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

すべての気体粒子は 運動エネルギーを持っており これは粒子質量（キログラム）と 速度（速度の大きさ）の 関数（メートル毎秒）です 衝突するたびに 個々のガス粒子の速度は 変化します したがって ガス粒子の集合体は 実際には 速度と運動エネルギーの 分布（範囲）を持っています つまり ある分子は 他の分子よりも 遅い速度で動いていますが 平均運動エネルギーは 変わらないということです 平均運動エネルギーは 速度の二乗の平均 つまり 平均二乗速度の平均に 関係しています さて ガス1モルの 平均運動エネルギーは アボガドロ定数NAを 導入することで表されます 粒子1個あたりの質量と 1モルあたりの粒子の アボガドロ定数の積は 1モルあたりの気体のモル質量を キログラムで表したものに 等しくなります 気体のモルの 平均運動エネルギーが 温度に正比例することを 運動分子理論から 思い出してください 複雑な導出により 比例定数は 3/2 Rであることが わかります 2つの式を組み合わせて 用語を並べ替えて 両側の平方根を取ると 平均二乗速度の 平方根を関連付ける また ルート-平均二乗 または RMS 速度と呼ばれる モル質量 およびガスの 絶対温度です RMS速度は モル質量に反比例し 温度に正比例します ヘリウムとアルゴンという 2つの気体が 同じ温度にあるとします ヘリウムの方が モル質量が小さいので 式はヘリウムの方が アルゴンよりも高いRMS速度を 持っていることを示しています 同じ温度で ヘリウム アルゴン 塩素という 3つのガスの分子速度の 分布をプロットしてみると 同じような傾向が観察ができます すべてのガスが同じ平均運動 エネルギーを持つにもかかわらず 最も軽いガスであるヘリウムは 分子速度の最も広い範囲に対応し 最も高いRMS速度と 最も広い速度分布の 両方を持っていることに 注意してください 気体の速度分布を異なる 温度でプロットすると 例えばアルゴンのよう より高い 温度ではRMS速度が増加し 速度分布が広がっていることが わかります つまり ガスは高温になるほど 速く移動します 例えば 高温の食品からの 香りの原因となるガス粒子は 低温の食品からの粒子よりも 速く移動します このように熱い食物は冷たい 食物よりも早く検出されます

分子速度と運動エネルギー

分子運動論は、様々な気体法則で記述されている挙動を定性的に説明します。 この理論の定理をより定量的に適用して、個々の法則を導き出すことができます。 
 
 気体試料中の分子は、平均運動エネルギーと平均速度を持つが、個々には異なる速度で移動します。 分子は、運動量が制限される弾性衝突を頻繁に起こしています。 衝突した分子は異なる速度で跳ね飛ばされるため、個々の分子はさまざまな速度を持ちます。 しかし、膨大な数の分子との衝突が関係するため、分子の速度分布と平均速度は一定です。 この分子の速度分布は マクスウェル-ボルツマン分布と呼ばれ、速度を持つ大量の気体試料中の分子の相対的な数を表します。 
 
 質量（ m ）と速度（ u ）を持つ粒子の運動エネルギー（ KE ）は、次の式で示されます。 
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />
 
 質量をキログラム単位で、速度をメートル / 秒単位で表現すると、ジュール単位のエネルギー値が得られる（J = kg·m2/s2）。 多数の気体分子に対応するために、速度と運動エネルギーの両方に平均値を使用します。 KMT では、粒子の二乗平均速度urmsは、速度の二乗平均の平方根として n = 粒子数で定義されます。 
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />
 
 粒子の１モルの平均運動エネルギー KEavg は、次のようになります。 
 
 <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />
 
 ここで、 M は kg/mol 単位で表されるモル質量です。 気体分子の１モルの KEavg は、気体の温度に正比例し、次の式で表されます。 
 
 <img alt="Eq4" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />
 
 ここで、 R は気体定数、T は<ケルビン温度です。 この方程式で使用する場合、気体定数の適切な形式は 8.314 J/mol⋅K （ 8.314 kg·m2/s2·mol·K ）です。 KEavg 用の次の 2 つの別々の方程式を組み合わせて再配置することで、分子速度と温度の関係を構築できます。 
 
 <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;" />
 
 気体の温度が上昇すると、 KEavg が上昇し、より多くの分子が高速に、より少ない分子が低速になり、全体的に高い速度に向かって分布が変化します。つまり、右側にシフトします。 温度が低下すると KEavg は減少し、より多くの分子が低速に、より少ない分子が高速になります。また、分布は全体的に低速に向かって左にシフトします。
 
 特定の温度では、すべての気体分子に同じ KEavg が存在します。 気体の分子速度は分子量に直接関係しています。 より軽い分子で構成される気体は、より高速な粒子と高いurmsを持ち、速度分布は比較的高い速度でピークを示します。 重い分子で構成される気体は、より低速な粒子、低いurms、比較的低い速度でピークを示す速度分布を持ちます。
 
 この文章は <a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory">、 Openstax, Chemistry 2e, Section 9.5: Kinety-Molecular Theory から引用したものです。</a>

運動分子理論は、さまざまなガスの法則によって記述される振る舞いを定性的に説明します。この理論の仮定は、...

Education

JoVE Core

化学

Gases

気体

KEY TERMS AND CONCEPTS

主要用語と概念

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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Energy Basics

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First Law of Thermodynamics

Energy Conservation

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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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Hess's Law

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Standard Enthalpy of Formation

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PS.Chm.7.2

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Gas Particle Speed Distributions and Temperature

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