Ways of Expressing Equilibrium Constants

In my previous post, I posted how to express the Equilibrium Constant Expressions for a given reaction, the standard format using molarity as unit for the concentration of reactants and products.  But we can't avoid the fact that we have different types of reactions, there are reactions which involve the same reacting species and involve all gases, and there are some the same reacting species but involve aqueous solutions. There are also reactions that the reacting species are of different phases.  This post will introduce to you the different ways of expressing equilibrium constant expression.

Homogeneous Equilibria

Homogeneous equilibrium applies to the reaction where the reacting species are in the same phase. Let us have an example: 

In the above reaction, it shows the dissociation of N2O4; the reactant is a gas and the product is a also a gas. We can express two equilibrium constant expressions in this type of reaction:

Kc denotes that the reacting species is expressed in molarity or mole per liter.  Since the reactant and the product in the above reaction are all gases the concentration can also be expressed in terms of their partial pressures.  In gases, at constant temperature the pressure P of a gas is directly related to the concentration in moles per liter; that is P=(n/V)RT.  Thus the above equation, the equilibrium constant can also be expressed using the partial pressures of gases.

PNO2 and PN2O4 are the equilibrium partial pressures (in atmospheres) of NO2 and N2O4 respectively.  On the other hand, the subscript in Kp tells us the equilibrium is expressed in terms of pressures.

Kc is not equal to Kp because the concentration of the reactants and the products are not the same with the partial pressures of the reactants and products.  The relationship between Kc and Kp can be derived using the ideal gas equation PV=nRT.  Since : 

and so Kc and Kp are related 

where 

               0.0821 L.atm/K.mol.  is the universal gas constant (R).  To use the above equation, the pressures in Kp must be in atm.  

In general Kc and Kp are not equal but in special case that the change in n is equal to zero therefore Kc = Kp.

And with regards to the unit of Kc and Kp, since the units are canceled out. there is no unit for K.

Let us have an example.  Write the Kc or Kp expressions of the following reactions if applicable:

We need to keep in mind the following:

     a.  Kp expression applies only to gaseous reaction.

     b.  The concentration of the solvent (particularly water) does not appear in the equilibrium constant expression.

Solution:

a.  

b.  

c.   

Heterogeneous Equilibria

Heterogeneous equilibrium is a reversible reaction involving reactants and products that are in different phases.  Example is the decomposition of calcium carbonate when heated, below is the equilibrium reaction:

There are three separate phases in the above reaction, two solid phases and one gas phase.  In writing equilibrium constant, not only pure liquid which is not included in the equilibrium constant but also pure solids.  Therefore the equilibrium constant expression of the above reaction is:

This was taken from

Since CaO and CaCO3 are solids, the concentration can be converted to 1, and so the final equilibrium constant expression is 

Kp can also be used since CO2 is a gas, therefore  Kp = PCO2.

Sample Problem:

Calculate the Kp and Kc of the reaction below at 800 degree Celsius. The pressure of CO2 is 0.236 atm.

                                       

Solution:

                  Kp = PCO2

                        =  0.236

so,

                  

            

In this case T = 800 + 273 = 1073 K, 🔺n =1. Substituting values, 

                

       

   

The Equilibrium Constant

I discussed in my previous post about chemical equilibrium, in which it is considered a dynamic process, wherein the two processes involved do not stop, they  occur at equal rate.

Two chemists in the name of Cato Guldberg and Peter Waage observed that there is a change in the mass of a substance participating in a reversible reaction produced a shift in equilibrium.  This principle is called the law of mass action.  Chemists studied the following type of reversible reaction:

They experimentally observed that the ratio of the product concentration raised to the powers of c and d to the reactant concentration raised to the powers of a and b, always got a constant value.  This is called the equilibrium constant, keq. Equilibrium constant (Keq) expression of the above reaction is written below:

where [A], [B], [C], [D] are the molar concentrations of reactants and products while a, b, c, and d are the coefficients in the reactants and products.  The above equation is the mathematical form of the law of mass action.   The relationship that is applied to every reversible reaction is called law of chemical equilibrium.

Let us have an example of writing the chemical equilibrium expression of some reversible reaction,

In writing the equilibrium constant expression, keq,  the concentration of the product raise to certain exponent is written as the numerator while the concentration of the reactant raise to a certain power is the denominator.  The exponent is taken from the coefficient of the reactants and products.  Therefore the chemical equilibrium constant expression of the equation above is:

To calculate the equilibrium constant, the concentration of the products are multiplied if there are two or more products and it is being divided to the product of the concentration of the reactants.  When the Keq value is greater than 1, it means that the equilibrium lies to the right and if the Keq value is less than 1 it means that the equilibrium lies to the left.

Let us try some more examples, write the equilibrium constant expression of the following:

Answer:

The Concept of Chemical Equilibrium

Chemical reactions are everywhere.  Some go in one direction only, the forward reaction and some go in two directions, the forward and backward reaction.  The latter is called reversible reaction and it is indicated by a double arrow.  Example, when a glass of water with cover is placed under the sun, it undergoes reversible reaction, the vaporization and condensation processes.  When the rate of vaporization process equalizes with the rate of condensation process, the equilibrium is reached.

Chemical equilibrium is a dynamic process.  It occurs when the rate of forward reaction and the backward reaction are equal and the concentration of the reactants and products no longer change with time.  Chemical equilibrium reaction involves different substances as reactants and products. Equilibrium involving two phases of the same substance just like the example given above, the vaporization and condensation processes is an example of physical equilibrium, because the changes that occurs are only physical processes.

