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Chapter 16: Problem 117

How many milliliters of concentrated hydrochloric acid solution \((36.0 \%\) HCl by mass, density \(=1.18 \mathrm{g} / \mathrm{mL})\) are required to produce 10.0 \(\mathrm{L}\) of a solution that has a pH of 2.05\(?\)

Short Answer

Expert verified
Approximately 7.69 mL of concentrated hydrochloric acid solution (36.0% HCl by mass, density = 1.18 g/mL) is required to produce 10.0 L of a solution with a pH of 2.05.

Step by step solution

01

Determine the concentration of HCl in the final solution

To find the concentration of HCl in the final solution, we use the formula for pH: pH = -log[H+]. In our case, we are given a pH value of 2.05, and we have to find the concentration of hydrogen ions [H+], which in the case of HCl solution equals [HCl]. So: \[2.05 = -\log([HCl])\]
02

Calculate the concentration of HCl

Now we solve for the concentration [HCl]. Take the inverse of the log using 10^(−pH): \([HCl] = 10^{-2.05}\] Calculate the concentration [HCl]: \([HCl] ≈ 8.91 × 10^{-3} \,\text{M}\)
03

Find the moles of HCl required for the final solution

We now have the concentration of HCl in the final solution, 8.91×10^(-3) M. The volume of the final solution is 10 L. We can find the moles of HCl required for this solution using the formula: Moles of HCl = Concentration × Volume Moles of HCl = \(8.91 × 10^{-3} \,\text{M} × 10 \,\text{L}\) Calculate the moles of HCl: Moles of HCl ≈ 0.0891 moles
04

Calculate the mass of HCl required

The mass of HCl required can be found by multiplying the moles of HCl by its molar mass (36.5 g/mol), as given in the problem: Mass of HCl = Moles of HCl × Molar mass Mass of HCl = \(0.0891 \,\text{moles} × 36.5\,\text{g/mol}\) Calculate the mass of HCl: Mass of HCl ≈ 3.25 g
05

Calculate the volume of concentrated HCl required

The concentrated HCl solution is given as 36% by mass with a density of 1.18 g/mL. To find the volume of concentrated HCl required, we can use the mass of HCl required, the percentage composition of HCl in the concentrated solution, and the density of the concentrated solution: Volume of concentrated HCl = (Mass of HCl required) / (Percentage composition × Density) Volume of concentrated HCl = \((3.25 \,\text{g}) / (0.36 × 1.18 \,\text{g/mL})\) Calculate the volume of concentrated HCl: Volume of concentrated HCl ≈ 7.69 mL So, approximately 7.69 mL of concentrated hydrochloric acid solution is required to produce 10.0 L of a solution with a pH of 2.05.

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