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

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating Equilibrium Concentrations

Concentrazioni di equilibrio sconosciute possono essere determinate dalla concentrazione iniziale dei reagenti e dalla costante di equilibrio, K, per la reazione. Si consideri la reazione in cui 0, 30 molare di azoto gassoso e 0, 40 molare di ossigeno gassoso reagiscano per produrre ossido di azoto, e dove K è 0, 10. Per calcolare le concentrazioni di equilibrio, i valori noti sono tabulati in una tabella ICE.

Per la variazione di concentrazione, l'aumento o la diminuzione per ciascun prodotto o reagente, rispettivamente, è indicata con x volte il suo coefficiente stechiometrico. La somma o la differenza viene utilizzata per trovare le concentrazioni di equilibrio, che vengono poi sostituite nell'espressione di equilibrio. Per risolvere per x, l'espressione viene espansa e tutti i termini vengono messi da parte per convertirla nella forma:ax al quadrato più bx più c.

Questa equazione può essere risolta usando la formula quadratica. La risoluzione produce due valori per x:0, 047 e 0, 065 negativo. Poiché la concentrazione negativa di una sostanza è impossibile, tale valore può essere rifiutato.

Usando 0, 047 per x, le concentrazioni di equilibrio di azoto, ossigeno e ossido nitrico sono pari, rispettivamente, a 0, 25, 0, 35 e 0, 094 molare. La condizione quadratica perfetta è una situazione ove è possibile utilizzare una scorciatoia per evitare la formula quadratica. Per esempio, le concentrazioni iniziali di azoto e ossigeno nella reazione di cui sopra erano 0, 30 molare ciascuna, l'equazione diventa un quadrato perfetto.

In questi casi, l'equazione può essere semplificata prendendo la radice quadrata di ambo i lati per risolvere x.

<ol>
	<li>Lim, Kieran F. "Utilizzo di calcolatrici grafiche e fogli di calcolo in chimica: risoluzione di problemi di equilibrio". Giornale di educazione chimica 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>

calcolo delle concentrazioni di equilibrio

Essere in grado di calcolare le concentrazioni di equilibrio è essenziale in molti settori della scienza e della tecnologia, ad esempio nella formulazione e nel dosaggio dei prodotti farmaceutici. Dopo che un farmaco è stato ingerito o iniettato, è tipicamente coinvolto in diversi equilibri chimici che influenzano la sua concentrazione finale nel sistema corporeo di interesse. La conoscenza degli aspetti quantitativi di questi equilibri è necessaria per calcolare una quantità di dosaggio che solleciterà l'effetto terapeutico desiderato.

Un tipo più impegnativo di calcolo dell'equilibrio può essere quello in cui le concentrazioni di equilibrio vengono derivate dalle concentrazioni iniziali e da una costante di equilibrio. Per questi calcoli, in genere è utile un approccio in quattro fasi:

<ol>
	<li>Identificare la direzione in cui procederà la reazione per raggiungere l’equilibrio.</li>
	<li>Sviluppare una tabella ICE.</li>
	<li>Calcolare le variazioni di concentrazione e, successivamente, le concentrazioni di equilibrio.</li>
	<li>Confermare le concentrazioni di equilibrio calcolate.</li>
</ol>

Calcolo delle concentrazioni di equilibrio

In determinate condizioni, la costante di equilibrio Kc per la decomposizione di PCl_5(g) in PCl_3(g) e Cl_2(g) è 0,0211. La procedura sopra descritta può essere utilizzata per determinare le concentrazioni di equilibrio di PCl_5, PCl_3 e Cl_2 in una miscela che inizialmente conteneva solo PCl_5 ad una concentrazione di 1,00 M.

Passaggio 1. Determinare la direzione in cui procede la reazione.

L'equazione bilanciata per la decomposizione di PCl5 è

<img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />

Perché inizialmente è presente solo il reagente, Q_c = 0, e la reazione procederà verso destra.

Passaggio 2. Sviluppare una tabella 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;">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>

Passaggio 3. Risolvere la variazione e le concentrazioni di equilibrio.

Sostituendo le concentrazioni di equilibrio nell'equazione della costante di equilibrio si ottiene

<img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />

Un'equazione della forma ax_2 + bx + c = 0 può essere riorganizzata per risolvere x:

<img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />

In questo caso, a = 1, b = 0,0211 e c = −0,0211. Sostituendo i valori appropriati per a, b e c si ottiene:

<img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />

Le due radici della quadratica sono quindi:

<img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />

Per questo scenario, solo la radice positiva è fisicamente significativa (le concentrazioni sono zero o positive), quindi x = 0,135 M. Le concentrazioni di equilibrio sono:

<img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />

Passaggio 4. Confermare le concentrazioni di equilibrio calcolate.

Si ottiene la sostituzione nell'espressione per K_c (per verificare il calcolo).

<img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />

La costante di equilibrio calcolata dalle concentrazioni di equilibrio è uguale al valore di K_c indicato nel problema (se arrotondato al numero appropriato di cifre significative).

Questo testo è adattato da <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>

Calcolo delle concentrazioni di equilibrio

Essere in grado di calcolare le concentrazioni di equilibrio è essenziale per molte aree della scienza e della tecnologia, ad esempio nella formulazione e nel dosaggio ...

Education

Didattica

JoVE Core

Chimica

Chemical Equilibrium

Equilibrio chimico

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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)

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

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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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Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.F

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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

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High School

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HS+C.P1U1.6

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Matter and Its Interactions

HS-PS1-6

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SC.912.P.12.13

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New York State Science Learning Standards

HS. Chemical Reactions

HS-PS1-6.

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Equilibrium Concentrations from an ICE Table

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