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

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating Equilibrium Concentrations

Aus der Anfangskonzentration der Reaktanten und der Gleichgewichtskonstante K für die Reaktion können unbekannte Gleichgewichtskonzentrationen bestimmt werden.
Betrachten Sie die Reaktion, bei der 0,30 molare Stickstoffgas und 0,40 molare Sauerstoffgas reagieren, um Stickstoffmonoxidgas zu erzeugen, und bei der K 0,10 beträgt. Zur Berechnung der Gleichgewichtskonzentrationen werden die bekannten Werte in einer ICE-Tabelle tabellarisch dargestellt.
Für die Konzentrationsänderung wird die Zunahme bzw. Abnahme für jedes Produkt bzw. jeden Reaktanten mit dem x-fachen seines stöchiometrischen Koeffizienten bezeichnet. Die Summe oder Differenz wird verwendet, um die Gleichgewichtskonzentrationen zu ermitteln, die dann in den Gleichgewichtsausdruck eingesetzt werden.
Um nach x aufzulösen, wird der Ausdruck erweitert und alle Terme werden auf eine Seite gelegt, um ihn in die Form ax2 + bx + c umzuwandeln. Diese Gleichung kann mit der quadratischen Formel gelöst werden.
Das Lösen ergibt zwei Werte für x: 0,047 und −0,065. Da die negative Konzentration eines Stoffes unmöglich ist, kann der Wert verworfen werden.
Bei Verwendung von 0,047 für x betragen die Gleichgewichtskonzentrationen von Stickstoff, Sauerstoff und Stickstoffmonoxid 0,25, 0,35 bzw. 0,094 molaren Konzentrationen.
Die perfekte quadratische Bedingung ist eine Situation, in der eine Abkürzung verwendet werden kann, um die quadratische Formel zu vermeiden.
Wenn zum Beispiel die Anfangskonzentrationen von Stickstoff und Sauerstoff in der obigen Reaktion jeweils 0,30 molar betrugen, wird die Gleichung zu einem perfekten Quadrat. In solchen Fällen kann die Gleichung vereinfacht werden, indem die Quadratwurzel beider Seiten genommen wird, um nach x aufzulösen.

<ol>
	<li>Lim, Kieran F. "Verwendung von Grafikrechnern und Tabellenkalkulationen in der Chemie: Lösung von Gleichgewichtsproblemen." Zeitschrift für chemische Bildung 85, Nr. 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>

berechnung von gleichgewichtskonzentrationen

Die Berechnung von Gleichgewichtskonzentrationen ist in vielen Bereichen der Wissenschaft und Technik von entscheidender Bedeutung – beispielsweise bei der Formulierung und Dosierung pharmazeutischer Produkte. Nachdem ein Medikament eingenommen oder injiziert wurde, ist es typischerweise an mehreren chemischen Gleichgewichten beteiligt, die seine endgültige Konzentration im interessierenden Körpersystem beeinflussen. Um eine Dosierung zu berechnen, die den gewünschten therapeutischen Effekt hervorruft, ist die Kenntnis der quantitativen Aspekte dieser Gleichgewichte erforderlich. Eine anspruchsvollere Art der Gleichgewichtsberechnung kann darin bestehen, dass Gleichgewichtskonzentrationen aus Anfangskonzentrationen und einer Gleichgewichtskonstante abgeleitet werden. Für diese Berechnungen ist typischerweise ein vierstufiger Ansatz sinnvoll: <ol> <li>Identifizieren Sie die Richtung, in der die Reaktion abläuft, um ein Gleichgewicht zu erreichen.</li> <li>Entwickeln Sie eine ICE-Tabelle.</li> <li>Berechnen Sie die Konzentrationsänderungen und anschließend die Gleichgewichtskonzentrationen.</li> <li>Bestätigen Sie die berechneten Gleichgewichtskonzentrationen.</li> </ol> Berechnung von Gleichgewichtskonzentrationen Unter bestimmten Bedingungen beträgt die Gleichgewichtskonstante Kc für die Zerlegung von PCl5(g) in PCl3(g) und Cl2(g) 0,0211. Das obige Verfahren kann verwendet werden, um die Gleichgewichtskonzentrationen von PCl5, PCl3 und Cl2 in einer Mischung zu bestimmen, die ursprünglich nur PCl5 in einer Konzentration von 1,00 M enthielt. Schritt 1. Bestimmen Sie die Richtung, in der die Reaktion verläuft. Die ausgeglichene Gleichung für die Zersetzung von PCl5 lautet <img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;"> Da zunächst nur der Reaktant vorhanden ist, ist Qc = 0 und die Reaktion verläuft nach rechts. Schritt 2. Entwickeln Sie eine ICE-Tabelle. <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;">Initial Concentration (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;">Change (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;">Equilibrium Concentration (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> Schritt 3. Berechnen Sie die Änderung und die Gleichgewichtskonzentrationen. Das Einsetzen der Gleichgewichtskonzentrationen in die Gleichgewichtskonstantengleichung ergibt <img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;"> Eine Gleichung der Form ax2 + bx + c = 0 kann umgestellt werden, um nach x aufzulösen: <img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;"> 

 In diesem Fall ist a = 1, b = 0,0211 und c = −0,0211. Ersetzt man a, b und c durch die entsprechenden Werte, erhält man: 

 <img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;"> Die beiden Wurzeln des Quadratischen sind daher <img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;"> Für dieses Szenario ist nur die positive Wurzel physikalisch aussagekräftig (die Konzentrationen sind entweder Null oder positiv), also ist x = 0,135 M. Die Gleichgewichtskonzentrationen sind <img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;"> Schritt 4. Bestätigen Sie die berechneten Gleichgewichtskonzentrationen. Die Einsetzung von Kc in den Ausdruck (zur Überprüfung der Berechnung) ergibt <img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;"> Die aus den Gleichgewichtskonzentrationen berechnete Gleichgewichtskonstante ist gleich dem in der Aufgabe angegebenen Wert von Kc (bei Rundung auf die richtige Anzahl signifikanter Stellen). Dieser Text ist adaptiert von <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>

Berechnung von Gleichgewichtskonzentrationen

Die Fähigkeit, Gleichgewichtskonzentrationen zu berechnen, ist für viele Bereiche von Wissenschaft und Technik unerlässlich – zum Beispiel bei der Formulierung und Dosierung ...

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Chemical Equilibrium

Chemisches Gleichgewicht

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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...

le chatelier's principle: changing concentration

le-chatelier-s-principle-changing-concentration

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...

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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...

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)

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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

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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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Chemical Reactions

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Equilibrium Concentrations from an ICE Table

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