Name: determining activation energy from temperature
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 34 s
Channel: JoVE

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Arrhenius Plots

화학 반응 속도는 온도 변화에 대단히 민감합니다. 이런 온도 의존성은 속도 상수, 절대 온도, 잦음률 및 활성화 에너지 사이의 관계를 나타내는 아레니우스 방정식을 사용하여 수학적으로 설명할 수 있습니다. 활성화 에너지 및 잦음률은 아레니우스 방정식을 비지수 형식으로 변환하여 그래프적 방법으로 결정할 수도 있습니다.

양변에 자연 로그를 취하면 선형 함수 방정식이 생성됩니다. 기울기 값은 기체 상수에 대한 활성화 에너지의 음수 값이며 y 절편은 잦음률의 자연 로그 값입니다. 이 방정식은 속도 상수의 자연 로그가 켈빈 단위를 가진 온도의 역함수로 표시되는 아레니우스 도식화라는 그래프를 생성하는 데 사용할 수 있습니다.

이 아레니우스 도식화를 사용하여 실험 및 반응의 동력학적 데이터를 설명하고 분석할 수 있습니다. 이 예제에서는 그래프가 직선으로 생성됩니다. 켈빈 단위의 기울기 값은 R에 대한 활성화 에너지의 음수 값과 동일하게 설정됩니다.

기체 상수에 값을 할당하고 활성화 에너지를 계산하면 몰당 93.1 킬로줄의 값을 얻습니다. 또한 y 절편값 26.8은 잦음률의 자연 로그와 같습니다. 따라서, A를 풀면 속도 상수와 같은 단위인 몰농도 당 초 단위를 가지는 값 4.36 곱하기 10의 11승이 얻어집니다.

동력학적 데이터가 제한되거나 그래픽 표시에 어려움이 있는 경우, 아레니우스 방정식의 두 포인트 형식을 사용하여 비그래픽 방식으로 활성화 에너지를 계산할 수 있습니다. 이러한 경우, 아레니우스 방정식의 비지수 형식은 서로 다른 두 온도값에서 속도 상수를 포함하도록 수정됩니다. 이후 식을 감산하고 재배열하면 두 가지 다른 온도에서 실험적으로 생성된 속도 상수로부터 활성화 에너지를 계산하는 데 사용되는 두 포인트 형식의 아레니우스 방정식이 생성됩니다.

값을 대입하면 이 반응에 대한 활성화 에너지는 몰당 145킬로줄로 계산됩니다.

아레니우스 플롯

아레니우스 방정식은 화학 반응의 활성화 에너지와 속도 상수 k와 관련이 있습니다. 아레니우스 방정식에서 k = Ae^−E^a^/RT, R은 8.314 J/mol·K 값을 갖는 이상 기체 상수, T는 켈빈 온도, E_a는 J/mole 단위의 활성화 에너지입니다. , e는 상수 2.7183이고, A는 주파수 인자라고 불리는 상수로, 충돌 빈도와 반응하는 분자의 방향과 관련이 있습니다.

아레니우스 방정식은 실험적 운동 자료로부터 반응의 활성화 에너지를 계산하는 데 사용될 수 있습니다. 반응의 E_a를 결정하는 편리한 접근 방식은 두 개 이상의 서로 다른 온도에서 k를 측정하는 것입니다. 이는 선형 방정식의 형태를 취하는 아레니우스 방정식의 수정된 버전을 사용합니다.

 <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;" />

ln k 대 1/T의 플롯은 기울기가 −E_a/R이고 y 절편이 ln A인 선형입니다.

다음 반응을 고려하십시오.

 <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;" />

이 반응의 활성화 에너지는 그림과 같이 반응 동역학 자료로부터 온도에 따른 속도 상수의 변화를 알면 결정할 수 있습니다.

<div class="overflow">
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">온도(K)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">속도 상수(L/mol/s)</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">555</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.52 ×10-7</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">575</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.22 × 10-6</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">645</td>
			<td style="color: black; border: 1px solid black; text-align: center;">8.59 × 10-5</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">700</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.16 × 10-3</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">781</td>
			<td style="color: black; border: 1px solid black; text-align: center;">3.95 × 10-2</td>
		</tr>
	</tbody>
</table>
</div>

제공된 자료를 사용하여 온도의 역수(1/T) 값과 k의 자연 로그(ln k)를 도출할 수 있습니다.

