if the pH of a half-neutralized acid solution is 5.4, how would you find the [H+] of the the solution. There is 1.0 g of L-ascorbic acid which was dissolved in 100 ml of water. That solution was split in two and 50 ml of the solution was titrated with 0.2 M NaOH (13 ml NaOH). then the other half of the solution was added to get the pH of 5.4. With this information how can I get the concentration of H+?
If the pH = 5.4 then
5.4 = -log(H^+)
-5.4 = log(H^+)
(H^+) = 3.98 x 10^-6
I didn't work through all the numbers to see if they match up but it doesn't matter what they are. If the pH is 5.4, then (H^+) is defined by that and nothing else.
oh ok.. thanks so much... So when you have the pH of a substance the [H^+] is always equal to 10^-pH?
is this then equal to the Ka of the acid solution?
Yes to the first question. (H^+) = 10^-pH.
At the half way point, which is what you had, then Ka = (H^+ or pKa = pH but that is only true at the half way point. You can see for a weak acid, such as HA
HA ==> H^+ + A^- and
Ka(H^+)(A^-)/(HA). Solving for (H^+) we get
(H^+) = Ka(HA)/(A^-). SO, when exactly half the HA has been neutralized, then there has been formed an equal amount of (A^-) so (HA)=(A^-) and (H^+) = Ka. You can take the -log of each side to obtain
-log(H^+) = -log Ka AND
pH = pKa. But remember, for this second part, this is true ONLY at the half way point to neutralization of the acid (Or, of course, when you make a buffer solution containing equal amounts of acid and salt).
To find the concentration of H+ in the half-neutralized acid solution, you will need to follow these steps:
Step 1: Find the moles of L-ascorbic acid dissolved
Given that you have 1.0 g of L-ascorbic acid, you need to convert this mass to moles. To do this, you need to know the molecular weight of L-ascorbic acid (C6H8O6). The atomic masses of carbon (C), hydrogen (H), and oxygen (O) are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. Adding up the atomic masses for one molecule of L-ascorbic acid gives us 176.13 g/mol.
Number of moles = Mass (g) / Molecular weight (g/mol)
Number of moles = 1.0 g / 176.13 g/mol
Step 2: Calculate the moles of L-ascorbic acid used in the 50 ml solution
Since the original solution was split in half, the 50 ml solution contains half of the moles of L-ascorbic acid.
Moles in 50 ml solution = (Number of moles) / 2
Step 3: Convert the volume of the NaOH used to moles
Given that 13 ml of 0.2 M NaOH was used in the titration, you can calculate the moles of NaOH used.
Moles of NaOH = Concentration (M) x Volume (L)
Moles of NaOH = 0.2 M x (13 ml / 1000 ml/L)
Step 4: Calculate the moles of OH- used in the neutralization reaction
Since NaOH is a strong base, it reacts in a 1:1 ratio with the acid. Therefore, the moles of OH- used are equal to the moles of NaOH used.
Moles of OH- = Moles of NaOH
Step 5: Calculate the moles of H+ that were neutralized
Since the reaction is 1:1 between acid and base, the moles of H+ neutralized are equal to the moles of OH-.
Moles of H+ neutralized = Moles of OH-
Step 6: Calculate the remaining moles of H+ in the solution
The remaining moles of H+ are equal to the initial moles of L-ascorbic acid minus the moles of H+ neutralized.
Moles of H+ remaining = Moles of L-ascorbic acid - Moles of H+ neutralized
Step 7: Calculate the concentration of H+ in the remaining solution
To calculate the concentration of H+ (expressed as [H+]), you need to divide the moles of H+ remaining by the volume of the solution (in liters).
[H+] = Moles of H+ remaining / Volume of the solution (L)
Given that the remaining solution is 50 ml (0.05 L), you can substitute the values and calculate the [H+].
Please note that this calculation assumes that L-ascorbic acid is a monoprotic acid and that the pH measurement is accurate.