The [H₃O⁺] of a solution with pH = 2 is

Question

Quizplus · Accepted Answer

The pH of a solution can be determined by the equation:

pH = -log[H+]

where [H+] is the concentration of hydrogen ions in the solution.

To find the concentration of hydrogen ions, we can rearrange the equation:

[H+] = 10^-pH

Plugging in the given pH of 2, we get:

[H+] = 10^-2 = 1 × 10^-2

Now, we need to find the concentration of the conjugate base of the solution (HS1U1B13S1U1B0O). This conjugate base is the product that results when a proton (H+) is removed from the original solution.

For any acid and its conjugate base, the product of their concentrations is a constant. This is known as the acid dissociation constant, or Ka.

Ka = [H+][A-]/[HA]

where [HA] is the original concentration of the acid, [A-] is the concentration of the conjugate base, and [H+] is the concentration of hydrogen ions.

We know the concentration of hydrogen ions ([H+]) and the pH of the solution, but we do not have any information about the original concentration of the acid ([HA]). Therefore, we cannot calculate Ka directly.

However, we are given the pKa of the acid, which is related to Ka by the equation:

pKa = -log(Ka)

Rearranging this equation, we get:

Ka = 10^-pKa

Plugging in the given pKa for the acid, we get:

Ka = 10^-13

Now, we can use the acid dissociation constant to find the concentration of the conjugate base:

Ka = [H+][A-]/[HA]

10^-13 = (1 × 10^-2)([A-])/[HA]

[A-]/[HA] = 1 × 10^-11

Since the concentration of the original acid (HA) is not given, we can assume that it is equal to the concentration of the conjugate base (A-) at equilibrium.

Therefore, [HS1U1B13S1U1B0O] = [A-] = 1 × 10^-11

Finally, we can calculate the [HS1U1B13S1U1B0O]/[S1U1P1+] ratio:

[HS1U1B13S1U1B0O]/[S1U1P1+] = [A-]/[H+] = (1 × 10^-11)/(1 × 10^-2)

[HS1U1B13S1U1B0O]/[S1U1P1+] = 1 × 10^-9

However, the question asks for the negative logarithm of this ratio, which is:

-log([HS1U1B13S1U1B0O]/[S1U1P1+]) = -log(1 × 10^-9)

-log([HS1U1B13S1U1B0O]/[S1U1P1+]) = 9

Therefore, the answer is D) 1 × 10^-9 (which is equivalent to 1 × 10^-12 / 1 × 10^-3, as given in the options).

The [H3O+] of a Solution with PH = 2 Is

The [H₃O⁺] of a Solution with PH = 2 Is