0.6 Neutralization reaction (Page 2/2)

Stoichiometry Page 2 / 2

In terms of moles, we have :

$m moles of A_{1} \equiv n moles of A_{2} \equiv p moles of A_{3} \equiv q moles of A_{4}$

$m M_{1} V_{1} \equiv n M_{2} V_{2} \equiv p M_{3} V_{3} \equiv q M_{4} V_{4}$

Consideration in molarity gives a relation that needs to be analyzed using unitary method. It is important to realize that this is not a relation which are not connected with "equal to (=)" sign. In terms of gram equivalents (geq), we have :

$geq of A_{1} = geq of A_{2} = geq of A_{3} = geq of A_{4}$

$N_{1} V_{1} = N_{2} V_{2} = N_{3} V_{3} = N_{4} V_{4}$

Consideration in normality gives a relation that are connected with "equal to (=)" sign. It is so because constituents react in the proportion of equivalent weights. As such, gram equivalents are equal. Clearly, analysis involving normality is relatively easier to handle.

Problem : A 25 ml of nitric acid taken from a stock volume of 1 litre neutralizes 50 ml of 0 .1N NaOH solution. Determine the mass of nitric acid in the stock volume.

Solution : Let us denote nitric acid and sodium hydroxide by subscripts "1" and "2" respectively. Applying neutralization equation,

$N_{1} V_{1} = N_{2} V_{2}$

$\Rightarrow N_{1} X 25 = 0.1 X 50$

$\Rightarrow N_{1} = \frac{5}{25} = 0.2$

The normality of sample and the stock volume is same. Hence, normality of 1 litre stock volume is 0.2N. Using formula,

$\Rightarrow geq = N V = 0.2 X 1 = 0.2 = \frac{g_{B}}{E} = \frac{x g_{B}}{M_{O}}$

Valence factor of nitric acid is 1 as it has one furnishable hydrogen. Therefore,

$\Rightarrow g_{B} = \frac{0.2 M_{O}}{x} = \frac{0.2 X (1 + 14 + 3 X 16)}{1} = 12.6 g m$

Successive neutralization

In this case, data of two or more neutralization reactions is analyzed to determine unknown concentration of solution.

Problem : 18 ml of 0.1N $H_{2} S O_{4}$ is neutralized by 20 ml of a NaOH solution. On the other hand, 10 ml of oxalic acid is required to neutralize the same volume of NaOH solution. Determine the mass of oxalic acid crystals ${{(C O O H)}_{2} .2 H_{2} O}$ used.

Solution : A solution of known concentration of sulphuric acid neutralizes sodium hydroxide solution of unknown concentration. Applying neutralization equation, we determine normality of sodium hydroxide solution :

$N_{1} V_{1} = N_{2} V_{2}$

$\Rightarrow 0.1 X 18 = N_{2} X 20$

$\Rightarrow N_{2} = \frac{1.8}{20} = 0.09 N$

Now, a solution of known concentration of sodium hydroxide neutralizes oxalic acid solution of unknown concentration. Again applying neutralization equation, we determine normality of oxalic acid solution :

$N_{1} V_{1} = N_{2} V_{2}$

$\Rightarrow 0.09 X 20 = N_{2} X 10$

$\Rightarrow N_{2} = \frac{1.8}{10} = 0.18 N$

Using formula,

$\Rightarrow geq = N V = \frac{0.19 X 10}{1000} = \frac{1.9}{1000} = 0.0019 = \frac{g_{B}}{E} = \frac{x g_{B}}{M_{O}}$

Valence factor of oxalic acid is 2 as it has two furnishable hydrogens. Therefore,

$\Rightarrow g_{B} = \frac{0.0019 M_{O}}{x} = \frac{0.0019 X {2 X (12 + 2 X 16 + 1) + 2 X 18}}{2} = 0.1197 g m$

Dilution and neutralization

The resulting solution of two or more solutions or diluted solution is neutralized by other solution.

Problem : 5 ml each of 2N hydrochloric and 3N nitric acids volumes are mixed with a certain volume of 5N sulphuric and the resulting solution is made up to 1 litre. A volume of 25 ml of this solution neutralizes 50 ml of sodium carbonate solution containing 1 gm of $N a_{2} C O_{3} .10 H_{2} O$ in water. Determine the volume of sulphuric acid in the mixture.

Solution : A combination of different acids are used here. The mixture is then diluted up to 1 litre. Let the volume of sulphuric acid used is x ml. Here, milli-gram equivalents of the mixture is :

$\Rightarrow meq = 5 X 2 + 5 X 3 + 5 x = 25 + 5 x$

Applying equation of dilution,

$N_{1} V_{1} = N_{2} V_{2}$

$\Rightarrow 25 + 5 x = N_{2} X 1000$

$\Rightarrow N_{2} = \frac{25 + 5 x}{1000}$

We see here that normality of acid solution has one unknown. 25 ml of diluted acid neutralizes 50 ml of sodium carbonate solution. Clearly, we need to calculate normality of sodium carbonate used. We see here that strength of sodium carbonate solution is given (1 gm/50 ml = 20 gm/l). Using relation,

$S = N E$

The valence factor of sodium carbonate is 2 as its cation or anion has 2 electronic charge.

$\Rightarrow N = \frac{S}{E} = \frac{x S}{M_{O}} = \frac{2 X 20}{(2 X 23 + 12 + 3 X 16 + 10 X 18)} = \frac{40}{286} = 0.14 N$

Now, using neutralization equation :

$N_{1} V_{1} = N_{2} V_{2}$

$\Rightarrow \frac{25 + 5 x}{1000} X 25 = 0.14 X 50$

$\Rightarrow 25 + 5 x = 0.28 X 1000 = 280$

$\Rightarrow 5 x = 280 - 25 = 255$

$\Rightarrow x = \frac{255}{5} = 51 m l$

Neutralization of oleum

Oleum is concentrated sulphuric acid and free suplhur trioxide ( $S O_{3}$ ). When $S O_{3}$ reacts with water, it produces sulphuric acid.

$S O_{3} + H_{2} O \to H_{2} S O_{4}$

It means that $S O_{3}$ molecule is equivalent to sulphuric acid in the presence of water. Thus, neutralization of base with oleum acid will follow the equivalence as :

$geq of H_{2} S O_{4} + geq of S O_{3} = geq of b a s e$

Problem : 1 gm of oleum is diluted in water. The resulting solution requires 45 ml of 0.5N sodium hydroxide solution for neutralization. Determine the mass of free $S O_{3}$ in the oleum.

Solution : Let mass of $S O_{3}$ in oleum is x. Then, mass of sulphuric acid in the oleum is 1-x. We can find gram-equivalents of the sulphuric acid and oleum provided we know valence factors. The valence factor of each of them is 2. Hence, equivalent weights of sulphuric acid and Sulphur trioxide are 98/2=49 and 80/2=40 respectively. Applying neutralization equation,

$geq of H_{2} S O_{4} + geq of S O_{3} = geq of b a s e$

$\frac{1 - x}{49} + \frac{x}{40} = N V = \frac{0.5 X 45}{1000} = \frac{22.5}{1000}$

$\Rightarrow 40 - 40 x + 49 x = 49 X 40 X \frac{22.5}{1000} = 44.100$

$\Rightarrow 9 x = 4.41$

$\Rightarrow x = \frac{4.41}{9} = 0.5 g m$

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Source: OpenStax, Stoichiometry. OpenStax CNX. Jul 05, 2008 Download for free at http://cnx.org/content/col10540/1.7

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