15.6: Applications of Equilibrium Constants, [ "article:topic", "reaction quotient", "showtoc:no", "license:ccbyncsa" ], Predicting the Direction of a Reaction with a Graph, $$\dfrac{(0.0600)^2}{0}=\text{undefined}$$, $$\dfrac{(0.0200)^2}{0.0600}=6.67 \times 10^{−3}$$. (ii) If Kc > 103, reactants predominate over products. Homogeneous and Heterogeneous Equilibria It should be noted that the equation used above identifies a situation of homogeneous equilibrium, in which all the substances are in the same phase or state of matter—gas, in this case. We previously saw that knowing the magnitude of the equilibrium constant under a given set of conditions allows chemists to predict the extent of a reaction. Applications of Equilibrium Constant (1) Judging the extent of reaction (i) If K c > 10 3, products predominate over reactants.If K c is very large, the reaction proceeds almost all the way to completion. By graphing equilibrium concentrations for a given system at a given temperature and pressure, we can predict the direction of reaction of that mixture when the system is not at equilibrium. $$K = 2.4 \times 10^{−4}$$ at 900 K. Huge amounts of hydrogen are produced from natural gas in this way and are then used for the industrial synthesis of ammonia. All rights reserved. Applications of Equilibrium Constants. Register & Get Sample Papers solutions instantly. Applications of Equilibrium Constant: Predicts the extent of reaction, which gives the degree of the disappearance of reactants. Increased Risk Factors of Tooth Decayâ¢ Eating a diet rich in sugar and starchâ¢ Sticky foods â â¦ (i) If Kc > 103, products predominate over reactants. Equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. Any point representing a pair of concentrations that does not lie on the line corresponds to a nonequilibrium state. Given: balanced chemical equation, $$K$$, amounts of reactants and products, and volume, A We must first find the initial concentrations of the substances present. An object in equilibrium has no acceleration, so it is either not moving or moving at a constant velocity. In industrial processes, it is important to get the product as quickly and as efficiently as possible. When a reaction system is at equilibrium, $$Q = K$$. 20,000+ Learning videos. Class 11 Medical - Applications of Equilibrium Constants Class 11 Engineering - Applications of Equilibrium Constants. All forces on the object balance out. Protection and Metering Department, National Electric Power Company, Amman 11181, Jordan. APPLICATIONS OF CHEMICAL EQUILIBRIUM 27 MAY 2014 Lesson Description In this lesson we: Discuss Le Chatelier’s Principle Discuss application of Le Chatelier’s Principle Summary Le Chatelier’s Principle If the equilibrium in an isolated system is disturbed by changing one of the equilibrium … Applications of Equilibrium Constant (1) Judging the extent of reaction (i) If K c > 10 3, products predominate over reactants.If K c is very large, the reaction proceeds almost all the way to completion. The following table lists data from three experiments in which samples of the reaction mixture were obtained and analyzed at equivalent time intervals, and the corresponding values of $$Q$$ were calculated for each. To predict in which direction a reaction will proceed. This statement defines the zeroth law of thermodynamics. Reaction Quotient (Q): (ii) If K c > 10 3, reactants predominate over products.If K c is very small, the reaction proceeds hardly at all. Use Equation $$\ref{15.6.1}$$ to determine $$Q$$ . The law is based on temperature measurement. (ii) If Q < K, the reaction will proceed in the direction of the products (forward reaction). A plot of $$[\ce{H_2O}]$$ versus $$[\ce{H_2}]$$ at equilibrium is a straight line with a slope of $$K$$ (Figure $$\PageIndex{3}$$). Calculate the average molar mass (in gm/mol)of an equilibrium mixture. We consider a general equilibrium problem defined on a convex set, whose cost bifunction may not be monotone. At elevated temperatures, methane ($$CH_4$$) reacts with water to produce hydrogen and carbon monoxide in what is known as a steam-reforming reaction: $\ce{CH4(g) + H2O(g) <=> CO(g) + 3H2(g)} \nonumber$. Equilibrium and Center of Gravity in Real Objects Before applying the concept of vector sums to matters involving equilibrium, it is first necessary to clarify the nature