How to Calculate Molarity of Standard Solution if Its Volume and the Weight of Primary Standard are Kown

Problem:
A student is preparing for the acid base titration, he was standardized a hydrochloric acid solution by titrating it with 0.3023 g of primary standard sodium carbonate with methyl red as indicator, and boiling the carbonate solution near the end point to remove carbon dioxide. If he needed 37.5 mL of acid required for the titration, so what is the hydrochloric acid molarity?

Solution 1


1. First we calculate the mol of sodium carbonate, but we need to calculate of its formula weight
    Formula weight of Na2CO3 = ( 2 x Ar Na) + (1 x Ar C) + ( 3 x Ar O)
                                                     = ( 2 x 22.99) + ( 1 x 12.01) + ( 3 x 16.00)
                                                     = 105.99 g/mol

                          Mol of Na2CO3 = g/formula weight
                                                      = 0.3023 / 105.99
                                                      = 2.8522. 10^-3 mol
                                                      = 2.8522 mmol


2. Write the chemical reaction
                                             
                                         2HCl + Na2CO3               2NaCl + H2O + CO2

From the reaction we know that mol HCl : mol Na2CO3 = 2 : 1 so the mol of HCl can be calculated

                                       Mol HCl = 2 x mol Na2CO3
                                                       = 2 x 2.8522 mmol
                                                       = 5.7044 mmol

3. because mol and volume of HCl is known, we can calculate its molarity
                            Molarity of HCl = mol/volume
                                                        = 5.7044 / 37.5
                                                        = 0.1521 M


Solution 2
We can solve the problem by calculate the mole equivalent, remember that one equivalent substance A will always react with one equivalent substance B in this case acid and base.

            Mol equivalent Na2CO3 = 2 x 2.8522 = 5.7044 meq

Since,                            meq acid = meq base
                                      NxV acid = NxV base
                                           N acid = ( NxV base ) / V acid
                                                       = 5.7044 / 37.5
                                                       = 0.1521 N
                                                       = 0.1521 M

(Remember 1 N of HCl is the same with 1 M of HCl, because 1 mol HCl = 1 meq of HCl)

Standard Solution

A standard solution is a solution that its concentration known accurately. Standard solution can be classify into two groups that is, a primary standard solution is a standard solution that prepared by dissolving an accurately weighed quantity of a highly pure substance and diluting to an accurately known volume in a volumetric flask.

A secondary standard solution is a solution that obtained from standardized a solution with primary standard solution. For example, sodium hydroxide is not sufficiently pure to prepare a standard solution directly and it is standardized by titrating a primary standard acid like such as oxalic acid. Oxalic acid is a solid that can be weighed accurately.

A primary standard should:

1. High in purity
   
2. Stable for drying temperature and stable in room temperature
   
3. Readily available
   
4. Have a high formula weight (but it is not necessary)
   
5. React with the solution to be standardized directly
   

In acid base titration, hydrochloric acid is usually used as strong acid titrant for the titration of bases, and sodium hydroxide is the usual titrant for titration acids. Because none of theme is primary standard solution, so solutions of approximate concentration are prepared and then standardized with primary solutions.

Standard Base Solution
Sodium hydroxide is usually used as the titrant when base is required. Sodium hydroxide solution is usually standardized by titrating a weighed quantity of primary standard potassium acid phthalate (KHP), and a phenolphthalein end point is used.


Standard Acid solution
Hydrochloric acid is the usual titrant for the titration of base. Hydrochloric acid solution is usually standardized with primary standard sodium carbonate, methyl red is used as indicator and the solution is boiled at the end point because the end point is not sharp. Tris(hydroxymethyl)aminomethane is recommended as the primary standard unless the HCl is being used to titrate carbonate samples. If a standardized NaOH solution is an available the HCl solution can be standardized by titrating it with NaOH solution. Phenolphthalein or Bromothymol blue can be used as indicator.

INDICATOR TRANSITION RANGE

The acid base indicator changes color over a pH range. This transition range depends on the ability of the observer to detect the small color changes. Our eyes can generally discern only one color if it 10 times as intense as the other. In this transition pH ranges indicator would have both forms are colored, only one color with more concentrated form is seen. With this basic we can calculate the pH transition of the indicator.

from the equation above we can predict that indicator changes its color from one color to another from pKa-1 to pKa + 1. During this transition the observed color is a mixture of the two colors, and in the midtransition the concentration of two form of indicator are equal then the pKa of indicator should be close to the pH of the equivalence point. If you on preparing acid base titration you better choose an indicator wit a pKa near the equivalence pH.

Here are ph transition ranges some indicators.

