsinden ve hızın saniyede metre cinsinden kullanılması, joule birimlerinde enerji değerleri verecektir (J = kg·m2/s2). Çok sayıda gaz molekülü ile başa çıkmak için, hem hız hem de kinetik enerji için ortalamalar kullanırız. KMT kapsamında, bir partikülün ortalama karekök hızı, urms, n tane partikülün hızlarının karelerinin ortalamasınn karekökü şeklinde tanımlanır:
 
 <img alt=""Eq2"" src=""https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-02.png"" style=""height: 40px;"" />
 
 Bir mol parçacık için ortalama kinetik enerji, KE avg ise şuna eşittir:
 
 <img alt=""Eq3"" src=""https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-03.png"" style=""height: 40px;"" />
 
 burada M kg/mol cinsinden molar kütledir. Bir mol gazın KEavg değeri, gazın sıcaklığı ile doğrudan ilişkilidir ve şu formül ile tanımlanabilir:
 
 <img alt=""Eq4"" src=""https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-04.png"" style=""height: 40px;"" />
 
 burada R gaz sabiti, T ise kelvin cinsinden sıcaklıktır. Bu denklemde kullanıldığında, gaz sabitinin uygun formu 8,314 J/mol⋅K (8.314 kg·m2/s2·mol·K) şeklindedir. KEavg için bu iki ayrı denklem, moleküler hız ve sıcaklık arasında bir ilişki elde etmek için birleştirilebilir ve şu şekilde yeniden düzenlenebilir:
 
 <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;"" />
 
 Bir gazın sıcaklığı artarsa, KEavg artar, daha fazla molekül daha yüksek hızlara sahiptir ve daha az molekül daha düşük hızlara sahiptir ve dağılım genel olarak daha yüksek hızlara, yani sağa doğru kayar. Sıcaklık azalırsa, KEavg azalır, daha fazla molekül daha düşük hızlara sahiptir ve daha az molekül daha yüksek hızlara sahiptir ve dağılım genel olarak daha düşük hızlara, yani sola doğru kayar. 
 
 Belirli bir sıcaklıkta, tüm gaz molekülleri aynı KEavg değerine sahiptir. Bir gazın moleküler hızı doğrudan moleküler kütle ile ilgilidir. Daha hafif moleküllerden oluşan gazlar, nispeten daha yüksek hızlarda zirveye ulaşan bir hız dağılımı ile daha yüksek hızlı parçacıklara ve daha yüksek bir urms değerine sahiptir. 
 
 Bu metin bu kaynaktan uyurlanmıştır: <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>

Moleküler Hız ve Kinetik Enerji

Kinetik moleküler teori, çeşitli gaz yasaları tarafından tanımlanan davranışları niteliksel olarak açıklar. Bu teorinin varsayımları bir şekilde uygulanabilir ...

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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 Particle Speed Distributions and Temperature

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