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-)

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