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Equilibrium Acids and Bases

Acid base equilibrium reactions between acids and bases. Acid base equilibrium represent the union of three major chemistry topics of reaction types, stoichiometry and equilibrium. Acid base equilibrium are intimately coupled to many of the processes involved in synthetic and analytical chemistry with reaction rates and selectivity, solubility equilibrium, partition equilibrium, catalytic cycles and chromatography. 

Two most important classes of chemical compounds are acids and bases. These compounds are around us in every material we bring in for use. Whether we drink fruit juice, analgesic, milk, baking soda, vinegar, soap or even toothpaste that we pop in our mouth in the morning. More closely, our fundamental unit of parental characters, DNA or deoxyribonucleic acid are nothing but combination of bases and amino acid chains. 

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Acid Base Equilibrium Definition

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Human use of acids and bases dates back thousands of years and long back vinegar was produced by converting alcohol into acetic acid by the action of bacteria. Alchemists discovered the preparation method of strong mineral acids and came the aqua regia or ability to melt precious metals like gold. Long after, Arrhenius defined acids as substances that dissociates in water to give hydrogen ions (H+) and defined base as substance that dissociates into hydroxide (OH-). Hydrogen ion is simply a hydrogen atom minus its electron as it consist of only proton inside the nucleus and one electron in the cloud. 

Acid: $HA + H_2O \rightarrow H^+ (aq) + A^-  (aq)$

Base: $BOH + H_2O \rightarrow OH^- (aq) + B^+ (aq)$

When an acid dissociate to produce hydrogen ions in water the hydrogen ions do not remain as individual ions but are pulled towards polar water molecules and form Hydronium ions $(H_3O^+)$. Arrhenius defined that an acid should state an acid is a substance that produces hydronium ions in solution. The important things to remember is that hydrogen ions do not exist as individual ions in water but become hydrated. Similarly, the presence of hydroxide ions are contained within bases contradict weak base ammonia. As per Arrhenius bases do not have to contain hydroxide ion to produce hydroxide in aqueous solution. When ammonia dissolved in water, the reaction shows:

$NH_3 (g) + H_2O (l) \leftrightarrow NH_4^+ (aq) + OH^- (aq)$

The classical acid base employs Henderson – Hasselbalch equation for classification of acid and base disorders into respiratory and metabolic forms for compensatory changes. This employs a limited charge equilibrium method or anion gap and help narrow differential diagnosis. On the basis of dissociation limits these are again further classified as strong and weak electrolytes. Strong electrolytes are always completely dissociated in solution and hence the parent substance disappears when dissolved in water. Solutions of strong electrolytes contain only the ions derived from the parent substances but none from the un dissociated parent molecules. Strong electrolyte solution doesn’t allow ordinary chemical reactions. 

Like when we mix a solution of HCl in water with a solution of NaOH, the usual way of writing is the normal pattern of  $NaOH + HCl \rightarrow NaCl + H_2O$, but NaOH solution has $Na^+$, $OH^-$ and H+ ions but not NaOH and similarly HCl has $Cl^-$, $OH^-$ and $H^+$ ions but not HCl. 

$H_2O \leftrightarrow H^+ + OH^-$

The Na+ and Cl- has not taken part in any reactions and no NaCl is formed. Ions such as Na+ or Cl- that are derived from strong electrolytes are ideally termed as strong ions. Compared to these the weak electrolytes are substances only partially dissociate when dissolved in water so that the parent as well as products of dissociation all exist together in solution. Equilibrium requires that the rate of dissociation equal the rate of recombination and leads to quantitative requirement on concentration of three molecular species.

$HA \leftrightarrow H^+ + A^-$ 

[H+] * [A-] = KA * [HA]

The equilibrium constant KA is usually called the dissociation constant and unit is equivalents per litre. The equilibrium constant is exponentially related to the standard free energy change per mole for the reaction. Dissociation reactions are rapid and equilibrium is achieved with half times on the order of microseconds or less. A quantity sometimes used to describe the status of dissociation equilibrium is degree of dissociation with a symbol α, defined as the concentration of one of the product ions divided by total concentration of weak electrolyte.

αA = $\frac{[A-]}{[A-] + [HA]}$  = $\frac{[A-]}{[ATOT]}$

The degree of dissociation may be expressed either as a percentage or as a decimal fraction. 

Weak Acid Base Equilibrium

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Amongst the most common weak acid is acetic acid. Only a few acetic acid molecules react with water to give acetate ions and hydronium ions and major species present in equilibrium in aqueous solutions are acetic acid and water. In this acid base reaction the water serves the role of base. 

