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

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating Equilibrium Concentrations

알려지지 않은 평형 농도는 반응물의 초기 농도와 반응의 평형 상수 K로 결정할 수 있습니다. 질소 기체 0.30 몰과 산소 기체 0.40 몰이 반응하여 산화질소를 생성하는 반응을 봅시다. 여기서 K는 0.10입니다.

평형 농도를 계산하기 위해 알려진 값을 ICE 표에 정리합니다. 농도 변화에 대해 각 생성물 또는 반응물에 대한 증가 또는 감소는 각 제품의 화학당량 계수의 x배로 나타냅니다. 합계 또는 차이를 사용하여 평형 농도를 계산하며 이 농도는 평형식으로 대입됩니다.

x를 풀기 위해 식을 확장하여 모든 항을 한쪽에 배치하여 ax의 두제곱 플러스 bx 플러스 c 형식으로 변환됩니다. 이 방정식은 2차식을 사용하여 풀 수 있습니다. 식을 풀면 x에 대해 두개 값 0.047과 마이너스 0.065가 얻어집니다.

물질의 농도에서 부의 값은 있을 수 없으므로 부의 값은 제외됩니다. x의 값으로 0.047을 사용하면 질소, 산소 및 산화질소의 평형 농도는 각각 0.25, 0.35, 0.094 몰이 됩니다. 완전 제곱 조건은 2차식을 피하기 위해 지름길을 사용할 수 있는 한 가지 상황입니다.

예를 들어, 위의 반응에서 질소와 산소의 초기 농도는 각각 0.30이었으며 방정식은 완전 제곱이 됩니다. 이런 경우 x를 풀기 위해 양측에 제곱근을 취함으로써 방정식을 단순화할 수 있습니다.

<ol>
	<li>Lim, Kieran F. "화학에서 그래픽 계산기 및 스프레드시트 사용: 평형 문제 해결." 화학 교육 저널 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>

평형 농도 계산

평형 농도를 계산할 수 있다는 것은 과학 및 기술의 여러 분야(예: 의약품의 제제 및 투여)에 필수적입니다. 약물을 섭취하거나 주사한 후에는 일반적으로 관심 있는 신체 시스템의 최종 농도에 영향을 미치는 여러 화학적 평형에 관여합니다. 원하는 치료 효과를 얻을 수 있는 복용량을 계산하려면 이러한 평형의 정량적 측면에 대한 지식이 필요합니다.

보다 어려운 유형의 평형 계산은 평형 농도가 초기 농도와 평형 상수로부터 파생되는 것일 수 있습니다. 이러한 계산에는 일반적으로 4단계 접근 방식이 유용합니다.

<ol>
	<li>반응이 진행되어 평형에 도달할 방향을 확인합니다.</li>
	<li>ICE 테이블을 사용합니다..</li>
	<li>농도 변화를 계산하고 이어서 평형 농도를 계산합니다.</li>
	<li>계산된 평형 농도를 확인합니다.</li>
</ol>

평형 농도 계산

특정 조건에서 PCl_5(g)를 PCl_3(g)와 Cl_2(g)로 분해하는 평형 상수 K_c는 0.0211입니다. 위의 절차는 처음에 1.00M 농도의 PCl_5만 포함된 혼합물에서 PCl_5, PCl_3 및 Cl_2의 평형 농도를 결정하는 데 사용할 수 있습니다.

Step 1. 반응이 진행되는 방향을 결정합니다.

PCl_5 분해에 대한 균형 방정식은 다음과 같습니다.

<img alt="Eq1" src="/files/ftp_upload/11390/11390_Equation 1.png" style="text-align: center; height: 50px;" />

초기에는 반응물만 존재하므로 Q_c = 0이고 반응은 오른쪽으로 진행됩니다.

Step 2. ICE 테이블을 개발합니다.

<div class="overflow">
<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;">초기 농도(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;">변경(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;">평형 농도 (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>
</div>

Step 3. 변화와 평형 농도를 구하세요..

평형 농도를 평형 상수 방정식에 대입하면 다음과 같습니다.

<img alt="Eq2" src="/files/ftp_upload/11390/11390_Equation 2.png" style="text-align: center; height: 170px;" />

ax^2 + bx + c = 0 형식의 방정식을 다시 배열하여 x를 풀 수 있습니다.

<img alt="Eq3" src="/files/ftp_upload/11390/11390_Equation 3.png" style="text-align: center; height: 90px;" />

이 경우 a = 1, b = 0.0211, c = −0.0211입니다. a, b, c에 적절한 값을 대입하면 다음과 같은 결과가 나옵니다.

<img alt="Eq4" src="/files/ftp_upload/11390/11390_Equation 4.png" style="text-align: center; height: 90px;" />

따라서 이차식의 두 근은 다음과 같습니다.

<img alt="Eq5" src="/files/ftp_upload/11390/11390_Equation 5.png" style="text-align: center; height: 50px;" />

이 시나리오에서는 양의 근만 물리적으로 의미가 있으므로(농도는 0이거나 양수임) x = 0.135 M입니다. 평형 농도는 다음과 같습니다.

<img alt="Eq6" src="/files/ftp_upload/11390/11390_Equation 6.png" style="text-align: center; height: 130px;" />

Step 4. 계산된 평형농도를 확인합니다.

계산을 확인하기 위해 K_c를 표현식으로 대체하면 다음과 같습니다.

<img alt="Eq7" src="/files/ftp_upload/11390/11390_Equation 7.png" style="text-align: center; height: 90px;" />

평형 농도로부터 계산된 평형 상수는 문제에 주어진 K_c 값과 같습니다(적절한 유효 숫자로 반올림했을 때).

이 문서는 에서 발췌되었습니다 <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>

평형 농도를 계산할 수 있다는 것은 과학 및 기술의 많은 영역(예: 배합 및 투여)에 필수적입니다.

Education

교육

JoVE Core

화학

하나

Chemical Equilibrium

화학 평형

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

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Pennsylvania State Academic Standards

Physical Science

Chemical Reactions

3.2.9-12.F

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Chemical reactions

Arizona Science Standards

High School

HS+C.P1

HS+C.P1U1.6

Next Generation Science Standards

Matter and Its Interactions

HS-PS1-6

Florida Department of Education

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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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Hydrogen Bonds

Hydrogen BondsHydrogen bonds are weak attractions between atoms that have formed other chemical bonds. One of these atoms is electronegative, like oxygen, ...

Construct an explanation to summarize the influences intermolecular forces have on the properties of chemical compounds.

PS.Chm.3.2

Analyze the structure of atoms and isotopes.

Equilibrium Concentrations from an ICE Table

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