Ionization of weak acids and bases

Weak acids and bases are miser kind of species, because even though they have H⁺ or OH^- ions, they don’t give them quickly and when they do give them, they only give a part of them. When weak acids/bases are dissolved in water they partly dissociate or ionize. To know how much H⁺ or OH^- ions they will release in water, we need to study their ionization reactions.

Let’s take an example of a weak acid HX and study its ionization in water:

HX_(aq) + H₂O_(l) ⇌ H₃O⁺_(aq)  + X^-_(aq)

If we have taken c mol/lit of HX initially at time t=0, when the concentration of H₃O⁺ and X^- were 0 and only a fraction of moles (α) underwent dissociation.

Suppose out of 1 mole of acid, α mole of acid undergoes dissociation.

Then from c moles of acid (c.α) will be dissociated.

At time t, (cα) moles of HX dissociate and produce (cα) moles of H₃O⁺ and (cα) moles of X^-. So at the time of equilibrium HX is left with (c-cα) moles/lit and H₃O⁺ and X^- each has (cα) moles/lit.

Dissociation Constant and Degree of Dissociation

Relation between Degree of Dissociation α and Dissociation Constant K_a:

Now we will calculate the equilibrium constant K_a  as it is the ionization reaction of an acid:

K_a = (cα) (cα)/ (c-cα)

K_a = cα² / (1- α)

K_a is the ionization or dissociation constant of acid HX and α is the degree of dissociation or the extent of ionization.

If we write equation of K_a in terms of molar concentration, we will get:

K_a = [H₃O⁺] [X^-]/ [HX]

Or

K_a = [H⁺] [X^-]/ [HX]

As you can see here that K_a is directly proportional to the H⁺ concentration, which means acids which have higher K_a value are stronger.

Similarly you can calculate the equilibrium constant K_b for a weak base. Let’s take an example of a weak base MOH and study its ionization in water:

MOH _(aq) ⇌ M⁺_(aq)  + OH^-_(aq)

If the initial concentration of MOH is c mole/lit and degree of dissociation is α, then at equilibrium MOH is left with (c-cα) moles/lit and M⁺ and OH^- each has (cα) moles/lit. So the K_b will be:

K_b = [M⁺] [OH^-]/ [MOH]

Or

K_b = cα² / (1- α)

K_b is directly proportional to the OH^- concentration, which means bases which have higher K_b value are stronger.

In the next post we will see if there is any relation between K_a and K_b.

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The pH Scale

When any compound gets dissolved in water, it dissociates and releases or accepts H+ ions. We can guess the nature of that compound by comparing the concentration of H₃O⁺ and OH^-. If it has

[H₃O⁺] > [OH^-] it will be acidic

[H₃O⁺] = [OH^-] it will be neutral

[H₃O⁺] < [OH^-] it will be basic

But how can we find out the strength of any acid or base? There is a scale to measure this strength, which is known as pHscale. To develop a scale it is wiser to choose one parameter, that’s why scientists have chosen the Hydrogen ion concentration.

The concentration of H⁺ and OH^-found experimentally in water is 1.0×10^-7 M. Other compounds also have H⁺ concentration in the same range. It will be quite difficult to memories and write such a large number for various compounds, so scientists have developed an easier way. They defined the H⁺ concentration in terms of log, so that they can cut these digits short to a single number.

If you take log of 1.0×10^-7 it will be -7. Again there is a problem, it is a negative value. To solve this problem, they have taken the negative log so that they can have positive values for scale. Let’s see how we calculate pH:

pH is negative log to the base 10 of concentration of hydrogen ion.

pH = -log [H⁺]

Thus the pH of water will be:

= -log [1.0×10^-7] = 7

Relation between pH, pOH and pKw

Why does pH scale range from 0 to 14?

How can we measure the strength of a particular compound in pH scale? What is its lower or upper limit? The pH scale ranges from 0 to 14. Let’s see why it is up to 14 only and not more than 14. When acidic H₃O⁺ and basic OH^- combine, they form water. If we study the dissociation of water we can solve the mystery of 14.

2H₂O ⇌ H₃O⁺ + OH^-

Or

H₂O + H₂O ⇌ H₃O⁺  + OH^-

One molecule of water acts as acid and gives off proton (H⁺) and other molecule acts as base and accepts that proton. Thus they establish equilibrium. Let’s calculate Equilibrium constant for above reaction:

K = [H₃O⁺][OH^-] / [H₂O]

Water is present here as a medium itself and its concentration is constant, so we can include it with K. Now K will become K_wwhich is called as ionic product of water.

K_w = [H₃O⁺]  [OH^-]

The concentration of H₃O⁺and OH^- found experimentally is 1.0×10^-7 M. Dissociation of H₂O produces same amount of H₃O⁺ and OH^-, that’s why we get equal concentration of H₃O⁺ and OH^-. Acidic and basic factors are equal in case of water, that’s why it is neutral in nature.