of equilibrium itself—what it is and what it is not. -production must ALWAYS be ECONOMIC which means produces the most product EFFICIENTLY concentration of products is much larger than that of […] A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. Thus the reaction in Equation $$\ref{15.6.4}$$ will proceed to the left as written, consuming $$\ce{H_2O}$$ and producing $$\ce{H_2}$$, which causes the concentration ratio to move down and to the right toward the equilibrium line. 8,000+ Fun stories. Initially, the added $$\ce{PbCO_3}$$ decomposes completely to $$\ce{CO_2}$$ because the amount of $$\ce{PbCO_3}$$ is not sufficient to give a $$\ce{CO_2}$$ concentration equal to $$K$$. The purpose of the study was to use both limit equilibrium methods (LEMs) and numerical simulations (finite element method (FEM)) to understanding the common factor imposing the selected slope into slope instabilities. (i) If Q > K, the reaction will proceed in the direction of reactants (reverse reaction). If $$Q = K$$, for example, then the system is already at equilibrium, and, If $$Q < K$$, then the ratio of the concentrations of products to the concentrations of reactants is less than the ratio at equilibrium. One idea: a patient lying in bed is in static equilibrium (static because he is not moving). We show that this problem can be solved by the inexact proximal point method if there exists a solution to the dual problem. Each experiment begins with different proportions of product and reactant: As these calculations demonstrate, $$Q$$ can have any numerical value between 0 and infinity (undefined); that is, $$Q$$ can be greater than, less than, or equal to $$K$$. (iii) If Q = K, the reaction mixture is already at equilibrium. Given: Molar mass of A 2 , B 2 and C 2 are 70,49 &21 gm/mol respectively. Such a graph allows us to predict what will happen to a reaction when conditions change so that $$Q$$ no longer equals $$K$$, such as when a reactant concentration or a product concentration is increased or decreased. Any point that lies below and to the left of the equilibrium curve (such as point A in Figure $$\PageIndex{4}$$) corresponds to $$Q < K$$, and the reaction in Equation $$\ref{15.6.5}$$ will therefore proceed to the right as written, causing the composition of the system to move toward the equilibrium line. Figure $$\PageIndex{4}$$: The Concentration of $$NH_{3(g)}$$ versus the Concentration of $$HI_{(g)}$$ for system in Reaction \ref{15.6.5} at Equilibrium. Important features and applications of the equilibrium constant are listed below - Expression for equilibrium constant is applicable only when concentrations of the reactants and products have attained constant value at equilibrium state. Thus the reaction in Equation $$\ref{15.6.3}$$ will proceed to the left as written, until $$[\ce{CO_2}] = K$$. We can calculate the other concentrations in a similar way: B We now compute $$Q$$ and compare it with $$K$$: \begin{align*} Q&=\dfrac{[\ce{CO}][\ce{H_2}]^3}{[\ce{CH_4}][\ce{H_2O}]} \\[4pt] &=\dfrac{(8.0 \times 10^{−3})(3.0 \times 10^{−3})^3}{(6.0\times 10^{−3})(4.0 \times 10^{−3})} \\[4pt] &=9.0 \times 10^{−6} \end{align*}. Application of equilibrium 1. By graphing a few equilibrium concentrations for a system at a given temperature and pressure, we can readily see the range of reactant and product concentrations that correspond to equilibrium conditions, for which $$Q = K$$. Industrial Applications. There are also various ways to state the zeroth law of thermodynamics. To reach equilibrium, the system must increase $$[\ce{CO_2}]$$, which it can do only by decomposing solid $$\ce{PbCO_3}$$ to form $$\ce{CO_2}$$ and solid $$\ce{PbO}$$. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. Thus the ratio of the concentrations of products to the concentrations of reactants is less than the ratio for an equilibrium mixture. At equilibrium, Q K = K, Complete List of Packages for Medical Preparation. The application of limit equilibrium analysis and numerical simulation in case of slope instability is described. If $$[\ce{H_2O}]$$ is doubled at equilibrium, then $$[\ce{H2}]$$ must also be doubled for the system to remain at equilibrium. At a given temperature, therefore, any system that contains solid $$\ce{PbCO_3}$$ and solid $$\ce{PbO}$$ will have exactly the same concentration of $$\ce{CO_2}$$ at equilibrium, regardless of the ratio or the amounts of the solids present. Learn with Videos. Copyright © 2010-2019 www.emedicalprep.com. Conversely, any point that lies above and to the right of the equilibrium curve (such as point B in Figure $$\ref{15.6.5}$$) corresponds to $$Q > K$$, and the reaction in Equation $$\ref{15.6.5}$$ will therefore proceed to the left as written, again causing the composition of the system to move toward the equilibrium line. The applications of microeconomics look at equilibrium on a per-product level rather than an entire market level in most cases. