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.
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
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