What volume of a concentrated HCl solution, which is 36.0% HCl by mass and has a density of 1.179 g/mL, should be used to make 5.20 L of an HCl solution with a pH of 1.70

The volume we need is 8.89 mL

Explanation:

We analyse dа ta:

36 % by mass → 36 g of HCl in 100 g of solution

Solution's density = 1.179 g/mL

5.20L → Volume of diluted density

pH = 1.70 → [H⁺] = 10⁻¹'⁷⁰ = 0.0199 M

HCl → H⁺ + Cl⁻

0.0199

pH can gives the information of protons concentrations, so as ratio is 1:1, 0.0199 M is also the molar concentration of HCl

Let's verify the molar concentration of the concentrated solution:

We convert the mass to moles: 36 g / 36.45 g/mol = 0.987 moles

As the solution mass is 100 g, we apply density to find out the volume:

Density = Mass / volume → Volume = Mass / Density

Volume = 100 g / 1.179 g/mL → 84.8 mL

Let's convert the volume from mL to L in order to define molarity

84.8 mL. 1L / 1000mL = 0.0848 L

Molarity → 0.987 mol / 0.0848L = 11.6M

Let's apply the dilution formula:

M concentrated. V concentrated = M diluted. V diluted

11.6 M. V concentrated = 0.0199M. 5.20L

V concentrated = (0.0199M. 5.20L) / 11.6M → 8.89*10⁻³L

We can say, that the volume we need is 8.89 mL