Name: equilibrium concentrations from an ice table
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 5 s
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Chemistry

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Calculating Equilibrium Concentrations

ניתן לחשב ריכוזי שיווי משקל לא ידועים על פי הריכוזים הראשוניים של המגיבים וקבוע שיווי המשקל K, של התגובה. חשבו על התגובה בה גז חנקן בריכוז מולרי של-0.30 וריכוז של-0.4 מולר גז חמצן מגיבים ויוצרים גז תחמוצת חנקן וכש-K הוא 0.10. כדי לחשב את הריכוזים בשיווי המשקל, הערכים הידועים מסודרים בטבלת ICE.שינוי הריכוזים, התוספת או ההפחתה לכל תוצר או מגיב, בהתאמה, יסומן על ידי X כפול המקדם הסטויכיומטרי שלו. הסכום או הפער משמש למציאת הריכוזים של שיווי המשקל, שלאחר מכן מוצבים במשוואת שיווי המשקל. על מנת לפתור עבור X, הביטוי מורחב וכל המונחים מועברים לצד אחד כדי להמיר אותם לצורה:c ועוד bx בריבוע ועוד ax.משוואה זו יכולה להיפתר באמצעות נוסחת השורשים לפתרון משוואה ריבועית הפיתרון נותן שני ערכי x:0.047 ומינוס 0.065. מכיוון שבלתי אפשרי שיהיה ריכוז שלילי לחומר, ניתן לדחות את הערך. בהצבת 0.047 ב-x, ריכוזh שיווי המשקל של חנקן, חמצן וחנקן חמצני שווים 0.25, 0.35 ו-0.094 מולר, בהתאמה.המצב הריבועי המושלם הוא מקרה אחד שבו ניתן להשתמש בקיצור דרך כדי להימנע ממשואה מהמעלה השנייה. לדוגמה, הריכוזים ההתחלתיים של חנקן וחמצן בתגובה לעיל היו 0.3 מולר כל אחד והמשוואה הופכת לריבוע מושלם. במקרים אלה, ניתן לפשט את המשוואה על ידי הוצאת שורש ריבועי משני הצדדים כדי לפתור עבור x.

<ol>
	<li>לים, קירן פ. "שימוש במחשבונים גרפיים וגיליונות אלקטרוניים בכימיה: פתרון בעיות שיווי משקל". כתב עת לחינוך כימי 85, מס '10 (2008): 1347. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed085p1347">https://pubs.acs.org/doi/pdf/10.1021/ed085p1347</a></li>
</ol>

חישוב ריכוזי שיווי משקל

<div style="direction:rtl">

היכולת לחשב ריכוזי שיווי משקל חיונית לתחומים רבים של מדע וטכנולוגיה - למשל, בניסוח ובמינון של מוצרים פרמצבטיים. לאחר שתרופה נבלעת או מוזרקת, היא בדרך כלל מעורבת בכמה שיוויי משקל כימיים המשפיעים על הריכוז הסופי שלה במערכת הגוף המעניינת. נדרש ידע על ההיבטים הכמותיים של שיוויי משקל אלה כדי לחשב כמות מינון שתבקש את האפקט הטיפולי הרצוי. 

סוג מאתגר יותר של חישוב שיווי משקל יכול להיות כזה שבו ריכוזי שיווי משקל נגזרים מריכוזים ראשוניים וקבוע שיווי משקל. עבור חישובים אלה, גישה של ארבעה שלבים שימושיים בדרך כלל: 
<ol style="padding-right: 35px; margin: 0;"> 
	<li style="text-align: right;">זהה את הכיוון שאליו תתקדם התגובה כדי להגיע לשיווי משקל.</li> 
	<li style="text-align: right;">פתח טבלת ICE.</li> 
	<li style="text-align: right;">חשב את שינויי הריכוז ולאחר מכן את ריכוזי שיווי המשקל.</li> 
	<li style="text-align: right;">אשר את ריכוזי שיווי המשקל המחושבים.</li> 
</ol> 

חישוב ריכוזי שיווי משקל 

בתנאים מסוימים, קבוע שיווי המשקל Kc לפירוק של PCl5(g) ל-PCl3(g) ו-Cl2(g)הוא 0.0211. ניתן להשתמש בהליך הנ"ל כדי לקבוע את ריכוזי שיווי המשקל של PCl5, PCl3 ו-Cl2 בתערובת שהכילה בתחילה רק PCl5 בריכוז של 1.00 M.

שלב 1. קבע את כיוון התגובה. 

