How much \(\mathrm{HCl}\) would you need to dissolve in 1.0 \(\mathrm{L}\) of water so that \(\left[\mathrm{OH}^{-}\right]=\) \(6.0 \times 10^{-12} \mathrm{M} ?\)

Short Answer

Expert verified
The concentration of \(\mathrm{HCl}\) required is 1.67 \times 10^{-3} \(\mathrm{M}\)

Step by step solution

01

Understanding the Self-Dissociation of Water

Water molecules can self-dissociate into hydrogen ions and hydroxide ions, given by the equation \[2 H2O \longleftrightarrow H3O+ + OH-\]. Because the system is at equilibrium, the law of mass action gives the equilibrium constant for water with respect to concentrations at 25 degrees Celsius as: \(K_w= [H3O+] \cdot [OH-] = 1.0 \times 10^{-14} M^2\).
02

Calculating the Concentration of Hydrogen Ions

We know the concentration of hydroxide ions and the equilibrium constant for water, which means we can find the concentration of hydrogen ions. By rearranging the equation, we get \[ [H3O+] = \frac{Kw}{[OH-]} \] and by substituting the values \[ [H3O+] = \frac{1.0 \times 10^{-14} M^2}{6.0 \times 10^{-12} M}\], we get [H3O+] = 1.67 \times 10^{-3} M.
03

Finding the Concentration of HCl

Because hydrochloric acid is a strong acid, it dissociates completely in water to form hydrogen ions and chloride ions. Thus, in a dilute solution, [H3O+] is practically equal to the concentration of the HCl dissolved. So the concentration of HCl needed to get the given [OH-] is 1.67 \times 10^{-3} M.

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