The pKa of HEPES is 7.55 at 20 degrees C, and its MW is 238.31. Calculate the amounts of HEPES in grams and of 1.0 M NaOH in milliliters that would be needed to make 300 mL of 0.2 M HEPES buffer at pH 7.2.
To calculate the required amounts of HEPES and NaOH, we need to consider the following steps:
Step 1: Calculate the moles of HEPES needed:
Moles of HEPES = Volume of HEPES buffer (L) × Concentration of HEPES (M)
Moles of HEPES = 0.3 L × 0.2 M = 0.06 moles
Step 2: Calculate the grams of HEPES needed:
Grams of HEPES = Moles of HEPES × Molecular weight of HEPES
Grams of HEPES = 0.06 moles × 238.31 g/mol = 14.29 grams
Step 3: Calculate the moles of NaOH needed:
Since HEPES is a zwitterionic buffer, we need to take into account the pKa and pH to determine how much NaOH is required to adjust the pH.
For HEPES, its pKa is 7.55, which means it functions as a buffer around this pH. If we want a pH of 7.2, we need to calculate the difference in moles of HEPES needed to adjust the pH.
The Henderson-Hasselbalch equation can be used to calculate the ratio of protonated (HA) to deprotonated (A-) HEPES species:
pH = pKa + log([A-]/[HA])
To calculate the ratio, subtract the pH from the pKa:
pKa - pH = 7.55 - 7.2 = 0.35
Take the antilog of this difference to calculate the ratio:
Ratio ([A-]/[HA]) = 10^(pKa - pH) = 10^0.35 ≈ 2.24
Since the ratio of protonated to deprotonated species is 2.24, the difference in moles required would be the same:
Moles of NaOH = 2.24 × Moles of HEPES = 2.24 × 0.06 moles = 0.1344 moles
Step 4: Calculate the volume of 1.0 M NaOH needed:
Volume of 1.0 M NaOH = Moles of NaOH / Concentration of NaOH
Volume of 1.0 M NaOH = 0.1344 moles / 1.0 M = 0.1344 L = 134.4 mL
Therefore, to make 300 mL of 0.2 M HEPES buffer at pH 7.2, you would need approximately 14.29 grams of HEPES and 134.4 milliliters of 1.0 M NaOH.
To calculate the amounts of HEPES in grams and 1.0 M NaOH in milliliters needed to make 300 mL of 0.2 M HEPES buffer at pH 7.2, we need to follow these steps:
Step 1: Calculate the moles of HEPES required.
The molar concentration of HEPES buffer (0.2 M) and the volume (300 mL) allow us to determine the number of moles of HEPES needed using the formula:
Moles = Molar concentration * Volume
Moles of HEPES = 0.2 M * 0.3 L
Moles of HEPES = 0.06 moles
Step 2: Calculate the grams of HEPES required.
To convert moles of HEPES to grams, we need the molecular weight of HEPES (MW = 238.31 g/mol):
Grams of HEPES = Moles of HEPES * Molecular weight
Grams of HEPES = 0.06 moles * 238.31 g/mol
Grams of HEPES = 14.29 grams (approx.)
Therefore, approximately 14.29 grams of HEPES are needed to make 300 mL of 0.2 M HEPES buffer at pH 7.2.
Step 3: Calculate the milliliters of 1.0 M NaOH required.
For the buffer, we need to ensure that the pH is adjusted to the desired value. To do this, we can use NaOH, a strong base. Firstly, we need to determine the required moles of NaOH using the pKa and Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
Given:
pH = 7.2 (desired pH)
pKa = 7.55 (pKa of HEPES)
[A-] = [HA] = concentration of HEPES in the buffer (0.2 M)
By rearranging the Henderson-Hasselbalch equation, we can calculate the ratio of [A-] to [HA]:
[A-]/[HA] = 10^(pH - pKa)
[A-]/[HA] = 10^(7.2 - 7.55)
[A-]/[HA] = 10^(-0.35)
[A-]/[HA] = 0.44 (approx.)
This means that in the buffer, the ratio of the concentration of the deprotonated form ([A-]) to the protonated form ([HA]) is approximately 0.44.
Step 4: Calculate moles of NaOH needed.
Since the ratio of [A-] to [HA] is 0.44, the concentration of [A-] is 0.44 times the total concentration of HEPES (0.2 M).
Concentration of [A-] = 0.44 * 0.2 M
Concentration of [A-] = 0.088 M
Since NaOH is a strong base and will produce hydroxide ions (OH-) in solution, we need to convert the [A-] concentration into moles to determine the required amount of NaOH.
Moles of NaOH = Concentration of [A-] * Volume
Moles of NaOH = 0.088 M * 0.3 L
Moles of NaOH = 0.0264 moles
Step 5: Calculate milliliters of 1.0 M NaOH needed.
To calculate the milliliters of 1.0 M NaOH needed, we can use the molarity and the number of moles of NaOH required:
Milliliters of NaOH = Moles of NaOH / Molarity
Milliliters of NaOH = 0.0264 moles / 1.0 M
Milliliters of NaOH = 26.4 mL (approx.)
Therefore, approximately 26.4 mL of 1.0 M NaOH are needed to make 300 mL of 0.2 M HEPES buffer at pH 7.2.
pH =pka + log [A-]/[HA]
7.2 = 7.55 + log [A-]/[0.2M]
[A-] = 0.4477M
So using that concentration 0.4477M x 300mL = 134.32 moles NaOH / 1M NaOH
= 134.32 mL NaOH amount needed right?
If we let HA = HEPES.
HA + NaOH ==> NaA + H2O
Use the Henderson-Hasselbalch equation.
pH = pKa + log (B/A)
7.2 = 7.55 = log (B/A)
Calculate (B)/(A)
Then you know (A) + (B) = 0.2
Using those two equations will allow you to calculate (A) and (B).
I assume you can finish. You want moles A and moles B for the equation. M x L = moles and since you know M and volume (you want 300 mL), you can calculate moles of each, plug those in to the equation at the top to see how much of the 1 M NaOH must be added to form the moles you want. Post your work if you get stuck.