$CH_{3}COOH + NH_{3} \leftrightarrow CH_{3}COO^- + NH4^+$

Here, acetate ion is the conjugate base of acetic acid and ammonium ion is the conjugate acid of ammonia.

Determine which conjugate acid is the stronger acid and then use this in the formation along with the fact that the stronger the acid, the weaker its conjugate base is. Since acetic acid is stronger acid which gives the acetate being weaker base. Conversely ammonium ion is the weaker base and that means ammonia is the stronger base. 

In acid base reaction, the equilibrium position always favours reaction of the stronger acid and stronger base to form the weaker acid and weaker base, hence at equilibrium, the major species present are weaker base.  

Acid base equilibrium problems

Problem 1:
What weak acid – weak base equilibrium is present when 0.15 mol of NaOH is added to 0.3 mol of acetic acid and diluted to 1L?

Solution: 
$CH_3COOH (aq) + OH^- (aq) \rightarrow CH_3COO^- (aq) + H_2O$

0.3 mol        0.15 mol     

0.15 mol         0 mol       0.15 mol    0.15 mol

The strong base is the limiting reagent and it’s neutralized completely. Portion of the acetic acid is converted to acetate ion. 
    
Problem 2:
What is the hydronium ion concentration of a solution prepared by adding 0.0250 mol of $HClO_4$ to water and the diluting up to 1.0 L?

Solution: 
The $HClO_4$ is considered a strong electrolyte and it dissociates completely in water. 

The reaction:

$HClO_4 + H_2O \rightarrow ClO_4^- (aq) + H_3O^+ (aq)$

$[H_3O^+]$ = [0.0250 / 1.0 L] = 0.025 M

pH Curves

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The basic criterion for identifying acid and base in aqueous solution is the concentration of hydrogen and hydroxide ions. When an acid dissolves in water, the water acts as base and readily accepts protons to form the hydronium ion. The water itself dissociates by small extent and produce hydrogen and hydroxide ions. At 25 degree C the concentration of hydronium and hydroxide ions in water are both equal to 1.0 * 10-7 M. The equilibrium constant for the above reaction is known as the ion product constant of water, symbolized by Kw and is equal to product of H+ and OH- molar concentration.

Ion concentration are small and negative exponent and the term pH means power of hydrogen. The relation is given by: pH = - log [H+] 
The pH is equal to negative log of hydrogen ion molar concentration. Similarly the pOH is also calculated. pOH = - log [OH-] 
As H+ ions are used uo OH- during titration the number H+ ions decrease due to reaction with OH-. The lower the [H+] higher is the pH. This increase in pH can also be seen by suing ph meter. Hence if we have to measure pH in this manner after each addition of an base, then it reflects in a specific manner in the graph for the experiment. This relation between the titrated value is better disolayed with the help of titration curve or in some cases termed as pH curve. 

pH Curves

Buffer Solutions

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A buffer is a solution whose pH changes very little when a small amounts of $H_3O^+$ or $OH^-$ ions are added to it. The pH buffer is an acid or base. The most common buffers consist of approximately equal molar amounts of a weak acid and salt of a weak acid. Buffers solution resist changes in pH inspite small addition of acid or base. Buffer solution are made to maintain specified acidic or basic pH values. This keeps spreading by identifying a region in a titration curve where buffer action is taking place. When a strong acid is added to the weak base like ammonia, the pH initially falls significantly after this the titration curve shows only a moderate fall in pH even though a strong acid is added to mixture. This portion is of titration curve where buffer action is occurring is called buffer zone. 

Buffer solutions are usually made by mixing suitable reactants in solution rather than by carrying out acid base titrations. Acidic buffer solutions maintain same pH value value less than 7 while basic buffer more than 7. Acidic buffer consist of solution of a weak acid and a salt that supplies the conjugate base of weak acid. While basic buffer consist of a solution of a weak base and a salt that supplies conjugate acid of weak base. 

Acid Base Indicators

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Acid base indicators are also known as pH indicators. The Acid base indicators are dye substances which change colour with pH. These are weak acids or bases when dissolved in water get slightly dissociate to forms ions. 
  • Acid base indicators are one component systems compared to three components required for colour change
  • Acid base indicators are generally soluble in organic solvent
  • Acid base indicators can be synthesized to give excellent purity and yield.
Examples are phenopthaeline, thymol blue, methyl red, methyl orange and bromothymol blue.
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