What is the pH at 25�C of a 0.17 M solution
of the acid HClO which has an ionization
constant of 3.5 × 10−8?
To determine the pH of a solution, you need to determine the concentration of hydrogen ions (H+) in the solution. In this case, we have a solution of the acid HClO, which ionizes to release H+ ions.
HClO ionizes according to the following equation:
HClO ⇌ H+ + ClO-
The ionization constant (also known as the acid dissociation constant or Ka) is a measure of the extent to which an acid dissociates in water. For HClO, the Ka value is given as 3.5 × 10^(-8).
To find the concentration of H+ ions in the solution, we need to set up an expression for the equilibrium constant (Ka) and solve for the concentration of H+ ions.
The equilibrium constant expression for the ionization of HClO is:
Ka = [H+][ClO-] / [HClO]
We are given the concentration of HClO as 0.17 M. Let's represent the concentration of H+ ions as x (since it is unknown).
Substituting the given values into the equilibrium constant expression:
3.5 × 10^(-8) = x * (0.17 - x)
This is a quadratic equation that we need to solve to find the concentration of H+ ions (x). Rearranging and simplifying the equation:
3.5 × 10^(-8) = 0.17x - x^2
Rearranging further:
x^2 - 0.17x + 3.5 × 10^(-8) = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -0.17, and c = 3.5 × 10^(-8). Plugging in these values:
x = (-(-0.17) ± √((-0.17)^2 - 4(1)(3.5 × 10^(-8)))) / (2(1))
Simplifying:
x = (0.17 ± √(0.0289 - 1.4 × 10^(-7))) / 2
Calculating the value inside the square root:
x = (0.17 ± √(-1.397 × 10^(-7))) / 2
Since the value inside the square root is negative, it means that there is no real solution for x. This indicates that the ionization of HClO in this concentration is negligible.
Therefore, the concentration of H+ ions in the solution is very small, resulting in a pH close to neutral (pH = 7).