The pH value of a solution can be calculated using the concentration of hydroxide ions ([OH-]) and the equilibrium constant for water (Kw), which is equal to 1.0 × 10^(-14) at 25°C.
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration ([H+]):
pH = -log[H+]
In neutral water, the concentration of hydrogen ions is equal to the concentration of hydroxide ions, so [H+] = [OH-]. Therefore, we can rearrange the equation to calculate the pH in terms of [OH-]:
pOH = -log[OH-]
pOH + pH = 14 (since pH + pOH = 14 in neutral water)
Now, let's calculate the concentration of hydroxide ions ([OH-]) in a solution of hydrochloric acid (HCl) with a pH of 3.7:
Given: pH = 3.7 Kw = 1.0 × 10^(-14)
Since pH + pOH = 14, we can calculate pOH as follows:
pH + pOH = 14 3.7 + pOH = 14 pOH = 14 - 3.7 pOH = 10.3
Now, we can calculate the concentration of hydroxide ions using pOH:
pOH = -log[OH-] 10.3 = -log[OH-]
Taking the antilog (inverse logarithm) of both sides, we get:
[OH-] = 10^(-pOH) [OH-] = 10^(-10.3)
Using a calculator, we find that [OH-] ≈ 4.99 × 10^(-11) M.
Therefore, the concentration of hydroxide ions in the HCl solution with a pH of 3.7 is approximately 4.99 × 10^(-11) M.