If we take negative log on both sides of the equation, we get:

-log K_w  = -log {[H⁺][OH^-]}

-log K_w  = -log [H⁺] + (-log [OH^-])
-log K_w = -log [1.0×10^-7] + (-log [1.0×10^-7])

-log K_w = 7+7 = 14

 pK_w      = pH + pOH = 14

It means that in every solution the product of H⁺ and OH^- ion concentration remains constant. And that’s why pH scale's limits are from 0 to 14.

In case of water there is equal concentration of H⁺ and OH^- ions, so it is neutral. Its pH is 7 which mean 7 is the midpoint in pH scale. If the solution of any compound has H+ concentration more than that of water’s H⁺ concentration [1.0×10^-7], then it will be acidic and will have pH less than 7, similarly if a solution has less H⁺ concentration than that of water then it will be basic and will have pH more than 7.

Strong acids and bases, when dissolved in water, quickly release H⁺ or OH^- ions, so we can get the exact concentration of these ions and we are able to calculate their pH easily. But how will you calculate the pH of weak acids or bases which don’t release all their H⁺ or OH^- ions. How can we get to know their H⁺concentration and how can we calculate their pH? In the next post we will try to calculate the pH of such weak acids and base.

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Lewis Acid Base Theory

You have studied the Lewis dot structure in earlier posts. The same G.N. Lewis who has given the Lewis dot structure has defined acid and base in more generalized term. Every species has electron pairs, so he gave his definition in the terms of electron pairs.

Lewis acids are those which accept electron pairs and Lewis bases are those which donate electron pairs. Let’s check that BF₃ fits in which category?

Lewis Acid and Base

Draw the Lewis dot structure of BF₃molecule. You will find that B has 6 electrons it has incomplete octet. That means it is ready to accept an electron pair to fulfill its octet. Thus it falls under the category of Lewis acids. It means that the species which have incomplete octet (electron deficit) can act as Lewis acid like AlCl₃, BCl₃, Mg²⁺ and so on.

Lewis Vs Bronsted theory

Lewis theory Vs Bronsted theory

Let’s check whether the Brönsted base NH₃ is also a Lewis base or not? When you draw the Lewis dot structure of NH₃ you will find that is has 3 bonded pairs and 1 lone pair of electrons. It can donate one lone pair of electron and acts as Lewis base. Species those are electron rich can act as Lewis base like H₂O, OH^-, Cl^-, O^2- and so on.

If you observe closely, the Brönsted concept and Lewis theory apparently do not have much difference. Brönsted base accepts H⁺(proton) and Lewis base donate electron pair which is the same thing, only difference is in the language.

NH_3(aq) ⟶ NH₄⁺_(aq) 

Brönsted base NH_3(aq) accepts H⁺and becomes  NH₄⁺_(aq). When you draw the structure you will find that NH₃ provides electrons to make bond with H⁺. It means that in either case (Brönsted and Lewis) base provides electrons. Similarly acid accepts electrons in both cases.

How do we know which acid or base is stronger? Is there any method to measure the strength?  In the next post we will explore it.

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Brönsted -Lowry Acid Base Theory

Johannes Brönsted and Thomas M. Lowry gave a generalized definition of acids and bases. They defined them by a common term “proton (H+)”. Acids are those which give proton and bases are those which accept proton.

Brönsted Acid and Base

Let’s see if this theory can explain the basic nature of NH₃.

NH_3(aq)+ H₂O_(l) ⇌ NH₄⁺_(aq) + OH^- _(aq)

Here NH₃accepts proton from H₂O, hence it is called as base.

Conjugate Acid - Base Pair

This theory not only defines acid and base but also clarifies their relation with each other. Acid and base are like the two sides of a coin. As either side of a coin cannot stay alone, acid and base also can’t stay alone. Each of them has its counterpart which is named as conjugate.

In the above equation NH₃ accepts proton and becomes NH₄⁺, here it acts as base.

NH_3(aq) ⟶  NH₄⁺_(aq) 

When you see the reverse reaction, you will see NH₄⁺donates proton and becomes NH₃, thus it acts as acid. NH₃is a base and NH₄⁺is its conjugate acid or vice versa.

NH_3(aq) ⟶ NH₄⁺_(aq) 

Similarly H₂O gives proton to NH₃ and becomes OH^- , so H₂O acts as an acid and OH^- is its conjugate base, which accepts proton from NH₄⁺in reverse reaction. Let’s see one more equation.

HCl_(aq)+ H₂O_(l) ⇌ H₃O⁺_(aq) + Cl^- _(aq)

Here HCl gives proton H⁺ and acts as acid, while H₂O accepts proton and acts as base. I hope now you can find their respective conjugate. HCl has its conjugate base Cl^- and H₂O has its conjugate acid OH^-.

Conjugate Acid-Base Pair

In the above two equations you have seen that H₂O acts as acid when it comes with NH₃ and acts as base when it comes with HCl. That means acid and base are comparative terms.

For example when 2 comes with 1, 2 looks bigger than 1 but if it comes with 3, it looks smaller. Similarly H₂O acts as acid when it comes with NH₃ and acts as base when it comes with stronger acid HCl.

Which factor decides the strength of an acid or base? Readiness to give off the proton decides the strength of any acid. If we compare two acids, the one which readily gives off the proton is the stronger acid. And similarly the one which accepts proton readily is the stronger base.