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The equilibrium constant K p (in atm) for the reaction is 9 at 7 atm and 300 K. A 2 (g) â B 2 (g) + C 2 (g). 9 min. Again, only those pairs of concentrations of $$\ce{H_2O}$$ and $$\ce{H_2}$$ that lie on the line correspond to equilibrium states. In whatever context it is used, it almost always refers to balance. In industrial processes the primary objective is to maximize the yield of products at a minimum cost in a shorter period of time. the degree of the disappearance of the reactants. Price is the most important factor in supply-and-demand equilibrium, so any internal factor that affects the cost of goods can affect price and equilibrium â¦ EATING SUGAR AND TOOTH DECAY STEPHANIE LEHSTEN 3. for which $$K = 4.65 \times 10^{−3}$$ at 298 K. We can write $$Q$$ for this reaction as follows: $Q=\dfrac{[\ce{NO2}]^2}{[\ce{N2O4}]} \label{15.6.2}$. Le-Chatelier’s principle of equilibrium is used in the industrial applications as the reaction scheme involves parameters like temperature, pressure, concentration of reaction species a change in even single parameter results in the change of equilibrium leads to undesired product formation. (ii) If K c > 10 3, reactants predominate over products.If K c is very small, the reaction proceeds hardly at all. This particular word is used extensively in the realms of physics as well as biology, chemistry and economics etc. As a result, for a given concentration of either $$\ce{HI}$$ or $$\ce{NH_3}$$, only a single equilibrium composition that contains equal concentrations of both $$\ce{NH_3}$$ and $$\ce{HI}$$ is possible, for which, $[\ce{NH_3}] = [\ce{HI}] = \sqrt{K}. If Kc is very large, the reaction proceeds almost all the way to completion. To understand how information is obtained using a reaction Quotient, consider the dissociation of dinitrogen tetroxide to nitrogen dioxide. The equilibrium constant (Kc) can be used to predict the extent of a reaction, i.e. Have questions or comments? In contrast, the reduction of cadmium oxide by hydrogen gives metallic cadmium and water vapor: \[\ce{CdO(s) + H2(g) <=> Cd(s) + H_2O(g)} \label{15.6.4}$. In this section, we describe how to quantitatively analyze the composition of a reaction mixture to make this determination. Applications of Chemcial Equilibrium in Industrial Production In Industrial Production... - Industrial Production used to produce compounds that can be harnessed and used in other applications. If $$Q > K$$, the reaction will proceed to the left as written. Missed the LibreFest? It may be noted that Q becomes equal to equilibrium constant (K) when the reaction is at the equilibrium state. Application of EquilibriumBy: Stephanie, Shawna, and Amber 2. Application of EquilibriumBy: Stephanie, Shawna, and Amber 2. Important features and applications of the equilibrium constant are listed below - Expression for equilibrium constant is applicable only when concentrations of the reactants and products have attained constant value at equilibrium state. By graphing equilibrium concentrations for a given system at a given temperature and pressure, we can predict the direction of reaction of that mixture when the system is not at equilibrium. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. In industrial processes the primary objective is to maximize the yield of products at a minimum cost in a shorter period of time. This phenomenon helps us in carrying out our… When a body ‘A’ is in thermal equilibrium with another body ‘b’, and also separately in thermal equilibrium with a body ‘C’, then body ‘B’ and ‘C’ will also be in thermal equilibrium with each other. Chemical Equilibrium - Real-life applications Photo by: Steven Baines. The expression for the reaction Quotient has precisely the same form as the equilibrium constant expression, except that $$Q$$ may be derived from a set of values measured at any time during the reaction of any mixture of the reactants and the products, regardless of whether the system is at equilibrium. 