Example of chemical equilibrium is the reversible reaction of nitrogen dioxide (NO2) and dinitrogen tetroxide (N2O4) 

The progress of reaction is easily monitored because there is a corresponding change in the color of the gases, N2O4 is a colorless gas while NO2 has dark brown color.  Let us say for example, an evacuated glass is injected with known amount of N2O4, and suddenly the color changes to dark brown, it means there is already a formation of NO2 gas.  The color intensifies until such time that equilibrium is reached.  Equilibrium is reached when there is no changed in color observed inside the evacuated glass

Advanced pH and pOH Calculations

In my previous post you learned how to calculate the pH and the [H+] of solution even without the calculator using the formula

But what about if the given hydrogen ion concentration is not base of 1 like for example 0.00024 M and the pH is not a whole number like for example 7.5 pH.  You might say, use calculator.  Yes you are right calculator can be used.  But this post will calculate pH and [H+] without the use of calculator.

Converting [H+] to pH

In this type of calculation the same formula will be used only that additional steps will be added.

Example,  a solution has a hydrogen concentration, [H+]  of  0.00015 M, what is the pH of the solution?

Solution:

The pH is expression is 

We have to recall some rules in logarithm.  The logarithm of a product is equal to the sum of the logarithm of each value.  That is, log a x b = log a + log b .  Applying rule to the above equation

Now its time to use logarithmic table as reference table for the logarithm of different numbers or you can have list of the logarithmic value of different numbers researched from the internet.  

Continuing the calculation,

This means that if a solution has hydrogen ion concentration of 0.00015 M has a pH of 3.82.

Another example: 

    

Stomach acid has a hydrogen ion concentration, [H+] of  0.020 M.  What is the pH of the stomach acid?

Solution:   

Converting pH to [H+]

In my previous blog [H+] is calculated using 

Let us see for example the pH is 3.80,

We have to remember the rule of exponent, to  multiply two exponential number, add the powers together. That is, .  Let us apply the rule on the above pH.

3.80 is the same as 0.20 + (-4).  

This time we need to use the antilogarithm table, 0.20 has antilog of 1.6, therefore 

This means that pH equal to 3.80 has a concentration of 0.000 16 M.

Another example:

Calculate the [H+] of seawater which has a pH of 7.85.

Solution:

pOH

What is pOH?  pOH expresses the basicity of the solution.  It is called the power of hydroxide.   The formula is the same with that of pH.  

The calculation is the same with pH and the [OH-].  Below is the summary between pH, pOH.

TRY THIS:

Calculate the pH of the following  [H+]

1.  0.000 000 047 M

2.  0.000 089 M

3.  0.000 003 7 M

Calculate the [H+] given the following pH

1.  pH = 3.25

2.  pH = 8.68 

3.  pH = 6.20

The pH Concept

In my previous post, I posted the definition of acids and bases and the properties of acids and bases. We learned that acids donates H+ ions in solution while bases donates OH- ions in solution.  pH is defined as the measure of acidity and basicity of substance in solution.  pH also measures the  H+ ion concentration in solution.  The range goes from 0 - 14 where pH 0-6 indicates that a solution is acidic,  pH 7 means neutral substances and pH 8-14 indicates basic substances.

Converting [H+] to pH

The pH scale expresses the molar hydrogen ion concentration [H+], as a power of 10.  It means pH is the negative logarithm of the molar hydrogen ion concentration. That is 

Example 1.

What is the pH of the solution if the hydrogen ion concentration, [H+] is 0.1 M?

Solution:

 The easiest way to calculate the concentration in pH is to express the concentration first to the power of 10.  See the calculation below:

The log of  is -1, since we get the - log the pH equals 1.

Example 2.

Calculate the pH of vinegar with hydrogen ion concentration of [H+] 0.001 M.

Solution:

Converting pH to [H+]

We can calculate the hydrogen ion concentration [H+] given the pH by rearranging the equation :

For example, if a solution has a pH of 5, what is the [H+]?  Look at  the solution below:

Just make the value of pH as the exponent and express it in concentration by molarity.

Another example:

Calculate the hydrogen ion concentration of a solution having pH of 4.

Solution:

TRY THIS:

Ionization of Water

We learned in my previous post the different weak electrolytes and strong electrolytes.  Strong electrolytes are 100% dissociated or ionized in water while weak electrolytes only few % are ionized in water.  Example is the salt in water solution, using electrical conductivity apparatus we can tell that its a strong electrolyte because it can produce very bright light while acetic acid on the other hand is a weak electrolyte, it only produce dim light in electrical conductivity apparatus.  Water on the other hand is an example of  weak electrolyte, lets see what happens in when water is combined with another water molecule:

Water molecule reacts with another water molecule forming hydronium ion and hydroxide ion.  The double arrow indicates that a reversible reaction occur, hydronium ion and hydroxide ion can also combine forming water molecules.  This is called autoprotolysis (or autoionization)  of water.  The bond breaking between water molecule and ions combining forming water molecules continues until the same rate happens, and this is called state of chemical equilibrium.

We can write simply the ionization of water molecules as follows:

The concentration of hydrogen ion in pure water is  mole per liter at . 

Since the ionization of water gives one H+ and OH-  , therefore the ionization of hyroxide ion is also  mole per liter at the same temperature.  The product of the concentration of the H+ and the OH- is called the equilibrium constant of water (symbol Kw).  Chemist use bracket [ ] to represents the concentration, therefore [H+] is the concentration of hydrogen ion and [OH-] is the concentration of hydroxide ion.  Kw of water can be calculated using the formula:

Calculating the Kw of water

Based from the calculation above Kw (equilibrium constant) of water is . Since Kw is constant whenever there is a change in the concentration of hydrogen ion the concentration of hydroxide ion is also changes or vise versa.

Example:

Calculate the hydroxide ion concentration [OH-] given the hydrogen ion concentration [H+]:

Solution:

  TRY THIS: