Name: estimating equilibrium with small changes
Uploaded: 2020-10-19T09:47:37.000Z
Duration: 2 min 20 s
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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

The Small x Assumption

Küçük x varsayımı, belirli koşullar altında denge ifadesinin çözümünü basitleştirmek ve ikinci dereceden formülü kullanmaktan kaçınmak için kullanılabilen bir yaklaşımdır. Bir reaksiyon için denge sabiti küçükse ve reaktanların başlangıç konsantrasyonları yeterince yüksekse, yalnızca küçük bir miktar reaktan ürünlere dönüştürülebilir. Bu koşullar karşılandığında, denge konsantrasyonları, başlangıç konsantrasyonlarındaki değişimin ihmal edilebilir olduğu varsayımı kullanılarak tahmin edilebilir.Ancak, varsayımın geçerli olduğunu göstermek için konsantrasyondaki değişikliğin başlangıç konsantrasyonlarının yüzde 5'inden daha az olduğu doğrulanmalıdır. 0, 66 molar karbonil diklorür gazının ayrışması, karbon monoksit ve klor gazı üretir ve bu reaksiyon için denge sabiti 2, 2×10⁻¹⁰'dur. Denge konsantrasyonlarını hesaplamak için değerler ICE tablosunda değişim ve denge konsantrasyonları ile birlikte tablo halinde verilmiştir.İfadedeki denge konsantrasyonlarını ikame ederek, K eşittir x kare bölü 0, 66 eksi x. K çok küçük olduğu için, karbonil diklorürün başlangıç konsantrasyonu olan x'teki değişikliğin ihmal edilebilir olması beklenir. Bu nedenle, 0, 66 eksi x, 0, 66'ya yaklaştırılabilir.Çözüldüğünde, x 1, 2×10⁻⁵ molara eşittir. Burada, x, karbonil diklorürün başlangıçtaki 0, 66 molar konsantrasyonunun yalnızca yüzde 0, 0018'idir ve bu, izin verilen maksimum yüzde 5'ten çok daha azdır. Böylece, küçük x varsayımı burada geçerlidir.ICE tablosundaki x değeri kullanıldığında, karbonil diklorürün denge konsantrasyonu önemli rakamlarla hala 0, 66 molar iken, klor konsantrasyonlarının her ikisi de are both 1, 2×10⁻⁵ molardır.

<ol>
	<li>Lim, Kieran F. "Kimyada grafik hesap makinelerini ve elektronik tabloları kullanma: Denge problemlerini çözme." Kimya Eğitimi Dergisi 85, no. 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>

küçük x varsayımı

Bir tepkimenin denge sabiti küçükse, denge konumu reaktanlardan yanadır. Bu tür reaksiyonlarda, reaktanların başlangıç konsantrasyonları yüksekse ve Kc değeri küçükse, konsantrasyonda ihmal edilebilir bir değişiklik meydana gelebilir. Bu gibi durumlarda, denge konsantrasyonu yaklaşık olarak başlangıç konsantrasyonuna eşittir.  Bu tahmin, bazı denge konsantrasyonlarının başlangıç konsantrasyonlarına eşit olduğu varsayılarak denge hesaplamalarını basitleştirmek için kullanılabilir. Ancak, bu varsayımı yapmak için, zayıf bir asit veya bazın konsantrasyonundaki değişiklik, yani x, başlangıç konsantrasyonunun %5'inden az olmalıdır. x %5'ten fazlaysa, denge denklemini çözmek için ikinci dereceden formül kullanılmalıdır.  
 
 Cebirsel Sadeleştirme Varsayımı Kullanılarak Denge Konsantrasyonlarının Hesaplanması
 
 0,15 M HCN çözeltisinin dengesindeki konsantrasyonlar nelerdir?
 
 <img alt="Eq1" src="/files/ftp_upload/11477/11477_Equation_1.png" style="text-align: center; height: 50px;" />
 
 Dengedeki her bir ürünün konsantrasyonlarını açıklamak için x’in kullanılması şu ICE tablosunu verir.
 <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;">Başlangıç Konsantrasyonu (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;">Değişim (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;">Denge Konsantrasyonu (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>
 
 Denge konsantrasyonu terimlerini Kc ifadesiyle değiştirin
 
 <img alt="Eq2" src="/files/ftp_upload/11477/11477_Equation_2.png" style="text-align: center; height: 95px;" />
 
 kuadratik formu yeniden düzenleyin ve x’i çözün.
 
 <img alt="Eq3" src="/files/ftp_upload/11477/11477_Equation_3.png" style="text-align: center; height: 95px;" />
 
 Bu yüzden, [H+] = [CN–] = x = 8,6 × 10–6 M and [HCN] = 0,15 – x = 0,15 M.
 
 Bu durumda konsantrasyondaki değişikliğin ilk konsantrasyondan önemli ölçüde daha az olduğuna (küçük K'nin bir sonucu) ve dolayısıyla ilk konsantrasyonun ihmal edilebilir bir değişiklik yaşadığına dikkat edin:
 
 <img alt="Eq4" src="/files/ftp_upload/11477/11477_Equation_4.png" style="text-align: center; height: 50px;" />
 
 Bu yaklaşım, ikinci dereceden bir denklemin köklerini çözme ihtiyacını ortadan kaldıran hesaplamaya daha uygun bir matematiksel yaklaşım sağlar:
 
 <img alt="Eq5" src="/files/ftp_upload/11477/11477_Equation_5.png" style="text-align: center; height: 135px;" />
 
 Hesaplanan x değeri gerçekten de başlangıç konsantrasyonundan çok daha azdır
 
 <img alt="Eq6" src="/files/ftp_upload/11477/11477_Equation_6.png" style="text-align: center; height: 50px;" />
 
 ve böylece yaklaşım doğrulanmış olur. Bu basitleştirilmiş yaklaşım, x için yaklaşımı doğrulamayan bir değer verecek olsaydı, hesaplamanın yaklaşım yapılmadan tekrarlanması gerekirdi.
 
 Bu metin bu kaynaktan uyarlanmıştır: <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>

Küçük x Varsayımı

Bir reaksiyonun küçük bir denge sabiti varsa, denge konumu reaktanları tercih eder. Bu tür reaksiyonlarda, konsantrasyonda ihmal edilebilir bir değişiklik ...

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Kimyasal Denge

KEY TERMS AND CONCEPTS

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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

estimating-equilibrium-with-small-changes

the equilibrium constant

Chemical Equilibrium and Kc Rules

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le chatelier's principle: changing concentration

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Shifting Equilibrium by Changing Concentration

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Finding Kc from Equilibrium Data

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le chatelier's principle: changing volume (pressure)

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le chatelier's principle: changing temperature

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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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