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

未知の平衡濃度は、反応物の初期濃度と反応の平衡定数Kから決定できます。
0.30モルの窒素ガスと0.40モルの酸素ガスが反応して一酸化窒素ガスを生成し、Kが0.10である反応を考えてみましょう。平衡濃度を計算するために、既知の値がICEテーブルに表にまとめられます。
濃度の変化については、各生成物または反応物の増加または減少は、それぞれその化学量論的係数のx倍で表されます。合計または差は、平衡濃度を見つけるために使用され、平衡式に代入されます。
x を解くために、式が拡張され、すべての項が片側に置かれて、ax2 + bx + c の形式に変換されます。この方程式は、二次方程式の公式を使用して解くことができます。
解析の結果は、x に対して 0.047 と −0.065 の 2 つの値になります。物質の負の濃度は不可能であるため、値を拒否できます。
x に 0.047 を使用すると、窒素、酸素、一酸化窒素の平衡濃度は、それぞれ 0.25、0.35、0.094 モルに等しくなります。
完全二乗条件は、2次式を避けるためにショートカットを使用できる1つの状況です。
例えば、上記の反応における窒素と酸素の初期濃度がそれぞれ0.30モルであった場合、方程式は完全な二乗になります。このような場合、方程式は、xを解くために両側の平方根を取ることによって単純化できます。

<ol>
	<li>「化学におけるグラフィックス計算機とスプレッドシートの使用:平衡問題の解決」 Journal of Chemical Education 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>

平衡濃度の計算

平衡濃度を計算することは、科学技術の多くの分野で不可欠です。例えば、医薬品の処方や投与においても同様です。医薬品は、摂取または注射された後、対象となる体内の最終的な濃度に影響を与えるいくつかの化学平衡に関与しています。望ましい治療効果を得るための投与量を計算するには、これらの平衡の定量的な側面に関する知識が必要です。
 より困難とされる平衡計算は、初期濃度と平衡定数から平衡濃度を導き出すものです。このような計算では、一般的に4つのステップのアプローチが有効です。
 <ol>
 <li>平衡に達するまでの反応の進行方向を明らかにする</li>
 <li>ICE表を作成する</li>
 <li>濃度変化を計算し、続いて平衡濃度を計算する</li>
 <li>算出された平衡濃度を確認する</li>
 </ol>
 平衡状態における濃度の計算
 ある条件下で、PCl5(g)をPCl3(g)とCl2(g)に分解する際の平衡定数Kcは0.0211です。上記の手順は、最初に1.00 Mの濃度のPCl5のみを含む混合物中のPCl5、PCl3、およびCl2の平衡濃度を決定するために使用することができます。
 Step 1. 反応の進行方向の決定
 PCl5の分解の平衡式は、
 <img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />
 最初は反応物しか存在しないので、Qc = 0となり、反応は右に進む。
 Step 2. ICE表の作成
 <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;">初期濃度 (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;">濃度変化 (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;">平衡濃度 (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>
 Step 3. 変化量と平衡濃度を解く
 平衡定数の式に平衡濃度を代入すると、次のようになります。
 <img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />
 ax2 + bx + c = 0という形の方程式は、xを解くために並べ替えることができます。
 <img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />
 この場合、a = 1、b = 0.0211、c = −0.0211となります。a、b、cに適切な値を代入すると、次のようになります。
 <img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />
 したがって、この二次関数の2つの解は、次のようになります。
 <img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />
 この問題では、解のうち正の値だけが物理的に意味を持つ（濃度はゼロか正のどちらかのため）ので、x = 0.135 Mとなり、平衡濃度は次の通りです。
 <img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />
 Step 4. 算出された平衡濃度の確認
 Substitution into the expression for Kc(to check the calculation) gives
 <img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />
 平衡濃度から計算された平衡定数は、問題で与えられたKcの値と等しい（適切な有効数字に丸めた場合）。
 上記の文章は以下から引用しました。 <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>

平衡濃度を計算できることは、科学技術の多くの分野にとって不可欠です—たとえば、製剤や投与...

Education

JoVE Core

化学

Chemical Equilibrium

化学平衡

KEY TERMS AND CONCEPTS

主要用語と概念

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

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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

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

chemistry

JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

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

HS+C.P1

HS+C.P1U1.6

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-6

Florida Department of Education

SC.912.P.12

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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