It is very easy to figure out the corresponding conjugates for acids and bases. If you want to find conjugate acid of any species just add proton (H⁺) to it and if you want to find conjugate base, subtract proton (H⁺) from it. Let’s practice few examples of conjugate acid- base pair:

Species	Conjugate Acid	Conjugate Base
NH3	NH4+	NH2-
H2O	H3O+	HO-
HSO4-	H2SO4	SO42-

Now you must be able to guess the nature of species and also to find the conjugate acid and base of any species. But what happens to those species which lack a Hydrogen? For example, how can we find out whether BF₃ is an acid or base? Arrhenius concept and Brönsted -Lowry acid base theory both are not able to help us in this case. So how do we find the right answer? In the next post we will try to find out its answer.

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What are Acid Base and Salt?

The name acid has been derived from the Latin word “acidus” which means sour. You must have experienced a number of foods which taste sour, like lemons, oranges, grapes and many others. Lemons have citric acid and ascorbic acid is found in oranges. You will be thrilled to know that your body also produces hydrochloric acid in stomach which helps in digestion of food. You can check yourself if something has acid in it or not by simply putting it on a litmus paper. If the paper turns red that means it has acid. Acid changes the colour of litmus paper to red. 

As everything has its counterpart, acid also has its counterpart which is named as Base. It tastes bitter. Baking soda, washing soda are common examples of bases. If you try a litmus paper test, a base will turn it into blue. And when acid and base come together they cancel the effect of each other and thus salt comes into existence. Table salt is the most abundant salt in the nature.

What are acid base and salt?

How can we define an acid and a base? Initially scientist Svante Arrhenius gave a theory which is named after him the Arrhenius theory. According to it acids are those substances which give hydrogen ion when dissolved in water.

HX_(aq) ⟶  H⁺ + X^-_(aq)

H⁺ is very reactive and can’t live alone so it combines with O of H₂O and forms H₃O⁺ ion, it is called hydronium ion. I have used X with H which represents halogens group 17 elements, but why? Think about it.

HX_(aq) + H₂O_(aq) ⟶  H₃O⁺ _(aq) + X^-_(aq)

And bases are the substances which give OH^- ion when dissolved in water.

MOH_(aq) ⟶ M⁺ + OH^-_(aq)

Here I have used M with OH and it represents metals of group 1, think about it too. Arrhenius theory fits well in this case, but it is limited to the aqueous solutions only. It doesn’t explain acidic or basic behaviour of substances lacking H⁺ or OH^-ions. Like ammonia NH₃ which is a base but doesn’t have OH^-ion.

In the next post we will see what solutions have been given by the scientists for such problems.

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Chemical Equilibrium at a Glance

Chemical Equilibrium at a Glance

Equilibrium Constant for a general reaction and its multiples

Le Chatelier’s principles

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Le Chatelier’s principle: Temperature change

In the last post we have seen how the system dealt with the concentration change and pressure change, today we will see what happens if we change the temperature or add some foreign substances like catalyst or noble gases to the system.

You know that equilibrium constant depends on temperature, if we change the temperature, system will no longer be in equilibrium. How can a system control its temperature itself? Energy is released when new bonds are formed and this provides heat to the system. And energy is needed when a bond is broken which is supplied by the system in the form of heat. Now you can guess how the system can deal with it.

When reactants combine to form products, some old bonds are broken and some new bonds are formed. And when we subtract the energies involved, we get to know how much energy is used or released in that particular reaction. If the energy of the reactants is more than that of the products, then energy will be released in the reaction, such reactions are called exothermic reactions. And its opposite is called endothermic reactions, here energy is required.

N_2(g) + 3H_2(g) ⇌ 2NH_3(g)  ......... ∆E = 92.38 kJ mol^-1

The above reaction is an example of exothermic reaction, which means some amount of energy is released. If we increase the temperature of the system, then the system will shift the reaction in backward direction so that it can consume some of the heat. And if we lower the temperature then system will make the forward reaction faster to produce more heat. That means if we want to produce more ammonia we have to keep the temperature low.  

Effect of Temperature change on Equilibrium

Effect of catalyst addition

Catalysts are those substances which speed up the reaction without being involved it in. Suppose you are participating in a race and suddenly you find that a furious dog is chasing you, then what will happen? Naturally you will run like hell. Here the dog is neither participating in the race nor is it involved the race, but its presence speeds up your running. So dog acts as a catalyst.

Catalysts can help a system to achieve equilibrium sooner but their presence don’t create any disturbance because they don’t participate in the reaction.

Similarly addition of noble gases don’t alter the equilibrium because they are noble in nature and do not participate in reaction.

So you have learnt how Le Chatelier’s principle help us to predict the direction of the reaction and help us to understand how a system deals with the changes. Now you will be able to understand what Le Chatelier’s principle states, it states that “a change in any of the factors that determine the equilibrium conditions of a system will cause the system to change in such a manner so as to reduce or to counteract the effect of the change”.

In the next post we will try to sum up all the findings of equilibrium.​

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