Question

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 4.60 L of an HCl solution with a pH of 1.60? Express your answer to two significant figures and include the appropriate units.

Answer 1

PH = 1.60

-log[H+] = 1.60

[H+] = 0.0251 M

thus

molarity of diluted HCl solution = 0.0251 M

36.0% HCl by mass means 36.0 g HCl remain in 100 g solution.

thus

volume of 36.0 % HCl solution = mass / density = 100 g / 1.179 g/mL = 84.82 ml

36.0 g HCl = mass / molar mass = 36.0 g / 36.5 g / mole = 0.9863 mole.

thus

molarity of HCl (36.0 %) = 0.9863 mole / 0.08482 L = 11.63 M

Using the dilution law,

V1 * S1 (before dilution) = V2 * S2 (after dilution)

or

V1 * 11.63 M = 4.60 L * 0.0251 M

or

V1 = 9.93 * 10^-3 L = 9.93 ml

thus

volume of a concentrated HCl solution = 9.936 ml