Question

Suppose 2.17 mol of HCl is dissolved in enough water to give 504.5 mL of solution.
What is the H3O+ concentration?
What is the pH?

Answer 1

HCl is a strong electrolyte: it means that the dissociation is nearly complete in water solution (pK_a=-9.3, or K_a=10^9.3). The reaction of dissociation of HCl in water is:

HCl + H₂O $\rightarrow$ H₃O⁺ + Cl^-.

As you can see, one mole of HCl gives one mole of the H₃O⁺ ions. Therefore, the concentration of H₃O⁺ is equal to the concentration of HCl:

$c(H_3O^+) = c(HCl) = \frac{2.17}{504.5·10^{-3}} = 4.30$ mol/L, or M.

The pH is defined as -log(c(H⁺)):

$pH = -log([H_3O^+]) = -log(4.30) = -0.63$ .

Don't worry about the negative pH. The misconception that pH lies between 0 and 14 is disclaimed in literature[1].

[1] : Kieran F. Lim, Journal of Chemical Education 2006 83 (10), 1465, DOI: 10.1021/ed083p1465

Answer: the concentration of H₃O⁺ is 4.30 M. The pH is -0.63.