המשוואה המאוזנת לפירוק PCl5 היא 
<img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;"> 

מכיוון שרק המגיב קיים בהתחלה, Qc= 0, והתגובה תתקדם ימינה. 

שלב 2. פתח טבלת ICE. 
<table style="margin-left: auto; margin-right: auto;"> 
	<tbody> 

		<tr> 
			<td style="color: black; border: 1px solid black; text-align: center;"></td> 
			<td style="color: black; border: 1px solid black; text-align: center;"> PCl5 (g) </td> 
			<td style="color: black; border: 1px solid black; text-align: center;"> PCl3 (g) </td> 
			<td style="color: black; border: 1px solid black; text-align: center;"> Cl2 (g)</td> 
		</tr> 
		<tr> 

			<td style="color: black; border: 1px solid black; text-align: center;">ריכוז ראשוני(M)</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">1.00</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">0</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">0</td> 
		</tr> 
		<tr> 

			<td style="color: black; border: 1px solid black; text-align: center;">שנה (M)</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">−x</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td> 
		</tr> 
		<tr> 

			<td style="color: black; border: 1px solid black; text-align: center;">ריכוז שיווי משקל (M)</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 − x</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">x</td> 
			<td style="color: black; border: 1px solid black; text-align: center;">x</td> 
		</tr> 
	</tbody> 
 </table> 

שלב 3. פתור את השינוי ואת ריכוזי שיווי המשקל. 

החלפת ריכוזי שיווי המשקל במשוואה קבועה של שיווי המשקל נותנת: 
<img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;"> 

ניתן לארגן מחדש משוואה בצורה ax2 + bx + c = 0 כדי לפתור את x: 
<img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;"> 

במקרה זה, a = 1, b = 0.0211, ו-c = -0.0211. החלפת הערכים המתאימים עבור a, b ו-c מניבה: 
<img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;"> 

שני השורשים של הריבוע הם, אם כן, 
<img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;"> 

עבור תרחיש זה, רק השורש החיובי הוא בעל משמעות פיזית (הריכוזים הם אפס או חיובי), ולכן x= 0.135 M. ריכוזי שיווי המשקל הם: 
<img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;"> 

שלב 4. אשר את ריכוזי שיווי המשקל המחושבים. 

החלפה לביטוי של Kc (לבדיקת החישוב) נותנת: 
<img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;"> 

קבוע שיווי המשקל המחושב מריכוזי שיווי המשקל שווה לערך Kc שניתן בבעיה (כאשר מעוגל למספר הראוי של הצורות המשמעותיות). 

טקסט זה מותאם מ<a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">Openstax, Chemistry 2e, Section 13.4 Equilibrium Calculations</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a></div>

היכולת לחשב ריכוזי שיווי משקל חיונית לתחומים רבים של מדע וטכנולוגיה – למשל, בניסוח ובמינון ...

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equilibrium concentrations from an ice table

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic effect.

A common approach is needed when equilibrium concentrations must be derived from starting values and a known Kc. The first step is to decide which way the reaction will move to reach equilibrium. Next, an ICE table is set up. ICE stands for initial, change, and equilibrium. After that, the concentration changes are solved and used to find the equilibrium concentrations. The final step is to check the answer.

The decomposition of PCl5(g) into PCl3(g) and Cl2(g) shows how this works. In the example, Kc is 0.0211, and the mixture starts with only PCl5 at 1.00 M. Because only the reactant is present at the start, Qc equals 0, so the reaction moves to the right. The ICE table gives an initial concentration of 1.00 M for PCl5 and 0 for the products, with changes of -x, +x, and +x.

Substituting the equilibrium values into the Kc expression leads to a quadratic equation. Solving it gives two roots, but only the positive root is physically meaningful because concentrations cannot be negative. In this case, x = 0.135 M. The equilibrium concentrations are then found for PCl5, PCl3, and Cl2. A final substitution into the Kc expression confirms that the calculated value matches the given equilibrium constant when rounded correctly.

