Question

the $k_{eq}$ for the reaction of water with water is called $k_w$
$\ce{h2o + h2o <=> h3o^{+1} + oh^{-1}}$
\\k_w = \frac{\ce{h3o^{+1}}\ce{oh^{-1}}}{\ce{h2o}^2} = \ce{h3o^{+1}}\ce{oh^{-1}} = (1 \times 10^{-7})^2 = 1 \times 10^{-14}\\
the inverse logarithm, or -log, of $\ce{h3o^{+1}}\ce{oh^{-1}} = 10^{-14}$ is $\ce{ph + poh = 14}$

1. what happens to the $\ce{h3o^{+1}}$ when base is added to neutral water?

the $\ce{h3o^{+1}}$ goes 1

1. what happens to the $\ce{ph}$ when base is added to neutral water?

an example of a decreased $\ce{h3o^{+1}}$ is $\ce{h3o^{+1}} = 1 \times 10^{-8}$ and $\ce{ph} = -\log10^{-8} = 8$
thus, adding acid makes the $\ce{ph}$ go 2

1. what happens to the $\ce{h3o^{+1}}$ when base is added to neutral water?

in the equation $\ce{h3o^{+1}}\ce{oh^{-1}} = 10^{-14}$, when $\ce{oh^{-1}}$ increases, the $\ce{h3o^{+1}}$ goes 3

1. what happens to the $\ce{poh}$ when base is added to neutral water?

when $\ce{oh^{-1}}$ increases, the $\ce{poh}$ goes 4 since the $\ce{poh} = -\log\ce{oh^{-1}}$
this can also be seen using $\ce{ph + poh = 14}$

Explanation:

Step1: Analyze Question 1

Bases increase $[OH^-]$. From $K_w = [H_3O^+][OH^-] = 10^{-14}$, if $[OH^-]$ increases, $[H_3O^+]$ must decrease to keep $K_w$ constant. So $[H_3O^+]$ goes down.

Step2: Analyze Question 2 (Note: Typo, should be base, but example uses acid. Correcting: For base, $[H_3O^+]$ decreases, $pH = -\log[H_3O^+]$, so $pH$ increases. But the example given is for acid: adding acid increases $[H_3O^+]$, so $pH = -\log[H_3O^+]$ decreases. So for the example's acid case, $pH$ goes down.

Step3: Analyze Question 3

From $[H_3O^+][OH^-] = 10^{-14}$, if $[OH^-]$ increases, $[H_3O^+]$ must decrease (inverse relationship) to maintain $K_w$. So $[H_3O^+]$ goes down.

Step4: Analyze Question 4

$pOH = -\log[OH^-]$. If $[OH^-]$ increases, $-\log[OH^-]$ decreases (since log of a larger number is larger, negative of that is smaller). So $pOH$ goes down.

Answer:

1. down
2. down (for the acid - adding case as per the example)
3. down
4. down