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

Step by step solution

01

Convert the pH to hydrogen ion concentration

We need to find the hydrogen ion concentration (\( [H^+] \)) of the solution with a pH of 2.05. We can use the formula: pH = - log\(_{10}\)(\[H^+\]) \[H^+\] = 10\(^{-\text{pH}}\) So, substitute the pH value into the formula to find \([H^+]\): \[H^+\] = 10\(^{-2.05}\) \[H^+\] = 8.91 × 10\(^{-3}\) mol/L
02

Calculate the moles of HCl needed

Now, we have to find the moles of HCl needed to produce 10.0 L of the desired solution. We can use the formula: moles = volume × concentration With the given values: moles = 8.91 × 10\(^{-3}\) mol/L × 10.0 L moles = 0.0891 mol
03

Determine the mass of HCl in the concentrated solution

We have been given that the concentrated HCl solution is 36.0% by mass and has a density of 1.18 g/mL. Therefore, we can calculate the mass of HCl per mL of concentrated solution: mass of HCl per mL = density × percentage by mass mass of HCl per mL = (1.18 g/mL) × 0.36 mass of HCl per mL = 0.4248 g/mL
04

Calculate the volume of concentrated HCl solution

Finally, we can now calculate the volume of the concentrated HCl solution required to produce 10.0 L of the desired solution. We will use the formula: volume of concentrated HCl = (moles of HCl needed) / (mass of HCl per mL) Substitute the values: volume of concentrated HCl = (0.0891 mol) / (0.4248 g/mL) volume of concentrated HCl ≈ 0.210 L or 210 mL Approximately, 210 mL of the concentrated hydrochloric acid solution is required to produce 10.0 L of the solution with a pH of 2.05.

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