1,* and . Compare $$Q$$ and $$K$$ to determine in which direction the reaction will proceed. Often, however, chemists must decide whether a system has reached equilibrium or if the composition of the mixture will continue to change with time. Predicts the direction of the reaction. Solve Easy, Medium, and Difficult level questions from Applications Of Equilibrium Constants Legal. Thus the left portion of the graph represents a system that is not at equilibrium because it contains only $$\ce{CO2(g)}$$ and $$\ce{PbO(s)}$$. So think of something that is not accelerating (not so easy if it must involve nursing). Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. In contrast, when just enough $$\ce{PbCO_3}$$ has been added to give $$[CO_2] = K$$, the system has reached equilibrium, and adding more $$\ce{PbCO_3}$$ has no effect on the $$\ce{CO_2}$$ concentration: the graph is a horizontal line. Example Definitions Formulaes. a) larger value of the equilibrium constant ( > 103 ) shows that forward reaction is favoured i.e. The Wikipedia defines equilibrium as the condition of a system in which competing influences are balanced. \nonumber\]. $$[\ce{CO}] = 8.0 \times 10^{−3} M$$, and. PDF | This presentation is useful to become familiar with problems about Chemical Equilibrium. For example, point A in Figure $$\PageIndex{3}$$ lies below the line, indicating that the $$[\ce{H_2O}]/[\ce{H_2}]$$ ratio is less than the ratio of an equilibrium mixture (i.e., $$Q < K$$). 1. Lina Alhmoud. For this system, $$K$$ is equal to the product of the concentrations of the two products: If we double the concentration of $$\ce{NH3}$$, the concentration of $$\ce{HI}$$ must decrease by approximately a factor of 2 to maintain equilibrium, as shown in Figure $$\PageIndex{4}$$. Calculating the equilibrium constant, which gives the relative amount of reactants and products. If $$1.2 \times 10^{−2}$$ mol of $$CH_4$$, 8.0 × 10−3 mol of $$H_2O$$, $$1.6 \times 10^{−2}$$ mol of $$CO$$, and $$6.0 \times 10^{−3}$$ mol of $$H_2$$ are placed in a 2.0 L steel reactor and heated to 900 K, will the reaction be at equilibrium or will it proceed to the right to produce $$\ce{CO}$$ and $$\ce{H_2}$$ or to the left to form $$\ce{CH_4}$$ and $$\ce{H_2O}$$? | Find, read and cite all the research you need on ResearchGate R is the universal gas constant and T is the temperature. The Haber process is a good example of an industrial process which uses the equilibrium principles that have been discussed. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. Graphs derived by plotting a few equilibrium concentrations for a system at a given temperature and pressure can be used to predict the direction in which a reaction will proceed. In such cases, the reaction in Equation $$\ref{15.6.4}$$ will proceed in whichever direction causes the composition of the system to move toward the equilibrium line. In this live Gr 12 Physical Sciences show we take a close look at Applications of Chemical Equilibrium. Applications of Equilibrium Constant: Predicts the extent of reaction, which gives the degree of the disappearance of reactants. Conversely, the point labeled B in Figure $$\PageIndex{2}$$ lies below the horizontal line, so it corresponds to a $$[\ce{CO_2}]$$ that is less than the equilibrium concentration of $$\ce{CO_2}$$ (i.e., $$Q < K$$). In explaining the principles and application of the Haber process and equilibrium constant, we must first understand that there is a relationship between these two above mentioned concepts and two other concepts known as free energy and electrode potential. Therefore, the reaction will proceed to the, If $$Q > K$$, then the ratio of the concentrations of products to the concentrations of reactants is greater than at equilibrium, so the reaction will proceed to the. Chapter 15 Applications of Equilibrium – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 6b0b76-YTFjO If Kc is very small, the reaction proceeds hardly at all. The reaction will therefore proceed to the right as written, forming $$\ce{H2}$$ and $$\ce{CO}$$ at the expense of $$\ce{H_2O}$$ and $$\ce{CH4}$$. However, in