WEAK BASE VERSUS STRONG ACID TITRATION

Weak base versus strong acid titration is an example of acid base titration. The titration of weak base 0.1 M ammonia that titrated with strong acid 0.1 M hydrochloric acid is shown below

At the beginning of the titration ( before the titration is started) we only have ammonia 0.1 M 100 mL. ammonia is a weak base so we can calculate the hydrogen ion concentration with the formula

When the titration is started some of ammonia reacts with hydrochloric acid to yield ammonium chloride and water, so in the Erlenmeyer flask contains ammonium chloride, ammonia, and water this means we have buffer system. As the titration proceeds the pH slowly decrease and the ratio of [NH4+]/[NH3] changes, and in the midpoint of the titration [NH4+] = [NH3], and the pH is equal to pH= 14-pKb. We calculate the pH by pH = (pKw-pKb) + log (CB/CBH+)

At the equivalence point , in the solution contains NH4Cl, because it is a salt from strong acid with weak base it will hydrolyzes partially and the pH at the equivalence will be acid, and the pH will be depends on the concentration ofNH4Cl. The formula for calculate the pH is

When hydrochloric acid is added the free H+ suppresses the ionization, and the pH of the solution is determined only with concentration excess of H+. We calculate the pH by [H+] = [ excess H+].

The indicator for this titration must have a transition range within about pH 4 to 7, so the methyl red is meet s this requirement. If phenolphthalein had been use as the indicator it would have gradually lots its color between pH 10 and 8 before the equivalence point was reach.

note :
CB       = concentartion of weak base (NH4OH)
CBH+ = concentration of the salt ( NH4Cl)

WEAK ACID VERSUS STRONG BASE

Another example of acid base titration is titration between weak acid and strong base. The titration curve of 0.1 M acetic acid 100 mL that titrated with 0.1 M sodium hydroxide is shown below:

At the beginning of the titration ( before the titration is started) we only have CH3COOH 0.1 M 100 mL. Acetic acid is a weak acid so we can calculate the hydrogen ion concentration with the formula  

When the titration is started some of acetic acid reacts with sodium hydroxide to yield sodium acetate and water, so in the Erlenmeyer flask contains sodium acetate, acetic acid, and water this means we have buffer system. As the titration proceeds the pH slowly increase and the ratio of [CH3COO-]/[CH3COOH] changes, and in the midpoint of the titration [CH3COO-] = [CH3COOH], and the pH is equal to pKa. We calculate the pH by pH = pKa + log ( CA^- / CHA).

At the equivalence point , in the solution contains CH3COONa, because it is a salt from strong base with weak acid it will hydrolyzes partially and the pH at the equivalence will be alkaline, and the pH will be depends on the concentration of CH3COONa. The formula for calculate the pH is

 

When sodium hydroxide is added the concentration of CH3COO- is suppressed, and the pH of the solution is determined only with concentration excess of OH-. We calculate the pH by
[OH-] = [ excess OH-].

The indicator for this titration must have a transition range within about pH 7 to 10, so the phenolphthalein is meet s this requirement. If other indicator such as methyl red had been use as the indicator it would have changing color shortly after the titration begin and would change to the alkaline color up to pH 6, before the equivalence was eve reached.


note :

CHA = concentraion in Molar of weak acid (CH3COOH)
CA^- = concentration in Molar of conjugated weak acid ( CH3COO-)

1. 
   

 

STRONG ACID VERSUS STRONG BASE

Acid-base titration that involves strong acid versus strong base, both the titrant and the analyte are completely ionized. The examples acid-base titrations of this type are titration between hydrochloric acid with sodium hydroxide or sulfuric acid with potassium hydroxide. The reaction and the titration curve between 0.1 M NaOH as titrant and 0.1 M HCl as analyte are describe bellow :

The H+ and OH- combine to form H2O and the other ions Na+ and Cl- remain unchanged so the net result of neutralization to a neutral solution of NaCl. The titration curve is constructed by plotting the pH of the solution as the function of the titrant added.

• In the beginning of titration there is only 0.1 M HCl so the initial pH is 1.0. to count the concentration of the H+ we use [H+] = [HCl initial]
  
• 
  
• When the 0.1 M NaOH began to add somepart of the H+ is reacted with OH- to yield H2O. So the concentration of H+ gradually decreases and the pH would be raised. The H+ concentration is calculated by [H+] = [HCl remaining]
  
• 
  
• When the equivalence point is approached (the point at which a stoichiometric reaction is complete), a neutral solution of NaCl with pH would be 7 is produced.
  
