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

As concentrações com equilíbrio desconhecido Podem ser determinadas a partir da concentração inicial dos reagentes e da constante de equilíbrio, K, para a reação. Consideremos a reação em que 0, 30 molar de nitrogénio gasoso e 0, 40 molar de oxigénio gasoso reagem para produzir gás de óxido nítrico e onde K é 0, 10. Para calcular as concentrações de equilíbrio, os valores conhecidos são tabelados numa tabela ICE.Para a alteração na concentração, o aumento ou a diminuição De cada produto ou reagente, respectivamente, é denotado por x vezes o seu coeficiente estequiométrico. A soma ou diferença é utilizada para encontrar as concentrações de equilíbrio, que são então substituídas na expressão de equilíbrio. Para resolver x, a expressão é expandida e todos os termos são colocados de um lado para a converter na forma:eixo ao quadrado mais bx mais c.Esta equação pode ser resolvida utilizando a fórmula quadrática. A resolução dos resultados em dois valores para x:0, 047 e negativo 0, 065. Como a concentração negativa de uma substância é impossível, o valor pode ser rejeitado.Utilizando 0, 047 para x, as concentrações de equilíbrio de nitrogénio, oxigénio, e óxido nítrico são 0, 25, 0, 35, e 0, 094 molar, respectivamente. A condição de quadrado perfeito é uma situação onde pode ser utilizado um atalho para evitar a fórmula quadrática. Por exemplo, as concentrações iniciais de nitrogénio e oxigénio na reação referida acima foram de 0, 30 molar cada, a equação torna-se um quadrado perfeito.Nestes casos, a equação pode ser simplificada, usando a raiz quadrada de ambos os lados para resolver x.

<ol>
	<li>Lim, Kieran F. "Usando calculadoras gráficas e planilhas em química: resolvendo problemas de equilíbrio." Jornal de Educação 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>

cálculo das concentrações de equilíbrio

Ser capaz de calcular concentrações de equilíbrio é essencial para muitas áreas de ciência e tecnologia, por exemplo, na formulação e dosagem de produtos farmacêuticos. Depois de um fármaco ser ingerido ou injetado, é envolvido tipicamente em diversos equilíbrios químicos que afetam a sua concentração final no sistema de interesse no corpo. O conhecimento dos aspectos quantitativos desses equilíbrios é necessário para calcular uma quantidade de dosagem que irá fornecer o efeito terapêutico desejado.
Um tipo mais desafiante de cálculo de equilíbrio pode ser aquele em que as concentrações de equilíbrio são derivadas das concentrações iniciais e de uma constante de equilíbrio. Para esses cálculos, uma abordagem de quatro passos é normalmente útil:
<ol>
<li>Identificar a direção na qual a reação irá avançar para atingir o equilíbrio.</li>
<li>Desenvolver uma tabela ICE.</li>
<li>Calcular as alterações de concentração e, posteriormente, as concentrações de equilíbrio.</li>
<li>Confirmar as concentrações de equilíbrio calculadas.</li>
</ol>
Cálculo das Concentrações de Equilíbrio
Em determinadas condições, a constante de equilíbrio Kc para a decomposição de PCl5(g) em PCl3(g) e Cl2(g) é 0,0211. O procedimento acima pode ser utilizado para determinar as concentrações de equilíbrio de PCl5, PCl3, e Cl2 em uma mistura que inicialmente continha apenas PCl5 a uma concentração de 1,00 M.
Passo 1. Determinar a direção em que a reação prossegue.
A equação equilibrada para a decomposição de PCl5 é
<img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />
Como apenas o reagente está presente inicialmente, Qc = 0, e a reação irá prosseguir para a direita.
Passo 2. Desenvolver uma tabela 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;">Concentração 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;">Alteração (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;">Concentração em Equilíbrio (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>
Passo 3. Resolver para a alteração e as concentrações de equilíbrio.
Substituir as concentrações de equilíbrio na equação da constante de equilíbrio dá
<img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />
Uma equação do formato ax2 + bx + c = 0 pode ser rearranjada para resolver para x:
<img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />
Neste caso, a = 1, b = 0,0211, e c = −0,0211. Substituir os valores apropriados para a, b, e c produz:
<img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />
As duas raízes da quadrático são, portanto,
<img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />
Para este cenário, apenas a raiz positiva é fisicamente significativa (as concentrações são zero ou positivas), e por isso x = 0,135 M. As concentrações de equilíbrio são
<img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />
Passo 4. Confirmar as concentrações de equilíbrio calculadas.
A substituição na expressão para Kc (para verificar o cálculo) dá
<img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />
A constante de equilíbrio calculada a partir das concentrações de equilíbrio é igual ao valor de Kc dado no problema (quando arredondado para o número adequado de valores significativos).
Este texto foi adaptado de <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>

Cálculo das Concentrações de Equilíbrio

Ser capaz de calcular concentrações de equilíbrio é essencial para muitas áreas da ciência e tecnologia - por exemplo, na formulação e dosagem ...

Education

JoVE Core

Química

Chemical Equilibrium

Equilíbrio Químico

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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)

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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Physical Science

Chemical Reactions

3.2.9-12.F

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New York State Science Learning Standards

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Equilibrium Concentrations from an ICE Table

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