Name: estimating equilibrium with small changes
Uploaded: 2020-10-19T09:47:37.000Z
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The Small x Assumption

L'hypothèse de x minuscule est une approximation qui peut être utilisée dans certaines conditions pour simplifier la résolution de l'expression d'équilibre et éviter d'utiliser la formule quadratique. Si la constante d'équilibre d'une réaction est faible et les concentrations initiales des réactifs sont suffisamment élevées, il est possible que seule une petite quantité de réactifs soit transformée en produits. Lorsque ces conditions sont réunies, les concentrations d'équilibre peuvent être rapprochées en supposant que le changement des concentrations initiales est négligeable.Cependant, il faut confirmer que le changement en concentration, x, est inférieure à 5 pour cent des concentrations initiales pour montrer que l'hypothèse était valide. La décomposition de 0, 66 molaire de dichlorure de carbonyle gazeux produit du monoxyde de carbone et du chlore gazeux, et la constante d'équilibre de cette réaction est de 2, 2 10⁻¹⁰. Pour calculer les concentrations d'équilibre, les valeurs sont tabulées dans le tableau ICE avec le changement et les concentrations d'équilibre.En substituant les concentrations d'équilibre dans l'expression, K est égal à x au carré divisé par 0, 66 moins x. Comme K est très faible, le changement de la concentration initiale, x, du dichlorure de carbonyle, devrait être négligeable. Par conséquent, 0, 66 moins x peut être rapproché de 0, 66.Une fois résolu, x est égal à 1, 2 10⁻⁵ molaire. Ici, x n'est que de 0, 0018%de la molaire initiale de 0, 66 concentration de dichlorure de carbonyle, qui est bien inférieur au maximum autorisé de 5%Ainsi, l'hypothèse du x minuscule est valable ici. En utilisant la valeur de x dans la table ICE, la concentration d'équilibre de dichlorure de carbonyle est toujours de 0, 66 molaire avec des chiffres significatifs, tandis que les concentrations de monoxyde de carbone et de chlore sont tous les deux de 1, 2 10⁻⁵ molaires.

<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>

négliger le changement de concentration initiale

Si une réaction a une petite constante d'équilibre, la position d'équilibre favorise les réactifs. Dans de telles réactions, un changement négligeable de la concentration peut se produire si les concentrations initiales des réactifs sont élevées et que la valeur de Kc est faible. Dans de telles circonstances, la concentration à l'équilibre est approximativement égale à sa concentration initiale.  Cette estimation peut être utilisée pour simplifier les calculs d'équilibre en supposant que certaines concentrations à l'équilibre sont égales aux concentrations initiales. Toutefois, pour faire cette supposition, le changement dans la concentration d'un acide ou d'une base faible, c'est-à-dire x, doit être inférieur à 5 % de sa concentration initiale. Si x est supérieur à 5 %, la formule quadratique doit être utilisée pour résoudre l'équation d'équilibre.   
 Calcul des concentrations à l'équilibre à l'aide d'une supposition de simplification algébrique 
 Quelles sont les concentrations à l'équilibre d'une solution de 0,15 M de HCN ? 
 <img alt="Eq1" src="/files/ftp_upload/11477/11477_Equation_1.png" style="text-align: center; height: 50px;" />
 L'utilisation de x pour représenter la concentration de chaque produit à l'équilibre donne ce 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;"> HCN (aq)           </td>
 <td style="color: black; border: 1px solid black; text-align: center;">H+ (aq) </td>
 <td style="color: black; border: 1px solid black; text-align: center;">CN− (aq) </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;">0,15 </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;">&8722;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;">0,15 − 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>
 Remplacez les termes des concentrations à l'équilibre dans l'expression de Kc 
 <img alt="Eq2" src="/files/ftp_upload/11477/11477_Equation_2.png" style="text-align: center; height: 95px;" />
 réorganisez la forme quadratique et résolvez pour trouver x
 <img alt="Eq3" src="/files/ftp_upload/11477/11477_Equation_3.png" style="text-align: center; height: 95px;" />
 Ainsi, [H+] = [CN–] = x = 8,6 × 10–6 M et [HCN] = 0,15 – x = 0,15 M. 
 Notez dans ce cas que le changement de concentration est significativement inférieur à la concentration initiale (conséquence du petit K), et que la concentration initiale présente donc un changement négligeable : 
 <img alt="Eq4" src="/files/ftp_upload/11477/11477_Equation_4.png" style="text-align: center; height: 50px;" />
 Cette approximation permet une approche mathématique plus rapide du calcul qui évite la nécessité de résoudre les racines d'une équation quadratique : 
 <img alt="Eq5" src="/files/ftp_upload/11477/11477_Equation_5.png" style="text-align: center; height: 135px;" />
 La valeur de x calculée est en effet beaucoup moins élevée que la concentration initiale 
 <img alt="Eq6" src="/files/ftp_upload/11477/11477_Equation_6.png" style="text-align: center; height: 50px;" />
 c'est pourquoi l'approximation était justifiée. Si cette approche simplifiée devait donner une valeur pour x ne justifiant pas l'approximation, le calcul devrait être répété sans procéder à l'approximation. 
 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-e

Négliger le changement de concentration initiale

Si une réaction a une petite constante d’équilibre, la position d’équilibre favorise les réactifs. Dans de telles réactions, un changement négligeable de la concentration peut ...

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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. The change in concentration is written as x. To use the shortcut, x must be less than 5% of the initial concentration. If x is greater than 5%, the quadratic formula is needed instead.

A solution of HCN shows how the approximation works. For a 0.15 M HCN solution, an ICE table gives HCN, H+, and CN− with initial concentrations of 0.15, 0, and 0 M. The change is −x for HCN and +x for each product, so the equilibrium concentrations are 0.15 − x, x, and x. Substituting these terms into the Kc expression and solving gives [H+] = [CN−] = 8.6 × 10−6 M and [HCN] = 0.15 M.

In this example, the calculated x is much smaller than the initial concentration. That means the initial HCN concentration changes very little. The shortcut is justified, and the calculation avoids solving a quadratic equation. If the result had not met the 5% rule, the calculation would need to be repeated without the approximation.

Estimating Equilibrium with Small Changes

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Le Chatelier's Principle in Heating and Cooling

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the small x assumption

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 a small equilibrium constant lets students use the 5% rule and an ICE table to estimate equilibrium concentrations without solving a quadratic.

Estimating Equilibrium with Small Changes | JoVE K12

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Estimating Equilibrium with Small Changes

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