simple terms, it can be said, “Systems that are in ther… Comparing the magnitudes of $$Q$$ and $$K$$ enables us to determine whether a reaction mixture is already at equilibrium and, if it is not, predict how its composition will change with time to reach equilibrium (i.e., whether the reaction will proceed to the right or to the left as written). The less expensive the process the better. (iii) If Kc is in the range 103 to 103, appreaciable concentration of both reactants and products are present. by Khaled Nusair. Watch the recordings here on Youtube! Thus, a reaction has a tendency to form products if Q < K and to form reactants if Q > K. Notice: JavaScript is required for this content. APPLICATION OF EQUILIBRIUM CONSTANT : www.citycollegiate.com. An application of this approach to … Lead carbonate decomposes to lead oxide and carbon dioxide according to the following equation: $\ce{PbCO3(s) <=> PbO(s) + CO2(g)} \label{15.6.3}$, Because $$\ce{PbCO_3}$$ and $$\ce{PbO}$$ are solids, the equilibrium constant is simply. There are two conditions of equilibrium, the first condition of equilibrium, and the second condition of equilibrium. Calculations Involving Equilibrium Constant. Equilibrium Constant and Reaction Quotient. R is the universal gas constant and T is the temperature. Save teachers time and engage students with a new, simpler interface! We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 2. industrial applications of equilibrium for AS-level chemistry Reaction Quotient (Q): Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. the concentration of products is much larger than that of the reactants at equilibrium.For Example: 1. At equilibrium, Q K = Kc = KpThus. (2) Predicting the direction of reaction: The concentration ratio, i.e., ratio of the product of concentrations of products to that of reactants is also known as concentration quotient and is denoted by Q. Applications of Equilibrium Constants. Calculate the molar concentrations of the reactants and the products. $$Q = 0.96$$. Thus the reaction in Equation \ref{15.6.4} will proceed to the right as written, consuming $$\ce{H_2}$$ and producing $$\ce{H_2O}$$, which causes the concentration ratio to move up and to the left toward the equilibrium line. The reaction Quotient ($$Q$$ or $$Q_p$$) has the same form as the equilibrium constant expression, but it is derived from concentrations obtained at any time. In this lesson we discuss equilibrium, Le Chatelier's principle, changing equilibrium conditions as well as look at graph examples. If $$Q = K$$, then the system is at equilibrium. Increased Risk Factors of Tooth Decay• Eating a diet rich in sugar and starch• Sticky foods – more likely to remain on the surface of the teeth.• This situation is represented in Figure $$\PageIndex{3}$$, which shows a plot of $$[\ce{CO_2}]$$ versus the amount of $$\ce{PbCO_3}$$ added. The Wikipedia defines equilibrium as the condition of a system in which competing influences are balanced. Important Questions on Applications Of Equilibrium Constants is available on Toppr. Predicts the direction of the reaction. Application of Equilibrium constant 1) Predicting the extent of reaction The magnitude of the equilibrium constant gives an idea of the relative amount of the reactants and the products. Conversely, point B in Figure $$\PageIndex{3}$$ lies above the line, indicating that the $$[\ce{H_2O}]/[\ce{H_2}]$$ ratio is greater than the ratio of an equilibrium mixture ($$Q > K$$). 2. The reaction in Equation \ref{15.6.3} will therefore proceed to the right as written, until $$[\ce{CO_2}] = K$$. According to the First condition of equilibrium sum of forces acting on a body is zero ( â F =0 ), While according to the second condition of equilibrium sum of torque acting on a body is zero ( â Ï = 0 ).. What is the equilibrium in physics? Statics and Equilibrium - Real-life applications Photo by: emese73. Equilibrium is one of the most common and perhaps well-known aspects of economics, both in micro and macro applications.The applications of microeconomics look at equilibrium on a per-product level rather than an entire market level in most cases. All you need to remember is that the composition of a system not at equilibrium will change in a way that makes $$Q$$ approach $$K$$: These points are illustrated graphically in Figure $$\PageIndex{1}$$. Because $$K = 2.4 \times 10^{−4}$$, we see that $$Q < K$$. In explaining the principles and application of the Haber process and equilibrium constant, we must first understand that there is a relationship between these two above mentioned concepts and two other concepts known as free energy and electrode potential. If $$Q < K$$, the reaction will proceed to the right as written. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Application of equilibrium 1. This particular word is used extensively in the realms of physics as well as biology, chemistry and economics etc. Applications of the Principles of Chemical Equilibrium to Reactions of Industrial Importance. EATING SUGAR AND TOOTH DECAY STEPHANIE LEHSTEN 3. Therefore, for the following general reaction: the reaction quotient is defined as follows: $Q=\dfrac{[C]^c[D]^d}{[A]^a[B]^b} \label{15.6.1}$. Points that do not lie on the line or curve represent nonequilibrium states, and the system will adjust, if it can, to achieve equilibrium. Knowledge of equilibrium constant for a given reaction is very helpful aid in laboratory analysis as well as in industry. In another example, solid ammonium iodide dissociates to gaseous ammonia and hydrogen iodide at elevated temperatures: $\ce{ NH4I(s) <=> NH3(g) + HI(g)} \label{15.6.5}$. $$K = 0.64$$ at 900 K. If 0.010 mol of both $$\ce{CO}$$ and $$\ce{H_2O}$$, 0.0080 mol of $$\ce{CO_2}$$, and 0.012 mol of $$\ce{H_2}$$ are injected into a 4.0 L reactor and heated to 900 K, will the reaction proceed to the left or to the right as written? The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. This phenomenon helps us in carrying out ourâ¦ Since (Q > K), so the reaction will proceed to the left, and $$CO$$ and $$H_2O$$ will form. To determine whether a system has reached equilibrium, chemists use a Quantity called the reaction Quotient ($$Q$$). For example, the point labeled A in Figure $$\PageIndex{2}$$ lies above the horizontal line, so it corresponds to a $$[\ce{CO_2}]$$ that is greater than the equilibrium concentration of $$\ce{CO_2}$$ (i.e., $$Q > K$$). In the water–gas shift reaction introduced in Example $$\PageIndex{1}$$, carbon monoxide produced by steam-reforming reaction of methane reacts with steam at elevated temperatures to produce more hydrogen: $\ce{CO(g) + H_2O(g) <=> CO2(g) + H2(g)} \nonumber$. Application of Equilibrium Optimizer Algorithm for Optimal Power Flow with High Penetration of Renewable Energy . Le-Chatelierâs principle of equilibrium is used in the industrial applications as the reaction scheme involves parameters like temperature, pressure, concentration of reaction species a change in even single parameter results in the change of equilibrium leads to undesired product formation. The reaction Quotient ($$Q$$) is used to determine whether a system is at equilibrium and if it is not, to predict the direction of reaction. Related Concepts. Thus any $$\ce{CO_2}$$ concentration that is not on the horizontal line represents a nonequilibrium state, and the system will adjust its composition to achieve equilibrium, provided enough $$\ce{PbCO_3}$$ and $$\ce{PbO}$$ are present. The magnitude of the equilibrium constant gives an idea of the relative amount of the reactants and the products.Case 1: The larger value of the equilibrium constant (>103) shows that forward reaction is favored i.e. Applications of the Principles of Chemical Equilibrium to Reactions of Industrial Importance. For example, we have $$1.2 \times 10^{−2} mol$$ of $$\ce{CH_4}$$ in a 2.0 L container, so, $[\ce{CH4}]=\dfrac{1.2\times 10^{−2} \, \text{mol}}{2.0\; \text{L}}=6.0 \times 10^{−3} M \nonumber$. what john forbes nash jr. said in his the simplicity of nash equilibrium enabled the growth of game theory as a legitimate discipline and enabled. It may be noted that Q becomes equal to equilibrium constant (K) when the reaction is at the equilibrium state. To reach equilibrium, the system must decrease $$[\ce{CO_2}]$$, which it can do only by reacting $$\ce{CO_2}$$ with solid $$\ce{PbO}$$ to form solid $$\ce{PbCO_3}$$. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. In whatever context it is used, it almost always refers to balance. Calculating the equilibrium constant, which gives the relative amount of reactants and products.

## applications of equilibrium

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