• 
  
• As we continue the the concentration of OH- rapidly increases , we then have a solution of NaOH plus NaCl. The OH- concentration is calculated with [OH-] = [excess titrant]
  

DILUTION

We often must prepare dilute solutions from more concentrated stock solutions. The millimole of stock solutions taken for dilution will be identical to the millimoles in the final diluted solution.

Example 1

You have a stock solution 0.200 M of KMnO4 and a series of 100 mL of volumetric flask. What volumes of the stock solution will you have to pipet into the flask to prepare standard solution of 0.005 M KMnO4?

Solution

Moles of 0.005 M KMnO4
= 0.005 x 100
= 0.5 mmol

We must pipet this amount from the stock solution
0.5 = 0.200 X x
    X= 0.5 / 0.200
       = 2.5 mL

Example 2

How much water should be added in 6.0 M 40 mL of H2SO4 solution to produce a 5.0 M H2SO4 solution ?

Solution

6.0 x 40 mL = 5.0 x Volume
Volume = 48 mL

The amount of water that should be added = 48 – 40 = 8 mL

NORMALITY

Useful unit of concentration in quantitative analysis is normality (N), a one normal solution contain one equivalent per liter.

An equivalent represents the mass of material providing avogadro’s number of reacting units. A reacting unit is a proton (in acid-base reaction) or an electron (in oxidation-reduction reaction). The normality of solution is calculated from:

The advantage of expressing concentration in normality and quantities as equivalent is that one equivalent of substance A will Always react with one equivalent of substance B. For the example one equivalent of KOH(=1 mol) will react with one equivalent of HNO3 (=1mol) or with one equivalent of H2SO4 (1/2 mol)

It useful to recognize that, since :

meq A = meq B

Once can calculate the volume of two solutions that will react by :

Na x mLA = NB x mLB

Example 1

Calculate the normality of the solution containing 14.205 g/L of Na2SO4 ( When SO42- reacts with two protons).

Solution

SO42- reacts with 2H+ to form H2SO4

Mol Na2SO4 per L
= 14.205 / 142.05
= 0.1 mol

Number of equivalents Na2SO4
= 0.1 x 2
= 0.2 eq

Normality = 0.2 eq / 1 L = 0.2 N

MOLARITY

Molarity of a solution is expressed as mole per liter or as millimoles per milliliter. Molar is abbreviated as M and we talk molarity of a solution when we speak of its concentration. The molarity of solution is calculated from:

Example 1

Calculate the molarity of a solution containing 10.0 g H2SO4 diluted to 250 mL?

Solution

Count the formula weight of H2SO4

= (2x1.00) + (1x32.07) + (4x16.00)
= 98.07 g/mol

The moles of H2SO4
= 10.0 / 98.07
= 0.10 mol
= 100 mmol

Molarity of H2SO4
= 100 mmol / 250 mL
= 0.4 mmol/ml = 0.4 M

MOLE

The chemist defined the mole as Avogadro’s number (6.022 x 10²³) of atoms, molecules, ions, or other species. The number of moles is calculated from:

             

Example 1

How many moles are present in 1.00 g of P4O6

Solution

The formula weight of P4O6
= (4x30.97) + (6x16.00)
= 219.88 g/mol

Mole of P4O6
= 1 / 219.88
 = 4.55 x 10^-3 mol


Example 2

Calculate the mass of 0.050 mol of dimethylnitrosamine (CH3)2N2O ?

Solution

We calculate the formula weight of dimethylnitrosamine, as follow:

= (2x12.01) + (6x1.00) + (2x14.01) + (1x16.00)
= 74.04 g/mol

Mass of (CH3)2N2O

= mol x formula weight
= 0.050 mol x 74.04 g/mol
= 3,702 g

ACID-BASE INDICATORS

In acid base titration, we wish to determine when the equivalence point is reached, the equivalence point means where the reaction is theoretically complete. In this point the titration process should be terminated. The other, the point at which the reaction is observed to be complete is called the end point.

We take a measurement in such way that the end point coincides with or is very close to the equivalence point. The most obvious way to determine end point is to measure the pH at different points of the titration, but usually more convenient to add indicator to the solution and visually detect the color change.

An indicator for acid-base titration is a weak acid or weak base that highly colored. The color of the ionized is markedly different from that of the un-ionized form. Since the indicator is a weak acid or base, the amount added should be kept minimal so that it does not contribute appreciably to the pH and so that only the small amount of the titrant will be required to cause the color change.

That is the color change will be sharper when the concentration is lower, because less acid or base required to convert it form one to another. Generally, a few tenths percent solution of the indicator is prepared and two or three drops are added to the solution to be titrated.

