Name: finding kc from equilibrium data
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 46 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

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Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating the Equilibrium Constant

Die Gleichgewichtskonstante Kc kann bestimmt werden, indem die entsprechenden Werte in den Gleichgewichtskonstantenausdruck eingefügt werden, wenn die Konzentrationen aller Reaktanten und Produkte im Gleichgewicht bekannt sind.
Ein gasförmiges Gemisch aus Schwefeldioxid und Sauerstoff bei 530 °C wird entsprechend der gezeigten Reaktion reagieren gelassen. Im Gleichgewicht enthält das Gemisch 0,10 molar Schwefeldioxid, 0,15 molar Sauerstoff und 10,88 molar Schwefeltrioxid. 
Durch Einsetzen der Werte in den Gleichgewichtsausdruck ergibt sich Kc × 7,9 104. 
Der Kc kann auch berechnet werden, solange die Anfangskonzentration aller Komponenten und die Gleichgewichtskonzentration von mindestens einer Verbindung bekannt ist.
Die unbekannten Gleichgewichtskonzentrationen können dann mit Hilfe der Reaktionsstöchiometrie berechnet werden. Eine ICE-Tabelle wird verwendet, um die Informationen für die Anfangs-, Änderungs- und Gleichgewichtskonzentrationen der Reaktion zu organisieren.
Wenn ein Reaktionsgemisch, das 0,11 molaren Stickstoff und 0,36 molaren Wasserstoff enthält, bei 500 °C ins Gleichgewicht gebracht wird, erzeugt es im Gleichgewicht 0,020 molare Ammoniak. Um den Kc zu berechnen, müssen die Gleichgewichtskonzentrationen von Stickstoff und Wasserstoff bestimmt werden.
Die Stöchiometrie der Reaktion zeigt, dass 1 Mol Stickstoffgas und 3 Mol Wasserstoffgas erforderlich sind, um 2 Mol Ammoniakgas zu erzeugen.
Die Änderung x bedeutet, wenn sie mit den Koeffizienten der Reaktanten und Produkte multipliziert wird, die Konzentration der verbrauchten Reaktanten und die Konzentration des erzeugten Produkts, um ein Gleichgewicht zu erreichen. 
Da 2x 0,020 ist, ist x gleich 0,010. Die Gleichgewichtskonzentration von Stickstoff und Wasserstoff kann dann bestimmt werden, indem die jeweilige Konzentrationsänderung von ihrer Anfangskonzentration abgezogen wird, die 0,10 bzw. 0,33 molar beträgt.
Setzt man Gleichgewichtskonzentrationen in der Kc-Expression ein, so ist Kc gleich 0,11.
Der Kp für Reaktionen mit Gasen kann mit Hilfe einer ICE-Tabelle berechnet und der Gleichgewichtsausdruck mit Partialdrücken geschrieben werden.

