# Which of the following pH measurements is the weakest acid; a pH of 4, a pH of 6, or a pH of 8?

Jun 20, 2018

...or rather, which $p H$ corresponds to the LEAST concentration of hydronium ion...${H}_{3} {O}^{+}$

#### Explanation:

And $p H = 8$ corresponds to the LEAST concentration of ${H}_{3} {O}^{+}$, the acidium ion in aqueous solution...

Water undergoes autoprotolysis…

$2 {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + H {O}^{-}$

And under standard conditions of pressure and temperature...we write and quantify the equilibrium expression...

${\underbrace{{K}_{w} = \left[{H}_{3} {O}^{+}\right] \left[H {O}^{-}\right] = {10}^{-} 14}}_{\text{autoprotolysis of water at 298 K}}$

Now as for any equation, we can divide, multiply it, subtract from, add to...so long as we do it to BOTH sides, and maintain the equality. One thing we CAN do is to take ${\log}_{10}$ OF BOTH SIDES...

${\log}_{10} \left({K}_{w}\right) = {\log}_{10} \left[{H}_{3} {O}^{+}\right] + {\log}_{10} \left[H {O}^{-}\right] = {\underbrace{{\log}_{10} \left({10}^{-} 14\right)}}_{\text{-14}}$

And on rearrangement …$+ 14 = - {\log}_{10} \left[{H}_{3} {O}^{+}\right] - {\log}_{10} \left[H {O}^{-}\right]$

And by definition...$+ 14 = {\underbrace{- {\log}_{10} \left[{H}_{3} {O}^{+}\right]}}_{\text{pH"underbrace(-log_10[HO^-])_"pOH}}$

And given this definition of $p H$, the LOWER NUMERICALLY the $p H$ the GREATER the CONCENTRATION of ${H}_{3} {O}^{+}$, the $\text{acidium ion}$

And so at $p H = 8$...$\left[{H}_{3} {O}^{+}\right]$ is LESS than $\left[H {O}^{-}\right]$ by TWO orders of magnitude,,,this solution is BASIC....and is LEAST ACIDIC...