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

Las concentraciones de equilibrio desconocidas se pueden determinar a partir de la concentración inicial de los reactivos y la constante de equilibrio, K, para la reacción. Considere la reacción donde reaccionan 0, 30 de gas nitrógeno molar y 0, 40 de gas oxígeno molar para producir gas óxido nítrico y donde K es 0, 10. Para calcular las concentraciones de equilibrio, los valores conocidos se tabulan en una tabla ICE.Para el cambio de concentración, el aumento o la disminución de cada producto o reactivo, respectivamente, se denota x veces su coeficiente estequiométrico. La suma o diferencia se usa para encontrar las concentraciones de equilibrio, que luego se sustituyen en la expresión de equilibrio. Para resolver x, la expresión se expande y todos los términos se colocan en un lado para convertirla en la forma:a x al cuadrado más bx más c.Esta ecuación se puede resolver usando la fórmula cuadrática. La resolución da como resultado dos valores para x:0, 047 y 0, 065 negativo. Como la concentración negativa de una sustancia es imposible, el valor puede rechazarse.Usando 0, 047 para x, las concentraciones de equilibrio de nitrógeno, oxígeno y óxido nítrico equivalen a 0, 25, 0, 35 y 0, 094 molar, respectivamente. La condición del cuadrado perfecto es una situación en la que se puede usar una alternativa para evitar la fórmula cuadrática. Por ejemplo, las concentraciones iniciales de nitrógeno y oxígeno en la reacción anterior fueron 0, 30 molar cada una, la ecuación se convierte en un cuadrado perfecto En tales casos, la ecuación se puede simplificar tomando la raíz cuadrada de ambos lados para resolver x.

<ol>
	<li>Lim, Kieran F. "Uso de calculadoras gráficas y hojas de cálculo en química: resolución de problemas de equilibrio". Revista de Educación Química 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>

calculando las concentraciones en equilibrio

La capacidad de calcular las concentraciones en equilibrio es esencial para muchas áreas de la ciencia y la tecnología, por ejemplo, en la formulación y dosificación de productos farmacéuticos. Después de ingerir o inyectar un fármaco, típicamente este se involucra en varios equilibrios químicos que afectan su concentración final en el sistema corporal de interés. Se requiere conocimiento de los aspectos cuantitativos de estos equilibrios para calcular una dosis que brinde el efecto terapéutico deseado.
 Un tipo de cálculo de equilibrio más difícil puede ser aquel en el que las concentraciones en equilibrio se derivan de las concentraciones iniciales y de una constante de equilibrio. Para estos cálculos, puede ser útil un enfoque de cuatro pasos:
 <ol>
 <li>Identifique la dirección en la que la reacción procederá para alcanzar el equilibrio.</li>
 <li>Desarrolle una tabla ICE.</li>
 <li>Calcule los cambios de concentración y, posteriormente, las concentraciones en equilibrio.</li>
 <li>Confirme las concentraciones en equilibrio calculadas.</li>
 </ol>
 Cálculo de las concentraciones en equilibrio
 En determinadas condiciones, la constante de equilibrio Kc para la descomposición de PCL5(g) en PCl3(g) y Cl2(g) es de 0,0211. El procedimiento anterior puede utilizarse para determinar las concentraciones en equilibrio de PCL5, PCl3 y Cl2 en una mezcla que inicialmente contenía sólo PCL a una concentración de 1,00 M.
 Paso 1.Determine la dirección en la que procede la reacción.
 La ecuación balanceada para la descomposición de PCL5 es
 <img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />
 Dado que al principio sólo está presente el reactivo, Qc = 0 y la reacción procederá hacia la derecha.
 Paso 2. Desarrolle una tabla 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;"> PCL3g)   </td>
 <td style="color: black; border: 1px solid black; text-align: center;"> Cl2g)   </td>
 </tr>
 <tr>
 <td style="color: black; border: 1px solid black; text-align: center;">Concentración inicial (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;">Cambio (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;">Concentración en equilibrio (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>
 Paso 3.Resuelva para hallar el cambio de concentración y las concentraciones en equilibrio.
 La sustitución de las concentraciones en equilibrio en la ecuación de la constante de equilibrio da
 <img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />
 Una ecuación de la forma ax2 + bx + c = 0 puede ser reorganizada para hallar el valor de x:
 <img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />
 En este caso, a = 1, b = 0,0211 y c = −0,0211. Si se sustituyen los valores adecuados para a, b y c, se produce:
 <img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />
 Las dos raíces cuadradas son, por lo tanto,
 <img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />
 Para este escenario, sólo la raíz positiva es físicamente significativa (las concentraciones son cero o positivas), y así x = 0,135 M. Las concentraciones en equilibrio son
 <img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />
 Paso 4.Confirme las concentraciones en equilibrio calculadas.
 La sustitución de Kc en la expresión (para verificar el cálculo) da
 <img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />
 La constante de equilibrio calculada a partir de las concentraciones en equilibrio es igual al valor de Kc indicado en el problema (cuando se redondea al número adecuado de cifras significativas).
 Este texto ha sido adaptado de<a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations"> Openstax, Química 2e, Sección 13.4 Cálculos de Equilibrio</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a>

Calculando las Concentraciones en Equilibrio

Ser capaz de calcular las concentraciones de equilibrio es esencial para muchas áreas de la ciencia y la tecnología, por ejemplo, en la formulación y la dosificación ...

Education

Educación

JoVE Core

Química

Chemical Equilibrium

Equilibrio químico

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

homogeneous-equilibria-for-gaseous-reactions

Relating Kc and Kp in Gas Equilibria

Gas-phase equilibrium can be written using either concentration or pressure. The equilibrium constant may be shown as Kc, which uses molar concentration, or as Kp, which uses partial pressure of the reactants and products. The link between Kc and Kp comes from the ideal gas equation and the definition of molarity. Molarity is the number of moles divided by volume. In the ideal gas equation, P stands for partial pressure, V for volume, n for number of moles, R for the gas constant, and T for...

le chatelier's principle: changing concentration

le-chatelier-s-principle-changing-concentration

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.

Equilibrium Concentrations from an ICE Table | JoVE K12

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Chemical Reactions

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New York State Science Learning Standards

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Equilibrium Concentrations from an ICE Table

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