Phenolphthalein is an example of an indicator which establishes this type of equilibrium in aqueous solution:

Several acid-base indicators are thymol blue, tropeolin OO, methyl yellow, methyl orange, bromphenol blue, bromcresol green, methyl red, bromthymol blue, phenol red, neutral red, phenolphthalein, thymolphthalein, alizarin yellow, tropeolin O, nitramine, and trinitrobenzoic

ACID BASE TITRATION-DEFINITION

Titration is a general class of experiment where a known property of one solution is used to infer an unknown property of another solution. An acid-base titration is a method in titration that allows quantitative analysis of the concentration of an unknown acid or base solution. Acid-base titration involves neutralization reaction that occurs between acids and bases. Acid-base titration can be dividing into:

1. Strong acid versus strong base
2. Weak acid versus strong base
3. Weak base versus strong acid


The equipments that involve in titration are usually Burette, Pipette, Acid/Base Indicator, Erlenmeyer flask, Standard solution, and Solution of unknown concentration, White Tile or white paper used to see a color change in the solution.

The standard solution is the solution that the concentration is known and usually takes place in the burette and called as “titrant”. The solution of unknown concentration called “analyte” and take place in the Erlenmeyer.

Before we start doing acid-base titration, we should choose a suitable acid-base indicator. We use indicator to determine the endpoint of the reaction. An indicator for an acid-base titration is a weak acid or weak base that is highly colored. The indicator changes color when the endpoint is reached.

First, the burette should be rinsed with the standard solution and it should be filled to the top of its scale. You should rinse the pipette with the unknown solution, and the conical flask with distilled water.

Solution of unknown concentration in a known volume should be taken with pipette and placed in Erlenmeyer and add a small amount of acid-base indicator. The standard solution should then be allowed from the burette into the Erlenmeyer. Let the standard solution out of the burette until the indicator changes color than record the value on the burette. Perform three or more titration, record the readings on the burette and then average these at the endpoint.

THE MEANING OF pH SCALE

In acid base titrations the concentration of H+ and OH- in aqueous solution can vary in wide ranges, to construct a plot of H+ concentration against some variable would be difficult if the concentration change from, say 10exp-1 to 10exp-13 M. In order of that, it is more convenient to compress the acidity scale by placing a logarithm basis. The pH of a solution was defined as :

pH = - log [H+]

a similar definition is made for the hydroxyl ion concentration:

pOH = - log [OH-]

The minus sign is used because most of the concentration encountered are less than 1 M, and this designation gives a positif number.

The product of the hydrogen ion concentration and the hydroxyl ion concentration in aqueous solution is always equal to 1.0 x 10exp14 at room temperature:

Kw = [H+][OH-] = 1.0 x 10^-14

Kw is the molar equilibrium constant. The above equation can be used to calculate the hydrogen ion concentration if the hydroxyl ion concentration is known, and vice versa. The equation in logarithm form can be written as :

- log Kw = -log[H+][OH-] = -log [H+] – log [OH-]

                                                    

Kw = pH + pOH

14= pH + pOH

WHAT'S ACID? AND WHAT'S BASE?

Acids were first recognized as a class of substances that taste sour and Bases sometimes called alkalis, are characterized by their bitter taste and slippery feel. Scientists have postulated some theories to defined acids and bases as follow :

Arrhenius Theory
An acid is any substance that ionizes in water to give hydrogen ions, and a base ionizes in water to give hydroxyl ions. This theory is obviously restricted to water as the solvent.

Theory of The Solvent Systems
Franklin introduced the solvent systems theory in 1905. This theory is similar with the Arhenius theory, but applicable also to other ionizable solvents. The theory said :An acid is defined as a solute that yields the cation of of the solvent while the base is a solute that yields the anion of the solvent.

See at the picture, when we dilute sodium ethoxide into ethanol, sodium ethoxide ionize to give C2H5O- ion. Because of diluting sodium ethoxide yields anoin of the solvent so we can say that sodium ethoxide is strong base. Meanwhile diluting ammonium chloride in liquid ammonia produced NH4+ ion, that is cation of the solvent. So we say that ammonium chloride is a strong acid.

Bronsted-Lowry Theory
This theory states that an acid is any substance that can donate a proton and a base is any substance that can accept a proton. For the example see this reaction below :

Acid1 and base1 or acid2 and base2 are called acid-base conjugated.


Lewis Theory
G. N. Lewis introduced electronic theory of acids and bases in 1923. This theori said that an acid is a substance that can accept an electron pair and the a base is a substance that can donate an electron pair.

In the first reaction the aluminium chloride is an acid because it accept electron pair from the ether. In the second reaction the water is a base because water gives its electron pair into proton.