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Equilibrium Expression

A chemical reaction can represent with the help of chemical equation in which reactants and products are written in terms of their chemical formulae. The reactants are always on left side and products are at right side separated by single or double headed arrow. The physical state of all the involve compounds are written as abbreviated forms in parenthesis. 

Chemical equations also provide information about change in energy during the chemical reaction. It can be written as ΔH (heat of reaction) with the reactant or product or after the chemical equation.  The sign of ΔH represents the endothermic and exothermic reaction. 

We use three types of arrows in chemical equations;

Single headed: Single headed arrow indicates that reactants convert to product and reaction can move only in one direction that is from reactant to product. Such reactions are called as irreversible reactions as these reactions cannot move in backward direction from product to reactants. For example thermal decomposition of potassium chlorate $(KClO_{3})$ form KCl and $O_{2}$. 

$KClO_{3} \rightarrow KCl + O_{2}$

Here reaction cannot move in backward direction to form potassium chlorate from potassium chloride and oxygen. Such reactions are called as irreversible reactions and here we use single headed arrow from reactants to products. 

Double headed arrow: Double headed arrows ( ) show direction of reaction on both sides.  One arrow indicates the direction from reactant to product that is called as forward reaction and another arrow directed from product to reactant that is called as backward reaction. For example reaction of hydrogen and iodine forms hydrogen iodide that is a reversible reaction  and can be represented as:
 
$H_{2} + I_{2} \leftrightarrow 2 HI$

Equilibrium arrow:
You must have seen  such arrows in many chemical equations. These are also for reversible reactions. It the reversible reactions, the system reach to a stage at which the rate of forward reaction is equal to rate of backward reaction. This state of reaction is called as equilibrium state of reaction. 

Equilibrium in Reverse Reaction
 
Overall we can say that a reversible reaction can be made to go in either direction and direction depends on the reaction conditions. For example; when steam passes over hot iron it produces a black, magnetic oxide of iron called triiron tetroxide, $Fe_{3}O_{4}$ with hydrogen gas which is swept away by steam. 

$3Fb_{3} + 4H_{2}O_{(g)} \rightarrow Fb_{3}O_{4(s)} + 4H_{2(g)}$
  
If we work with same products and pass hydrogen gas over hot triiron tetroxide, $Fe_{3}O_{4}$ it reduces to Fe and steam.

$FB_{3}O_{4(s)} + 4H_{2(g)} \rightarrow 3Fe_{s} + 4H_{2}O_{g}$
      
So we can say that this is a reversible reaction under different reaction conditions. If we remove the products of one reaction they cannot react and show the backward reaction. That is the reason, reversible reactions are possible only in a closed system in which substances are either added or lost from the system. 

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Chemical Equilibrium Expression

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On the basis of direction, the chemical reactions can be classified as reversible and irreversible reactions. Irreversible reactions cannot move in both directions so it can only show the change from reactants to products. Usually reactions are irreversible in nature. Many reactions are reversible in nature as reactants can convert to product and products can again convert to reactants. The conversion of reactants to products is called as forward reaction and reverse reaction known as backward reaction.

When the rates of forward and backward reaction become equal to each other, the concentration of reactants and products exhibit no net change over time. This condition of reversible reaction is a called as Chemical equilibrium. It does not mean that the chemical reaction has stopped at this stage but that the consumption and formation of compounds have reached a balanced condition. Or we can say that quantities of reactants and products have achieved a constant ratio but they may or may not equal to each other. It is also called as dynamic equilibrium as the chemical reaction does not stop at that point but the concentration of both reactants and products remain constant. The equilibrium expression for a chemical reaction expressed the change in concentration of reactants and products. It may be expressed in terms of the concentration of the products and reactants. For example for the given chemical reaction the equilibrium expression can be written as

$jA + kB \rightarrow lC + mD$

The equilibrium expression will be: 

K = $\frac{([C]^l[D]^m)}{([A]^j[B]^k)}$

Here:
  • K = Equilibrium constant 
  • [A], [B] = Molar concentrations of reactants 
  • [C], [D] = Molar concentration of products
  • j, k, l, m = Coefficients in a balanced chemical equation
In equilibrium constant expression the chemical species in the aqueous and gaseous phases are only parts of equilibrium expression. The reactants and products in liquids and solids do not change and cannot be part of equilibrium expression.