berechnung der gleichgewichtskonstante

Die Gleichgewichtskonstante für eine Reaktion wird aus den Gleichgewichtskonzentrationen (oder -drücken) ihrer Reaktanten und Produkte berechnet. Wenn diese Konzentrationen bekannt sind, umfasst die Berechnung lediglich ihre Substitution in den Kc-Ausdruck. Gasförmiges Stickstoffdioxid bildet beispielsweise Distickstofftetroxid nach dieser Gleichung: <img alt="Eq1" src="/files/ftp_upload/11388/11388_Equation_1.png" style="text-align: center; height: 50px;"> Wenn 0,10 mol NO2 bei 25 °C in einen 1,0-l-Kolben gegeben werden, ändert sich die Konzentration, sodass im Gleichgewicht [NO2] = 0,016 M und [N2O4] = 0,042 M sind. Der Wert der Gleichgewichtskonstante für die Reaktion kann sein wie folgt berechnet: <img alt="Eq2" src="/files/ftp_upload/11388/11388_Equation_2.png" style="text-align: center; height: 90px;"> Als nächstes wird ein etwas anspruchsvolleres Beispiel gegeben, bei dem die Reaktionsstöchiometrie verwendet wird, um Gleichgewichtskonzentrationen aus den bereitgestellten Informationen abzuleiten. Die grundlegende Strategie dieser Berechnung ist für viele Arten von Gleichgewichtsberechnungen hilfreich und basiert auf der Verwendung von Begriffen für die anfänglich vorhandenen Reaktanten- und Produktkonzentrationen, für deren Veränderung im Verlauf der Reaktion und für ihre Werte, wenn das System das Gleichgewicht erreicht. Für diesen mathematischen Ansatz wird üblicherweise das Akronym ICE verwendet, und die Konzentrationsterme werden normalerweise in einem tabellarischen Format, einer sogenannten ICE-Tabelle, erfasst. Berechnung einer Gleichgewichtskonstante Jodmoleküle reagieren reversibel mit Jodidionen unter Bildung von Trijodidionen. <img alt="Eq3" src="/files/ftp_upload/11388/11388_Equation_3.png" style="text-align: center; height: 50px;"> Wenn eine Lösung mit den Konzentrationen von I2 und I− jeweils 1,000 × 10−3 M vor der Reaktion eine Gleichgewichtskonzentration von I2 von 6,61 × 10−4 M ergibt, wie lautet dann die Gleichgewichtskonstante für die Reaktion? Zur Berechnung der Gleichgewichtskonstanten werden Gleichgewichtskonzentrationen für alle Reaktanten und Produkte benötigt: <img alt="Eq4" src="/files/ftp_upload/11388/11388_Equation_4.png" style="text-align: center; height: 90px;"> Es werden die Anfangskonzentrationen der Reaktanten und die Gleichgewichtskonzentration des Produkts angegeben. Aus diesen Informationen lassen sich Begriffe für die Gleichgewichtskonzentrationen der Reaktanten ableiten und alle Informationen in einer ICE-Tabelle darstellen. <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;">      I2 (aq)        </td> <td style="color: black; border: 1px solid black; text-align: center;">I− (aq) </td> <td style="color: black; border: 1px solid black; text-align: center;">   I3− (aq)     </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;">1.000 × 10−3</td> <td style="color: black; border: 1px solid black; text-align: center;">1.000 × 10−3</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;">  1.000 × 10−3 − x  </td> <td style="color: black; border: 1px solid black; text-align: center;">    1.000 × 10-3 − x  </td> <td style="color: black; border: 1px solid black; text-align: center;">x</td> </tr> </tbody> </table> Im Gleichgewicht beträgt die Konzentration von I2 6,61 × 10−4 M, sodass <img alt="Eq5" src="/files/ftp_upload/11388/11388_Equation_5.png" style="text-align: center; height: 90px;"> Die ICE-Tabelle kann nun mit numerischen Werten für alle ihre Konzentrationen aktualisiert werden: <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;">I2 (aq) </td> <td style="color: black; border: 1px solid black; text-align: center;">I− (aq) </td> <td style="color: black; border: 1px solid black; text-align: center;">I3− (aq)</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;"> 1.000 × 10−3 </td> <td style="color: black; border: 1px solid black; text-align: center;">  1.000 × 10−3  </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;"> −3.39 × 10−4 </td> <td style="color: black; border: 1px solid black; text-align: center;">  −3.39 × 10−4  </td> <td style="color: black; border: 1px solid black; text-align: center;">  +3.39 × 10-4  </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;"> 6.61 × 10−4 </td> <td style="color: black; border: 1px solid black; text-align: center;">  6.61 × 10−4  </td> <td style="color: black; border: 1px solid black; text-align: center;"> 3.39 × 10−4 </td> </tr> </tbody> </table> Schließlich können die Gleichgewichtskonzentrationen in den Kc-Ausdruck eingesetzt und gelöst werden: <img alt="Eq6" src="/files/ftp_upload/11388/11388_Equation_6.png" style="text-align: center; height: 90px;"> 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>

Berechnung der Gleichgewichtskonstante

Die Gleichgewichtskonstante für eine Reaktion wird aus den Gleichgewichtskonzentrationen (oder Drücken) ihrer Reaktanten und Produkte berechnet. Wenn diese ...

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Chemical Equilibrium

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KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 calculate the equilibrium constant for the reaction.

A more advanced example uses reaction stoichiometry to find equilibrium concentrations from the information given. This method is useful for many equilibrium calculations. It tracks the amount present at the start, how it changes as the reaction proceeds, and the amount present at equilibrium. The acronym ICE is used for this approach, and the values are often organized in an ICE table.

The iodine example shows how this works. I2 reacts reversibly with iodide ions to form triiodide ions. If a solution starts with 1.000 × 10^-3 M I2 and 1.000 × 10^-3 M I−, and the equilibrium concentration of I2 is 6.61 × 10^-4 M, the equilibrium constant can be found for the reaction.

To do this, the initial concentrations of the reactants and the equilibrium concentration of the product are used to build an ICE table. The table shows I2, I−, and I3− with initial, change, and equilibrium entries. From the given equilibrium value for I2, the other concentrations can be calculated, including 6.61 × 10^-4 M for I2 and I− and 3.39 × 10^-4 M for I3−.

Once the equilibrium concentrations are known, they are substituted into the Kc expression and solved. This same strategy links the ICE table to the final equilibrium constant. It is a practical way to handle equilibrium problems in chemistry.

Finding Kc from Equilibrium Data

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...

homogeneous equilibria for gaseous reactions

homogeneous-equilibria-for-gaseous-reactions

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

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 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...

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

Use equilibrium concentrations and ICE tables to find Kc in chemistry. See how nitrogen dioxide and iodine examples connect data to the equilibrium constant.

Finding Kc from Equilibrium Data | JoVE K12

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Finding Kc from Equilibrium Data

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