Equilibrium Concentrations from an ICE Table

equilibrium-concentrations-from-an-ice-table

the equilibrium constant

Chemical Equilibrium and Kc Rules

Chemical equilibrium and the equilibrium constant Kc describe how reactants and products are balanced in a reaction. In the oxidation of sulfur dioxide, a mixture that starts with reactants only has no product at first. As the reaction moves forward toward equilibrium, reactant concentrations decrease and product concentration increases. When equilibrium is reached, the concentrations of both stay constant. A reaction can also begin with only products present. In that case, the reaction moves...

homogeneous equilibria for gaseous reactions

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Relating Kc and Kp in Gas Equilibria

Gas-phase equilibrium can be written using either concentration or pressure. The equilibrium constant may be shown as Kc, which uses molar concentration, or as Kp, which uses partial pressure of the reactants and products. The link between Kc and Kp comes from the ideal gas equation and the definition of molarity. Molarity is the number of moles divided by volume. In the ideal gas equation, P stands for partial pressure, V for volume, n for number of moles, R for the gas constant, and T for...

le chatelier's principle: changing concentration

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Shifting Equilibrium by Changing Concentration

Chemical equilibrium is a dynamic balance. At equilibrium, the forward and reverse reactions happen at equal rates. If the system is stressed in a way that changes one rate more than the other, it is no longer at equilibrium and will shift until balance is restored. This behavior is described by Le Châtelier’s principle. Changes in concentration are a major stress on an equilibrium system. Reaction rates depend mainly on concentration and temperature. For that reason, changing the amount of a...

calculating the equilibrium constant

Finding Kc from Equilibrium Data

The equilibrium constant, Kc, can be found from the equilibrium concentrations of reactants and products. When those concentrations are known, the calculation is straightforward. The values are placed into the Kc expression for the reaction. One example uses nitrogen dioxide and dinitrogen tetroxide. When 0.10 mol NO2 is added to a 1.0-L flask at 25 °C, the concentrations change until equilibrium is reached. At equilibrium, [NO2] is 0.016 M and [N2O4] is 0.042 M, and these values are used to...

reaction quotient

Using Q to Track Equilibrium Changes

Reaction quotient Q helps track how far a reversible reaction has moved toward equilibrium. For a balanced reaction such as m A + n B ⇌ x C + y D, Q comes directly from the stoichiometric coefficients in the equation. When concentrations are used, the expression is written as Qc. For gases, a similar form uses partial pressures. These expressions use relative concentration and pressure values, not absolute values. That means reaction quotients are dimensionless and have no units. As a reaction...

dynamic equilibrium

Chemical Equilibrium in Reversible Reactions

Chemical equilibrium in reversible reactions happens when a reaction moves in both directions at the same time. A reversible reaction uses a double arrow to show that products can turn back into reactants. At equilibrium, the concentrations of reactants and products stay constant over time because the forward and reverse reaction rates are equal. The video uses the reversible decomposition of colorless dinitrogen tetroxide to brown nitrogen dioxide as an example. At time zero, there is finite...

calculating equilibrium concentrations

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic...

le chatelier's principle: changing volume (pressure)

le-chatelier-s-principle-changing-volume-pressure

Gas Equilibrium Under Volume Changes

Gas-phase equilibrium can shift when the volume of the system changes. In these reactions, a change in pressure changes concentration because the partial pressure of an ideal gas is proportional to its molar concentration. That means pressure changes affect equilibrium in the same way as concentration changes. When the volume of a gas mixture changes, the concentrations of reactants and products change together. Since every gas in the equilibrium occupies the same space, the same volume change...

le chatelier's principle: changing temperature

le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle in Heating and Cooling

Le Chatelier's principle helps explain how chemical equilibrium responds to heating and cooling. A system at equilibrium will shift to restore balance after a temperature change, but the equilibrium constant, K, will not stay the same. Instead, the mixture reaches a new equilibrium with a different composition. This temperature effect is different from a concentration change, which shifts equilibrium without changing K. To understand why temperature matters, the reaction can be written with...

the small x assumption

Estimating Equilibrium with Small Changes

A small equilibrium constant can make equilibrium calculations easier. In these reactions, the equilibrium position favors the reactants. When the initial reactant concentration is high and the Kc value is small, the change in concentration may be negligible. In that case, the equilibrium concentration is close to the initial concentration. This idea helps simplify weak acid and weak base problems. Chemists can assume that some equilibrium concentrations are equal to the initial concentrations.

key terms and concepts

Learn how to find equilibrium concentrations with an ICE table, use Kc, and check answers with a PCl5 decomposition example for high school chemistry.

Equilibrium Concentrations from an ICE Table | JoVE K12

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Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

surface-tension-capillary-action-and-viscosity

Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

Hydrogen Bonds

Hydrogen BondsHydrogen bonds are weak attractions between atoms that have formed other chemical bonds. One of these atoms is electronegative, like oxygen, ...

Construct an explanation to summarize the influences intermolecular forces have on the properties of chemical compounds.

PS.Chm.3.2

Analyze the structure of atoms and isotopes.

Equilibrium Concentrations from an ICE Table

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