How to Write an Equilibrium Expression?

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A reversible reaction always moves in forward and backward direction and the direction of reaction depends on different reaction conditions.

A reversible reaction must be carried out in a closed vessel so that after certain time the reaction achieve the stage of equilibrium. At equilibrium the ratio of the concentration of the reactants and the products remains constant and that constant value is called as equilibrium constant. Let’s discuss how to write the equilibrium expression for any reversible reaction.  The reaction at equilibrium can be shown as below; 

$aA(aq) + bB(aq) \leftrightarrow cC(aq) + dD(aq)$

In an equilibrium expression for a reaction the concentrations of the products are divided by the concentration of the reactants with the coefficients of each equation acting as exponents. 

We have to mention the physical state of reactants and products as either the gas (g) or aqueous phases (aq). 

Equilibrium Expression

The value of equilibrium constant provides information about the chemical reaction. Large value of equilibrium constant implies more concentration of products than reactants and it indicates that the equilibrium lies to the right. On the contrary small value of K implies more reactants than products and the reaction lies to the left. 

For the gaseous reactions the equilibrium constant can be represent in terms of Kp which is equilibrium constant in terms of pressure. The relation between Kc and Kp can be expressed as;

$K_{p}$ = $K_{c}(RT)^{\delta n}$

Here:
  • Δn= Coefficients of the gaseous products - Coefficients of the gaseous reactants. 
  • R =  Gas constant (see the gas laws page) 
  • T = Temperature (Kelvin)
Here Q represents the expression for initial concentration or pressure values of reactant and products. The expression for Q is same as of equilibrium expression, only change is that here we used initial concentration or pressure instead of equilibrium values. 
 
The comparison of value of Q and K helps to determine the direction of reaction. 
  • Q > K : Higher value of Q indicates more concentration of products so to attain the equilibrium the reaction will move to left ; backward direction.
  • Q = K: It is condition of equilibrium for given reaction so it will not shift in either direction.
  • Q< K: Lesser value of Q indicates that concentration of products is less than reactant and to attain the equilibrium the reaction must move to right (forward direction).
We can calculate the equilibrium constant with the help of ICE table (Initial, change and equilibrium concentrations). We can determine the equilibrium concentration with initial concentrations and that can be further used to calculate equilibrium constant. At equilibrium also the reactions don't stop but the rate of forward and backward reactions are in balance so there will be no net change in the concentrations of chemical species. In other words we can say that chemical equilibrium is an example of a dynamic balance between the forward and reverse reactions. 

Equilibrium Expression Examples

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We know that equilibrium is a balance condition between the forward and backward rates of a reversible chemical reaction. At this stage of chemical reaction, a balance exists also between the concentrations of the reactants and products. For any given reaction the concentrations of the reactants and the products at equilibrium will be related with each other.

The reaction of nitrogen gas and hydrogen gas form ammonia. This is typical chemical reaction of Haber’s process. It is a reversible reaction which attains equilibrium stage at a certain point of time. 

$N_{2(g)} + 3H_{2(g)} \leftrightarrow 2NH_{3(g)}$

We always require a balance chemical equation with physical states of reactants and products to write the equilibrium expression. We know that equilibrium expression is ratio of concentration of products and reactants for the balance chemical equation.

$K_{eq}$ = $\frac{[products]}{reactants}$
 
So for the given chemical equation, we can write the equilibrium constant expression as given below;
 
$N_{2}(g) + 3H_{2}(g) \leftrightarrow 2NH_{3}(g)$

$K_{eq}$ = $\frac{[NH_3]^2}{[N_2][N_2]^3}$

Here Keq is equilibrium constant which is a measure of the extent to completion of reaction. The terms in square brackets indicates the concentration of reactants and products at equilibrium. The concentration terms of each product and reactant are raising it to a power that equals to its coefficient in the balanced equation.