<div class="overflow">
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1/T (K-1)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">ln k</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1.80 ×10-3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">–14.860</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1.74 ×10-3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">–13.617</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1.55 ×10-3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">–9.362</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1.43 ×10-3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">–6.759</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">1.28 ×10-3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">–3.231</td>
		</tr>
	</tbody>
</table>
</div>

 <img alt="Image1" src="/files/ftp_upload/11380/11380_Image 1.png" style="height: 350px;" />

ln k 대 1/T를 사용하여 파생된 자료 점을 플로팅할 때 그림과 같이 ln k와 1/T 사이의 선형 관계를 나타내는 선 그래프가 생성됩니다.

활성화 에너지에 해당하는 선의 기울기는 두 개의 실험 자료 쌍을 사용하여 추정할 수 있습니다.

 <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;" />

활성화 에너지를 도출하는 또 다른 접근법은 서로 다른 두 온도에서 속도 상수를 활용하는 것입니다. 이 접근 방식에서 아레니우스 방정식은 편리한 2점 형식으로 재배열됩니다.

 <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;" />

방정식을 다시 정리하면 활성화 에너지에 대한 식이 생성됩니다.

 <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;" />

두 개의 자료 쌍을 대체하고 추가 계산을 수행하면 활성화 에너지 값이 몰당 줄 또는 몰당 킬로줄 단위로 산출됩니다.

 <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;" />

이 대안적인 2점 접근법은 그래픽 접근법과 동일한 결과를 산출합니다. 그러나 실제로는 실제 실험 자료로 작업하는 동안 그래픽 접근 방식이 일반적으로 더 신뢰할 수 있는 결과를 제공합니다.

이 문서는 에서 발췌되었습니다 <a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory</a>.

Arrhenius 방정식은 화학 반응에 대한 활성화 에너지와 속도 상수 k를 관련시킵니다. Arrhenius 방정식에서 k = Ae−Ea/RT, R은 ...

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determining activation energy from temperature

The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules.

Experimental kinetic data can be used to find the activation energy of a reaction. One practical method is to measure k at two or more temperatures. The Arrhenius equation can then be rewritten in a linear form. A plot of ln k versus 1/T gives a straight line. The slope equals −Ea/R, and the y-intercept equals ln A.

For example, a reaction with known rate constants at 555 K, 575 K, 645 K, 700 K, and 781 K can be analyzed this way. The rate constants are 3.52 × 10−7, 1.22 × 10−6, 8.59 × 10−5, 1.16 × 10−3, and 3.95 × 10−2 L/mol/s, respectively. These values can be converted to 1/T and ln k. The resulting data set can then be plotted to show the linear relationship between ln k and 1/T.

The slope of the line gives the activation energy. It can be estimated from any two experimental data pairs on the graph. Another option is the two-point form of the Arrhenius equation. This rearranged equation uses rate constants at two temperatures to calculate Ea directly. Both methods give the same result. In practice, the graphical method is often more reliable when working with real experimental data.

Determining Activation Energy from Temperature

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The Arrhenius equation links activation energy and the rate constant, k, for chemical reactions. It is written as k = Ae−Ea/RT. In this equation, R is the ideal gas constant with a value of 8.314 J/mol·K, T is the temperature on the kelvin scale, Ea is the activation energy in J/mole, e is the constant 2.7183, and A is the frequency factor. The frequency factor depends on collision frequency and the orientation of reacting molecules. Experimental kinetic data can be used to find the activation...

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Learn how the Arrhenius equation uses temperature and rate constants to find activation energy with a graph or a two-point calculation.

Determining Activation Energy from Temperature | JoVE K12

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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 ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

phase-transitions-sublimation-and-deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Melting Points

Melting Points in Organic Chemistry
The melting point of a compound is the temperature at which the solid phase transitions into the liquid phase at a ...

Boiling Points

Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

Explain how physical and chemical properties of substances are related to their usage in everyday life such as in sunscreen, cookware, industrial applications, and fuels.

IPC.7.C

Emission Spectra

When solids, liquids, or condensed gases are heated sufficiently, they radiate some of the excess energy as light. Photons produced in this manner have a ...

Metal Flame Emission

Metal Flame Emission
Flame testing is an analytical technique where a sample is placed in a flame, and the characteristic flame color is used to identify ...

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution ...

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that ...

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are ...

Explain how electrons can transition from a high energy level to a low energy state, emitting photons at different frequencies for different energy transitions.

IPC.7.D

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a ...

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that ...

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of ...

Explain how atomic energy levels and emission spectra present evidence for the wave particle duality.

IPC.7.E

Science concepts. The student knows that relationships exist between the structure and properties of matter. The student is expected to:

Determining Activation Energy from Temperature

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