What is the hydrogen ion concentration of a solution prepared by diluting 50. mL of 0.10 M Hno3 (aq) with water to 500. mL? I'm going over some...

There are a
few formulas to take care of this, but the most general way would be to calculate the number of
moles of hydrogen ions you have, and then just figure out what the concentration is in the new
amount of water, and find the pH by the log formula.

Step 1:
Find moles of H+ Ions

This part is pretty easy. We're going to
assume that all of the HNO3 dissociates into H+ and NO3-. This means that given the HNO3
concentration of 0.10 M, we will have a H+ concentration of 0.10 M.

To find
the moles, we simply multiply our concentration by our volume. Keep in mind, M = mol/L, so we'll
need to get our volume into liters before we multiply:

Moles H+ = 0.10 M * 50
mL * 1 L/1000 mL = 0.0050 Mol H+

Step 2: Find [H+] in the new
solution

Recall, concentration is simply how many moles per
liter, meaning we just divide our number of moles by the liters of
solution. Keep in mind we will have added 500 mL water to 50 mL of solution, so our total volume
is 550 mL = 0.55 L.

[H+] = Moles H+/Volume = 0.0050 mol / 0.55 L = 0.0091
M

This answer sounds pretty reasonable, because we diluted the solution by
roughly a factor of 10.

We're almost done! Now we just need to get the
pH.

Step 3: Find the pH

To
find the pH, we simply take the negative log (base 10) of the concentration:

pH = -log(0.0091) = 2.0

Side note: I
know some may cry foul because I didn't take into consideration the fact that water dissociates
into hydrogen ions, too. This is where we look at our answer and see whether it makes sense to
worry about the water's H+ ions' effect on pH. Because the pH of water is 7, that means it is
contributing a H+ concentration of 0.0000001 M, which we can say is "0.0000000" when
we see that the [H+] of our combined solution is 5 orders of magnitude higher. In other words,
the [H+] of water is so small as to not affect the outcome.