Equilibrium Expression Formula

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The reaction between acetic acid with ethanol forms ethyl acetate (an ester) with water. The reaction is called as esterification reaction. The balance chemical equation can be written as; 

$CH_3COOH(i) + CH_{3}CH_{2}OH(i) \leftrightarrow CH_{3}COOCH_{2}CH_{3}(i) + H_{2}(i)$
 
The equilibrium expression for the given reaction can be written as;

$K_{c}$ = $\frac{[CH_{3}COOH_{2}CH_{3}][H_{2}O]}{[CH_{3}COOH][CH_{3}CH_{2}OH]}$

The reverse reaction of esterification is hydrolysis of ester that forms acetic acid and alcohol. The equilibrium in the hydrolysis of esters is shown as below;

$CH_{3}COOCH_{2}CH_{3(i)} + H_{2}O(i) \leftrightarrow CH_{3}COOH(i) + CH_{3}CH_{2}OH(i)$
 
The equilibrium constant expression Kc will be; 

$K_{C}$ = $\frac{[CH_{3}COOH][CH_{3}CH_{2}OH]}{[CH_{3}COOH_{2}CH_{3}][H_{2}O]}$
 
The Contact process is used for the formation of sulfur trioxide from sulfur dioxide and oxygen. It is a reversible reaction and the balance chemical equation can be written as; 

$2SO_{2}(g) + O_{2}(g) \leftrightarrow 2SO_{3}(g)$
  
The equilibrium constant expression for this reaction will be ratio of concentration of sulfur trioxide and concentration of both reactants; sulfur dioxide and oxygen.

$K_{s}$ = $\frac{[SO_{3}]^{2}}{[SO_{2}]^{2}[O_{2}]}$
 
If the physical states of reactants and products are different, the reaction is said to be in a heterogeneous equilibrium. For example the reaction of steam with red hot carbon results the formation of hydrogen gas and carbon monoxide gas. 
          
In the equilibrium expression for this reaction will not include solid red hot carbon as it is in solid state and change in concentration for this can be taken as negligible. Hence the equilibrium constant expression for this can be as below; 

$K_{c}$ = $\frac{[H_2][CO]}{[H_2O]}$ 

Similarly in the reaction of solid copper with silver nitrate solution (Ag+ ions) forms copper(II) nitrate ( Cu+2 ions) and solid Ag. The reaction can be written as given below.

$Cu_{(s)} + 2Ag^{+}aq \leftrightarrow Cu^{2+}aq + 2Ag(s)$
  
Here one reactant copper and one product silver on the right are solids so they will not be part of equilibrium constant expression.

$K_{c}$ = $\frac{Cu^{2+}}{[Ag^+]^2}$
 
We know that thermal decomposition of calcium carbonate results the formation of solid calcium oxide and carbon dioxide gas. If the calcium carbonate is heated in a closed system, equilibrium is established that prevents the escape of carbon dioxide gas.

$CaCO_{3(s)} \leftrightarrow CaO_{3} + CO_{2(g)}$
  
Hence the equilibrium constant expression will involve only concentration of carbon dioxide.

Kc  =$[CO_{[2]}$ 

Equilibrium Expression for Acid Dissociation

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On the basis of strength of acids, they can be classified as strong and weak acids. Strong acids ionize 100% (completely) and form hydrogen ions and respective anion. It means there will be no more un-dissociate molecules in the solutions.  Unlike strong acids, weak acids cannot ionize completely and some un-dissociate molecules remain in the solution. At a certain stage, the equilibrium is established between un-dissociate molecules and hydrogen ions. The equilibrium for acid dissociation can be written as; 

$HA + H_2O \leftrightarrow H_{3}O^{+} + A^{-}$ 

The equilibrium constant, Keq for acid dissociation is called as acid dissociation constant which is expressed as Ka.

K = $\frac{[H_{3}O^{+}][A-]}{[HA]}$
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