Name: equilibrium concentrations from an ice table
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 5 s
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PS.Chm.5.2

Calculating Equilibrium Concentrations

Des concentrations à l'équilibre inconnues peuvent être déterminées à partir de la concentration initiale des réactifs et de la constante d'équilibre, K, pour la réaction. Considérons la réaction où 0, 30 molaire d'azote gazeux et 0, 40 L'oxygène gazeux molaire réagit pour produire du gaz d'oxyde nitrique et où K est 0, 10. Pour calculer les concentrations d'équilibre, les valeurs connues sont tabulées dans un tableau ICE.Pour le changement de concentration, l'augmentation ou la diminution pour chaque produit ou réactif, respectivement, est noté x fois son coefficient stoechiométrique. La somme ou la différence est utilisée pour trouver les concentrations d'équilibre, qui sont ensuite substituées dans l'expression d'équilibre. Pour résoudre x, l'expression est développée et tous les termes sont mis de côté pour le convertir sous la forme:ax au carré plus bx plus c.Cette équation peut être résolue en utilisant la formule quadratique. La résolution donne deux valeurs pour x:0, 047 et moins 0, 065. Comme la concentration négative d'une substance est impossible, la valeur peut être rejetée.En utilisant 0, 047 pour x, les concentrations d'équilibre d'azote, d'oxygène et d'oxyde nitrique égaux respectivement à 0, 25, 0, 35 et 0, 094 molaire. L'état carré parfait est une situation où un raccourci peut être utilisé pour éviter la formule quadratique. Par exemple, les concentrations initiales d'azote et l'oxygène dans la réaction ci-dessus étaient de 0, 30 molaire chacun, l'équation devient un carré parfait.Dans ces cas, l'équation peut être simplifié en prenant la racine carrée des deux côtés à résoudre pour x.

<ol>
	<li>Lim, Kieran F. « Utilisation de calculatrices graphiques et de tableurs en chimie : résoudre des problèmes d’équilibre. » Journal de l’éducation chimique 85, n° 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>

calcul des concentrations d'équilibre

Il est essentiel de pouvoir calculer les concentrations à l'équilibre dans de nombreux domaines de la science et de la technologie, par exemple dans la formulation et le dosage des produits pharmaceutiques. Après l'ingestion ou l'injection d'un médicament, il est généralement impliqué dans plusieurs équilibres chimiques qui impactent sa concentration ultime dans le système corporel d'intérêt. La connaissance des aspects quantitatifs de ces équilibres est nécessaire pour calculer une dose qui sollicitera l'effet thérapeutique désiré. 
 Un type plus difficile de calcul d'équilibre peut être celui dans lequel les concentrations à l'équilibre sont déduites à partir des concentrations initiales et d'une constante d'équilibre. Pour ces calculs, une approche en quatre étapes est généralement utile : 
 <ol>
 <li>Identifier le sens dans lequel la réaction se poursuivra pour atteindre l'équilibre ; </li>
 <li>Concevoir un tableau ICE ; </li>
 <li>Calculer les changements de concentration et, par la suite, les concentrations d'équilibre ; </li>
 <li>Confirmer les concentrations à l'équilibre calculées. </li>
 </ol>
 Calcul des concentrations à l'équilibre 
 Dans certaines conditions, la constante d'équilibre Kc pour la décomposition de PCl5(g) en PCl3(g) et Cl2(g) est de 0,0211. La méthode ci-dessus peut être utilisée pour déterminer les concentrations à l'équilibre de PCl5, PCl3 et Cl2 dans un mélange qui contenait initialement seulement PCl5 à une concentration de 1,00 M. 
 Étape 1. Déterminer le sens de la réaction. 
 L'équation équilibrée pour la décomposition de PCl5 est 
 <img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />
 Étant donné que seul le réactif est initialement présent, Qc = 0, et la réaction se fera vers la droite. 
 Étape 2. Concevoir un tableau 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;">Concentration initiale (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;">Changement (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;">Concentration à l'équilibre (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>
 Étape 3. Résoudre pour déterminer le changement et les concentrations à l'équilibre. 
 La substitution des concentrations à l'équilibre dans l'équation de la constante d'équilibre donne 
 <img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />
 Une équation de la forme ax2 + bx + c = 0 peut être réorganisée pour résoudre x : 
 <img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />
 Dans ce cas, a = 1, b = 0,0211 et c = −0,0211. Le remplacement de a, b et c par les valeurs appropriées donne : 
 <img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />
 Les deux racines du quadratique sont donc, 
 <img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />
 Pour ce scénario, seule la racine positive est physiquement significative (les concentrations sont soit zéro, soit positives), et donc x = 0,135 M. Les concentrations à l'équilibre sont 
 <img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />
 Étape 4. Confirmer les concentrations à l'équilibre calculées. 
 La substitution dans l'expression de Kc (pour vérifier le calcul) donne 
 <img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />
 La constante d'équilibre calculée à partir des concentrations à l'équilibre est égale à la valeur de Kc donnée dans le problème (lorsqu'elle est arrondie au nombre approprié de chiffres significatifs). 
 Ce texte a été adapté d'<a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">Openstax, Chimie 2e, Section 13.4 Calculs d'équilibre</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a>

Calcul des concentrations d'équilibre

Être capable de calculer les concentrations à l’équilibre est essentiel dans de nombreux domaines de la science et de la technologie, par exemple, dans la formulation et le dosage ...

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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

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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)

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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.

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Equilibrium Concentrations from an ICE Table

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