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

קצב התגובה הכימית רגיש ביותר לשינויים בטמפרטורה. התלות בטמפרטורה מוסברת מתמטית באמצעות משוואת ארניוס המביעה את הקשר בין קבוע הקצב, הטמפרטורה המוחלטת, מקדם התדירות ואנרגיית השפעול. ניתן למצוא את אנרגיית השפעול ואת מקדם התדירות גם באופן גרפי באמצעות המרת משוואת ארניוס לצורה שאינה מעריכית.אם נפעיל את הלוגריתמים הטבעי על שני האגפים, נוצרת משוואה לפונקציה לינארית. ערך השיפוע תואם לערך השלילי של אנרגיית השפעול חלקי קבוע הגזים, והחיתוך עם ציר ה-Y תואם ללוגריתם הטבעי של מקדם התדירות. משוואה זו יכולה לשמש אותנו ביצירת גרף הנקרא גרף ארניוס, בו הלוגריתם הטבעי של קבוע הקצב מוצג כפונקציה של הערך ההופכי לטמפרטורות בקלווין.נתונים קינטים מניסויים ותגובות. ניתנים להצגה ולניתוח באמצעות גרף ארניוס בדוגמה זו, הגרף מניב קו ישר. ערך השיפוע הנתון בקלווין מוצב כשווה לערך השלילי של אנרגיית השפעול חלקי R.אחרי שנציב ערך בקבוע הגזים ונפתור עבור אנרגיית השפעול, נקבל ערך של 93.1 קילוג'ול למול.כמו כן, הערך שלנקודת החיתוך עם ציר ה-Y של 26.8 שווה ללוגריתם הטבעי של מקדם התדירות. וכך, אם נפתור עבור A נקבל ערך של 10¹¹×4.36 ביחידות של אחד חלקי מולריות שניות, אותה יחידה של קבוע הקצב. במקרה של מידע קינטי מוגבל או של קשיים בייצוג גרפי, ישנה גרסת שתי נקודות של משוואת אהרניוס בה ניתן להשתמש כדי לחשב את אנרגיית השפעול באופן שאינו גרפי.במקרים אלה, הצורה הלא-מעריכית של משוואת ארניוס משתנה כך שתכיל את קבועי הקצב בשתי טמפרטורות שונות. צמצום אגפים וסידור מחדש של הביטוי מניב את התצורה הזו של משוואת ארניוס, בה משתמשים כדי לחשב את אנרגיית השפעול מתוך קבועי קצב נסיוניים בשתי טמפרטורות שונות. אם נציב את הערכים במשוואה, אנרגיית השפעול המתקבלת לתגובה זו היא 145 קילוג'ול למול.

גרפים של ארניוס

<div style="direction:rtl">

 משוואת ארניוס מתייחסת לאנרגיית ההפעלה וקבוע הקצב, k, לתגובות כימיות. במשוואת ארניוס, k = Ae−Ea/RT, R הוא קבוע הגז האידיאלי, בעל ערך של 8.314 J/mol·K, T היא הטמפרטורה בסולם קלווין, Ea היא אנרגיית ההפעלה ב-ג'ול/מול. , e הוא הקבוע 2.7183, ו-A הוא קבוע הנקרא גורם התדירות, שקשור לתדירות ההתנגשויות ולכיוון המולקולות המגיבות. 

 ניתן להשתמש במשוואת ארניוס כדי לחשב את אנרגיית ההפעלה של תגובה מנתונים קינטיים ניסיוניים. גישה נוחה לקביעת ה-Ea לתגובה כוללת מדידה של k בשתי טמפרטורות שונות או יותר. הוא משתמש בגרסה שונה של משוואת ארניוס שלובשת צורה של משוואה ליניארית: 
 <img alt="Eq1" src="/files/ftp_upload/11380/11380_Equation_1.png" style="height: 200px;"> 

 גרף של ln k לעומת 1/T הוא ליניארי עם שיפוע שווה ל-−Ea/R ו-Y-חתך שווה ל-ln A. 

 שקול את התגובה הבאה: 
 <img alt="Eq2" src="/files/ftp_upload/11380/11380_Equation_2.png" style="height: 50px;"> 

 ניתן לקבוע את אנרגיית ההפעלה של תגובה זו אם השונות בקבוע הקצב עם הטמפרטורה ידועה מהנתונים הקינטיים של התגובה, כפי שמוצג. 
 <table style="margin-left: auto; margin-right: auto;">
<tbody>
<tr>
<td style="color: black; border: 1px solid black; text-align: center;">טמפרטורה (K)</td>
<td style="color: black; border: 1px solid black; text-align: center;">קבוע קצב (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>

 ניתן להשתמש בנתונים שסופקו כדי לגזור את הערכים של היפוך הטמפרטורה (1/T) והלוגריתם הטבעי של k (ln k). 
 
 <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>

 <img alt="תמונה 1" src="/files/ftp_upload/11380/11380_Image 1.png" style="height: 350px;"> 

 בשרטוט נקודות הנתונים הנגזרות עם ln k לעומת 1/T, נוצר גרף קווי המציג קשר ליניארי בין ln k ו- 1/T, כפי שמוצג. 

 ניתן להעריך את שיפוע הקו, המתאים לאנרגיית ההפעלה, באמצעות שני זוגות מנתוני הניסוי. 
 <img alt="Eq3" src="/files/ftp_upload/11380/11380_Equation_3.png" style="height: 350px;"> 

 גישה חלופית בהפקת אנרגיית הפעלה כוללת ניצול של קבוע הקצב בשתי טמפרטורות שונות. בגישה זו, משוואת ארניוס מסודרת מחדש לצורה נוחה של שתי נקודות: 
 <img alt="Eq4" src="/files/ftp_upload/11380/11380_Equation_4v2.png" style="height: 75px;"> 

 בסידור מחדש של המשוואה נוצר ביטוי לאנרגיית ההפעלה. 
 <img alt="Eq5" src="/files/ftp_upload/11380/11380_Equation_5.png" style="height: 75px;"> 

 על ידי החלפה של כל שני זוגות נתונים וחישוב נוסף מניב את הערך של אנרגיית ההפעלה בג'ול למול או קילו-ג'ול למול. 
 <img alt="Eq6" src="/files/ftp_upload/11380/11380_Equation_6.png" style="height: 135px;"> 

 גישה חלופית זו של שתי נקודות מניבה את אותה תוצאה כמו הגישה הגרפית. עם זאת, בפועל, הגישה הגרפית בדרך כלל מספקת תוצאות אמינות יותר תוך כדי עבודה עם נתונים ניסיוניים בפועל. 

 טקסט זה מותאם מ <a href="https://openstax.org/books/chemistry-2e/pages/12-5-collision-theory">Openstax, Chemistry 2e, Section 12.5: Collision Theory</a>.</div>

משוואת ארניוס מקשרת בין אנרגיית ההפעלה לבין קבוע הקצב, k, עבור תגובות כימיות. במשוואת ארניוס, k = Ae−Ea/RT, R הוא ...

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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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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 ...

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy ...

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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