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

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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

Неизвестные равновесные концентрации могут быть определены из начальной концентрации исходных веществ и константы равновесия K для реакции. Рассмотрим реакцию, в которой 0, 30 моль газообразного азота и 0, 40 моль газообразного кислорода реагируют с образованием газообразного оксида азота и где K равно 0, 10. Для расчета равновесных концентраций известные значения занесены в таблицу концентраций.Для изменения концентрации увеличение или уменьшение для каждого продукта или исходного вещества, соответственно, обозначается как x, умноженное на его стехиометрический коэффициент. Сумма или разность используются для нахождения равновесных концентраций, которые затем подставляются в выражение равновесия. Чтобы найти x, выражение расширяется, и все члены переносятся в одну сторону, чтобы преобразовать его в форму:ax в квадрате плюс bx плюс c.Это уравнение можно решить, используя формулу корней квадратного уравнения. Решение дает два значения для x:0, 047 и минус 0, 065. Поскольку отрицательная концентрация вещества невозможна, это значение можно отклонить.Используя 0, 047 для x, равновесные концентрации азота, кислорода и оксида азота равны 0, 25, 0, 35 и 0, 094 молярных долей соответственно. Условие идеального квадрата это одна из ситуаций, когда можно сократить решение, чтобы избежать квадратной формулы. Например, если начальные концентрации азота и кислорода в указанной выше реакции составляли по 0, 30 моль, уравнение превращается в полный квадрат.В таких случаях уравнение можно упростить, взяв квадратный корень из обеих частей для определения x.

<ol>
	<li>Лим, Киран Ф. "Использование графических калькуляторов и электронных таблиц в химии: решение проблем равновесия." Журнал химического образования 85, No10 (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>

Расчет равновесных концентраций

Способность рассчитать равновесные концентрации имеет важное значение для многих областей науки и техники, например, при разработке и дозировании фармацевтических продуктов. После проглатывания или введения препарата он обычно участвует в нескольких химических равновесии, которые влияют на его конечную концентрацию в системе интереса. Знание количественных аспектов этих равновесий необходимо для расчета дозы, которая будет добиваться желаемого терапевтического эффекта. 
 Более сложным типом расчета равновесия может быть расчет равновесных концентраций, производных от начальных концентраций и константы равновесия. Для этих расчетов обычно используется четырехэтапный подход: 
 <ol>
 <li>Определите направление, в котором реакция будет двигаться к равновесию. </li>
 <li>Разработайте ледяной стол. </li>
 <li>Рассчитайте изменения концентрации и затем равновесные концентрации. </li>
 <li>Подтвердите расчетные концентрации равновесия. </li>
 </ol>
 Расчет равновесных концентраций 
 При определенных условиях равновесная константа Kc разложения PCL5(g) на PCl3(g) и Cl2(g) составляет 0.0211. Описанная выше процедура может использоваться для определения равновесных концентраций PCL5, PCl3 и Cl2 в смеси, которая изначально содержала только PCL5 в концентрации 1.00 M. 
 Шаг 1. Определите направление, в котором идет реакция. 
 Сбалансированное уравнение разложения PCL5 составляет 
 <img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />
 Поскольку изначально присутствует только реагент, QC = 0, и реакция будет идти вправо. 
 Шаг 2. Разработайте ледяной стол. 
 <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;">Начальная концентрация (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;">Изменение (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;">Равновесная концентрация (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>
 Шаг 3. Решите для изменения и равновесных концентраций. 
 Подстановка равновесных концентраций в уравнение равновесной константы дает 
 <img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />
 Уравнение формы ax2 + bx + c = 0 можно изменить для решения для x: 
 <img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />
 В этом случае a = 1, b = 0.0211 и c = -0.0211. Подстановка соответствующих значений для a, b и c дает: 
 <img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />
 Таким образом, два корня квадрата являются 
 <img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />
 Для этого сценария физически значимым является только положительный корень (концентрации равны нулю или положительны), и поэтому x = 0.135 M. равновесные концентрации являются 
 <img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />
 Шаг 4. Подтвердите расчетные концентрации равновесия. 
 Подстановка в выражение для Kc (для проверки вычисления) дает 
 <img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />
 Константа равновесия, рассчитанная на основе равновесных концентраций, равна значению Kc, данному в задаче (округляется до правильного количества значительных цифр). 
 Этот текст был адаптирован к расчетам<a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations"> равновесия Openstax, Химия 2е изд., раздел 13.4</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a>

Возможность расчета равновесных концентраций имеет важное значение для многих областей науки и техники, например, для разработки и дозирования ...

Education

JoVE Core

Химия

Один

Chemical Equilibrium

Химическое равновесие

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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

le-chatelier-s-principle-changing-temperature

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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Equilibrium Concentrations from an ICE Table

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