The label of a bottle containing a solution So of hydrochloric acid carries the following indications :hydrochloric acid of density 1190g/l percentage by mass 37%. We introduce a volume V=4.2ml of So in a volumetric flask of volume 500ml containing about 100ml of distilled water and we complete the volume with distilled water until the linemark. The new solution is noted S.

 Determine the concentration of the solution S prepared. 
In order to verify this concentration we titrate S by using a sloution B of potassium hydroxide of concentration 4×10^-2 mol/l. In 20ml of this solution we pour Vs ml of the solution S and we measure the pH after each addition. V at equivalence 8.1 ml at pH 7.

 Deduce theoretically the pH the solution obtained after the addition of 7mlof S to the 20ml of the basic solution .

To determine the concentration of the solution S prepared, we need to use the given information about the initial solution So and the dilution process.

1. Initial Solution So:
The label of the bottle indicates that the hydrochloric acid has a density of 1190 g/L and a percentage by mass of 37%.

To calculate the mass of the hydrochloric acid in the solution So, we can use the density and the volume of the solution given that the volume used is 4.2 mL.

Mass = Density x Volume
Mass = 1190 g/L x 4.2 mL/1000 mL = 4.998 g

Since the label indicates that the percentage by mass of the hydrochloric acid is 37%, the mass of the solution So can be calculated as follows:

Mass of Solution So = Mass of Acid / (Percentage by Mass / 100)
Mass of Solution So = 4.998 g / (37 / 100) = 13.514 g

2. Dilution Process:
The solution So is diluted by adding it to a volumetric flask with a volume of 500 mL containing about 100 mL of distilled water. The volume is then completed with distilled water until the linemark.

To calculate the concentration of the diluted solution S, we can use the formula:

Concentration of S = (Volume of So / Total Volume of S) x Concentration of So

First, let's calculate the total volume of solution S:
Total Volume of S = Volume of So + Volume of Water
Total Volume of S = 4.2 mL + 100 mL + (500 mL - 100 mL) = 504.2 mL

Now we can calculate the concentration of the solution S:
Concentration of S = (4.2 mL / 504.2 mL) x Concentration of So

3. Titration of Solution S:
To verify the concentration of solution S, it is titrated using a solution B of potassium hydroxide with a concentration of 4 × 10^-2 mol/L. In 20 mL of solution B, Vs mL of solution S is added, and the pH is measured after each addition.

At the equivalence point (when the moles of acid and base are equal), Vs is given as 8.1 mL, and the pH is 7.

To deduce the theoretical pH after adding 7 mL of solution S to 20 mL of the basic solution, we need to use the concept of equivalence and the stoichiometry of the acid-base reaction.

Given that Vs is 8.1 mL at pH 7, we can assume that Vs mL of the base solution is required to neutralize the acid.

Thus, 8.1 mL = Vs mL

Using the ratio of the volumes and the stoichiometry of the acid-base reaction, we can deduce the theoretical pH after adding 7 mL of solution S to 20 mL of the basic solution.