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

mixtures-of-gases-dalton-s-law-of-partial-pressures-and-mole-fractions

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

순수한 기체의 압력은 입자와 주변 표면 사이의 분자 충돌의 합입니다. 주어진 부피에서 입자의 수가 적은 기체 샘플은 입자가 많은 샘플보다 낮은 압력을 가합니다. 하지만 다른 기체가 섞여 있다면 압력은 어떻게 될까요?

다성분 기체 혼합물의 경우 압력은 모든 기체 분자의 충돌의 합입니다. 혼합물의 매 성분은 같이 있는 다른 기체와 무관하게 자체의 압력을 가하는 것으로 추정됩니다. 이러한 개별적인 성분의 압력을 부분 압력이라고 합니다.

이상적인 기체 혼합물의 총 압력은 성분들의 부분 압력의 합과 같습니다. 이 관찰 결과가 돌턴의 부분압력의 법칙입니다. 이상적인 기체 법칙을 적용하여 개별적인 기체 성분의 부분 압력을 측정 가능한 변수로 대체합니다.

혼합물의 기체는 같은 부피를 차지하고 같은 온도에 있기 때문에 방정식을 단순화할 수 있습니다. 개별적인 성분별 몰의 합은 모든 기체 성분의 몰의 총 개수인 n total과 같습니다. 따라서 기체 혼합물의 총 압력은 n-total과 기체 상수, 온도를 곱한 값에 부피로 나누어 준 값과 같습니다.

성분의 몰 수를 혼합물의 총 몰 수로 나눈 것이 몰 분율입니다. 돌턴의 부분 압력법칙에서 n-total 대신에 몰 분율을 대입하면 전체 압력에 대한 표현이 나옵니다. 다시 재배열하면 혼합물에서 기체의 부분 압력은 몰 분율과 혼합물의 총 압력을 곱한 것과 같습니다.

따라서 기체 혼합물에서 임의의 성분, i의 부분 압력은 i의 몰 분율에 총 압력을 곱한 것과 같습니다. 예를 들어, 헬륨과 아르곤 두 가지 기체로 채워진 용기에서 아르곤의 부피가 40퍼센트라고 가정합시다. 이는 아르곤의 몰 분율이 0.4임을 의미합니다.

총 압력이 4 기압이라면 헬륨의 부분 압력은 얼마입니까? 기체의 부분 압력에 대한 방정식을 사용하면 아르곤의 부분 압력은 몰 분율에 총 압력을 곱한 것과 같습니다. 따라서 아르곤의 부분 압력은 0.4 곱하기 4 기압으로서 1.6기압이 됩니다.

부분압력의 합은 총압력과 같기 때문에 아르곤의 부분압력을 총압력에서 뺄 수 있도록 방정식을 재배열할 수 있습니다. 따라서 헬륨의 부분압력은 2.4 기압입니다.

가스 혼합물: dalton의 부분 압력 및 몰분율 법칙

개별 가스가 서로 화학적으로 반응하지 않는 한, 가스 혼합물의 개별 가스는 서로의 압력에 영향을 미치지 않습니다. 혼합물의 각 가스는 용기에 단독으로 존재할 때 발휘되는 것과 동일한 압력을 발휘합니다. 혼합물의 각 개별 기체가 가하는 압력을 부분압력이라고 합니다.

이는 세 가지 서로 다른 가스 A, B, C를 포함하는 혼합물에서 P_A가 가스 A의 부분압이라면; P_B는 가스 B의 부분압력입니다. P_C는 가스 C의 부분압력입니다. 그러면 총 압력은 방정식 1로 제공됩니다.

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-01.png" style="height: 40px;" />

이것이 Dalton의 부분압력 법칙입니다. 이상 기체 혼합물의 전체 압력은 구성 가스의 부분압력의 합과 같습니다.

n_A, n_B, n_C를 혼합물에 포함된 각 기체의 몰수로 설정합니다. 각 가스가 이상기체 방정식을 따른다면 부분압력은 다음과 같이 쓸 수 있습니다.

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-02.png" style="height: 40px;" />

모든 가스는 동일한 온도에 있고 동일한 부피를 차지하므로 방정식 1을 대체하면 다음과 같습니다.

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-03.png" style="height: 40px;" />

방정식은 일정한 온도와 일정한 부피에서 기체 샘플의 총 압력이 존재하는 기체의 총 몰수에 의해 결정된다는 것을 나타냅니다.

가스 혼합물의 경우, 혼합물에 있는 특정 물질의 몰수를 존재하는 모든 물질의 총 몰수로 나눈 값으로 정의되는 몰분율 χ라는 양을 도입하는 것이 편리합니다. 수학적으로 B와 C의 혼합물에서 물질 A의 몰분율은 다음과 같이 표현됩니다.

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-04.png" style="height: 40px;" />

마찬가지로, B와 C의 몰분율은 다음과 같습니다.

<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;" />

A의 몰분율에 대한 방정식과 부분압에 대한 방정식을 결합하면 다음이 제공됩니다.

<img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-07.png" style="height: 40px;" />

가스 A의 부분압은 몰분율을 통해 가스 혼합물의 전체 압력과 관련됩니다.

즉, 가스 혼합물의 가스 압력은 몰분율과 혼합물의 전체 압력의 곱입니다.

이 문서는 에서 발췌되었습니다 <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>

가스 혼합물: Dalton의 부분 압력 및 몰분율 법칙

개별 가스가 서로 화학적으로 반응하지 않는 한, 가스 혼합물의 개별 가스는 서로의 압력에 영향을 미치지 않습니다. 각 가스 ...

Education

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JoVE Core

화학

하나

Gases

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KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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Pressure Units and Tools for Gas Measurement

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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...

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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.

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Kinetic Molecular Theory and Gas Behavior

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PS.Chm.7.1

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Gas Pressure in Mixtures: Partial Pressures

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