### Video Transcript

Which of the following equations
can be used to calculate the concentration of hydronium ions? (A) The concentration of OH− equals
10 to the pOH. (B) The concentration of OH− equals
10 to the negative pOH. (C) The concentration of H3O+
equals 10 to the negative pOH. (D) The concentration of H3O+
equals 10 to the negative pH. Or (E) the concentration of H3O+
equals 10 to the pH.

In order to determine which
equation can be used to calculate the concentration of hydronium ions, we need to
know what a hydronium ion is. Hydronium ions are formed in an
acid–base reaction when water molecules accept a proton or H+ ion. The chemical symbol of a hydronium
ion is H3O+. We can indicate the concentration
of hydronium ions by placing the chemical symbol inside of brackets. We can see that answer choices (C),
(D), and (E) contain the term “concentration of hydronium ions.” Answer choices (A) and (B) contain
the term “concentration of hydroxide ions.” So we can eliminate these answer
choices.

We can see from the answer choices
that the concentration of hydronium ions must be related to either the pOH or the
pH. Both the pH and pOH are unitless
values that are used as a more practical method to represent the concentration of
specific ions. The pOH can be calculated by taking
the negative logarithm of the concentration of hydroxide ions, while the pH can be
calculated by taking the negative logarithm of the concentration of hydronium
ions. We can see then that the pOH is not
directly related to the hydronium ion concentration. Therefore, we can eliminate answer
choice (C).

We now know that pH and the
concentration of hydronium ions are related. But we need to rearrange this
equation in order to calculate the concentration of hydronium ions. To do this, we need a basic
understanding of logarithms. The logarithm used in this equation
is a base 10 logarithm. To better understand this function,
let’s consider the value 1000, a multiple of 10. 1000 is equal to 10 times 10 times
10. In other words, 1000 is equal to 10
to the third power. The base 10 logarithm of a number
is equal to the power to which 10 must be raised in order to obtain that number. So the base 10 logarithm of 1000 is
equal to three.

Now that we have a basic
understanding of logarithms, we can relate these two general equations to the pH
equation. In the pH equation, the
concentration of hydronium ions is 𝑥. But before we can determine 𝑦,
we’ll need to move the negative sign. We can accomplish this by dividing
both sides of the equation by negative one. This gives us negative pH equals
the logarithm of the concentration of H3O+. Now we can see that negative pH is
𝑦 and the concentration of H3O+ is 𝑥. We can then write an equation
following the format 𝑥 equals 10 to the power of 𝑦. This gives us the equation
concentration of H3O+ equals 10 to the negative pH. This matches the equation shown in
answer choice (D).

Therefore, the equation that can be
used to calculate the concentration of hydronium ions is answer choice (D). The concentration of H3O+ equals 10
to the negative pH.