Commercial hydrochloric acid (HCl) is typically labeled as being 38.0 % (weight %). The density of HCl is 1.19 g/mL. a) What is the molarity of the commercial HCl solution? b) What is the molality of the commercial HCl solution? c) How many liters of the above commercial HCl solution do you need in order to prepare 5.00 L of a 6.00 M HCl solution?

[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]

We are given:

Molarity of solution = ?

Molar mass of HCl = 36.5 g/mol

Volume of solution = 84.034 mL

Mass of HCl = 38 g

Putting values in above equation, we get:

[tex]\text{Molality of commercial HCl solution}=\frac{38\times 1000}{36.5\times 84.034}\\\\\text{Molality of commercial HCl solution}=12.39M[/tex]

Hence, the molarity of commercial HCl solution is 12.39 M.

For b:

To calculate the molality of solution, we use the equation:

[tex]Molarity=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}[/tex]

Where,

[tex]m_{solute}[/tex] = Given mass of solute (HCl) = 38 g

[tex]M_{solute}[/tex] = Molar mass of solute (HCl) = 36.5 g/mol

[tex]W_{solvent}[/tex] = Mass of solvent = 100 - 38 = 62 g

Putting values in above equation, we get:

[tex]\text{Molality of commercial HCl solution}=\frac{38\times 1000}{36.5\times 62}\\\\\text{Molality of commercial HCl solution}=16.79m[/tex]

Hence, the molality of commercial HCl solution is 16.79 m.

For c:

To calculate the molarity of the diluted solution, we use the equation:

[tex]M_1V_1=M_2V_2[/tex]

where,

[tex]M_1\text{ and }V_1[/tex] are the molarity and volume of the concentrated solution

[tex]M_2\text{ and }V_2[/tex] are the molarity and volume of diluted solution

We are given:

[tex]M_1=6M\\V_1=5.00L\\M_2=12.39M\\V_2=?L[/tex]

Putting values in above equation, we get:

[tex]6\times 5=12.39\times V_2\\\\V_2=2.42L[/tex]

Hence, the volume of commercial HCl solution needed is 2.42 L.