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

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating the Equilibrium Constant

La costante di equilibrio, Kc, può essere determinata sostituendo i valori corrispondenti nell'espressione della costante di equilibrio, se sono noti le concentrazioni di tutti i reagenti e deii prodotti all'equilibrio. Una miscela gassosa di anidride solforosa e ossigeno a 530 gradi Celsius è lasciata reagire secondo la reazione mostrata. In equilibrio, la miscela contiene anidride solforosa 0, 10 molare, ossigeno 0, 15 molare e anidride solforosa 10, 88 molare.

Sostituendo i valori nell'espressione di equilibrio, Kc è uguale a 7, 9 10⁴. Il Kc può anche essere calcolato, purché sia nota la concentrazione iniziale di tutti i componenti e la concentrazione di equilibrio di almeno un composto. Le concentrazioni di equilibrio sconosciute possono, dunque, essere calcolate usando la stechiometria della reazione.

Una tabella ICE viene utilizzata per organizzare le informazioni per le concentrazioni iniziale, di cambiamento e di equilibrio della reazione. Quando si lascia che una miscela di reazione contenente azoto 0, 11 molare e idrogeno 0, 36 molare raggiunga l'equilibrio a 500 gradi Celsius, questa produce ammoniaca 0, 020 molare all'equilibrio. Per calcolare il Kc, è necessario determinare le concentrazioni di equilibrio dell'azoto e dell'idrogeno.

La stechiometria della reazione mostra che sono necessarie 1 mole di azoto gassoso e 3 moli di idrogeno gassoso per produrre 2 moli di ammoniaca gassosa. La variazione, x, se moltiplicata per i coefficienti dei reagenti e dei prodotti, denota la concentrazione dei reagenti consumati e la concentrazione del prodotto necessario per raggiungere l'equilibrio. Poiché 2x equivale a 0, 020, x è uguale a 0, 010.

La concentrazione di equilibrio di azoto e idrogeno può, quindi, essere determinata sottraendo la rispettiva variazione di concentrazione dalla loro concentrazione iniziale che è rispettivamente pari a 0, 10 e 0, 33 molare. Sostituendo le concentrazioni di equilibrio nell'espressione Kc, Kc equivale a 0, 11. Il Kp per le reazioni che coinvolgono i gas può essere calcolato utilizzando una tabella ICE e l'espressione di equilibrio scritta con pressioni parziali.

calcolo della costante di equilibrio

La costante di equilibrio di una reazione viene calcolata dalle concentrazioni di equilibrio (o pressioni) dei suoi reagenti e prodotti. Se queste concentrazioni sono note, il calcolo prevede semplicemente la loro sostituzione nell'espressione K_c.

Ad esempio, il biossido di azoto gassoso forma tetrossido di diazoto secondo questa equazione:

<img alt="Eq1" src="/files/ftp_upload/11388/11388_Equation_1.png" style="text-align: center; height: 50px;" />

Quando si aggiungono 0,10 mol di NO_2 in un pallone da 1,0 L a 25 °C, la concentrazione cambia in modo che all'equilibrio, [NO_2] = 0,016 M e [N_2O_4] = 0,042 M. Il valore della costante di equilibrio per la reazione può essere calcolato come segue:

<img alt="Eq2" src="/files/ftp_upload/11388/11388_Equation_2.png" style="text-align: center; height: 90px;" />

Di seguito viene fornito un esempio leggermente più impegnativo, in cui la stechiometria della reazione viene utilizzata per ricavare le concentrazioni di equilibrio dalle informazioni fornite. La strategia di base di questo calcolo è utile per molti tipi di calcoli di equilibrio e si basa sull'uso di termini per le concentrazioni di reagenti e prodotti inizialmente presenti, su come cambiano man mano che la reazione procede e su cosa sono quando il sistema raggiunge l'equilibrio. L'acronimo ICE è comunemente usato per riferirsi a questo approccio matematico e i termini di concentrazione sono solitamente raccolti in un formato tabellare chiamato tabella ICE.

Calcolo di una costante di equilibrio

Le molecole di iodio reagiscono in modo reversibile con gli ioni ioduro per produrre ioni triioduro.

<img alt="Eq3" src="/files/ftp_upload/11388/11388_Equation_3.png" style="text-align: center; height: 50px;" />

Se una soluzione con le concentrazioni di I_2 e I− entrambe uguali a 1.000 × 10^−3 M prima della reazione dà una concentrazione di equilibrio di I_2 di 6,61 × 10^−4 M, qual è la costante di equilibrio per la reazione?

Per calcolare le costanti di equilibrio, sono necessarie le concentrazioni di equilibrio per tutti i reagenti e i prodotti:

<img alt="Eq4" src="/files/ftp_upload/11388/11388_Equation_4.png" style="text-align: center; height: 90px;" />

Vengono fornite le concentrazioni iniziali dei reagenti e la concentrazione di equilibrio del prodotto. Queste informazioni possono essere utilizzate per derivare termini per le concentrazioni di equilibrio dei reagenti, presentando tutte le informazioni in 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;">      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>

All'equilibrio la concentrazione di I_2 è 6,61 × 10^−4 M quindi

<img alt="Eq5" src="/files/ftp_upload/11388/11388_Equation_5.png" style="text-align: center; height: 90px;" />

La tabella ICE può ora essere aggiornata con valori numerici per tutte le sue concentrazioni:

<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>

Infine, le concentrazioni all'equilibrio possono essere sostituite nell'espressione K_c e risolte:

<img alt="Eq6" src="/files/ftp_upload/11388/11388_Equation_6.png" style="text-align: center; height: 90px;" />

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>

Calcolo della costante di equilibrio

La costante di equilibrio per una reazione è calcolata dalle concentrazioni di equilibrio (o pressioni) dei suoi reagenti e prodotti. Se questi ...

Education

Didattica

JoVE Core

Chimica

Chemical Equilibrium

Equilibrio chimico

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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

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)

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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

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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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Physical Science

Chemical Reactions

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Finding Kc from Equilibrium Data

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