# Question 72592

Nov 12, 2016

Here's what I got.

#### Explanation:

For starters, the thing to remember about neutral solutions is that they have a pH equal to $7$ at room temperature. This means that you mislabeled the $\text{pH} = 7.00$ solution as being basic, when in fact, it is neutral.

Now, a neutral solution kept at room temperature always has

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{pH " + " pOH} = 14}}}$

In terms of the concentration of hydronium cations, ${\text{H"_3"O}}^{+}$, which can also be represented as ${\text{H}}^{+}$, and hydroxide anions, ${\text{OH}}^{-}$, you have

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\left[{\text{H"_3"O"^(+)] * ["OH}}^{-}\right] = {10}^{- 14}}}}$

A neutral solution must have

$\left[{\text{H"_3"O"^(+)] = ["OH}}^{-}\right]$

which means that at $\text{pH} = 7.00$, you have

["H"_3"O"^(+)] = ["OH"^(-)] = 1.0 * 10^(-7)"M"

Consequently, an acidic solution will always have

{("pH" < 7), ("pOH" > 7) :} " " and " " {(["H"_3"O"^(+)] > 1.0 * 10^(-7)"M"), (["OH"^(-)] < 1.0 * 10^(-7)"M") :}

and a basic solution will always have

{("pH" > 7), ("pOH" < 7) :} " " and " " {(["H"_3"O"^(+)] < 1.0 * 10^(-7)"M"), (["OH"^(-)] > 1.0 * 10^(-7)"M") :}

Remember, an acidic solution has a higher concentration of hydronium cations than of hydroxide anions, and so its pH falls below $7.00$.

A basic solution has a higher concentration of hydroxide anions than of hydronium cations, and so its pH rises above $7.00$.

With this in mind, where would the solution that has

["OH"^(-)] = 5.7 * 10^(-3)"M"

be placed? Since it's clear that

$5.7 \cdot {10}^{- 3} > 1.0 \cdot {10}^{- 7}$

you should say that this solution is basic, not acidic. How about the solution that has

["OH"^(-)] = 1.9 * 10^(-13)"M"#

where would that be placed? This time, you have

$1.9 \cdot {10}^{- 13} < 1.0 \cdot {10}^{- 7}$

so this solution is clearly acidic, i.e. its hydronium concentration is $> 1.0 \cdot {10}^{- 7} \text{M}$.

Use this explanation to double-check the rest of your solutions.