You are instructed to create 500. mL of a 0.25 M phosphate buffer with a pH of 7.7. You have phosphoric acid and the sodium salts NaH2PO4, Na2HPO4, and Na3PO4 available. (Enter all numerical answers to three significant figures.)
H3PO4(s) + H2O(l) equilibrium reaction arrow H3O+(aq) + H2PO4−(aq)
Ka1 = 6.9 ✕ 10−3
H2PO4−(aq) + H2O(l) equilibrium reaction arrow H3O+(aq) + HPO42−(aq)
Ka2 = 6.2 ✕ 10−8
HPO42−(aq) + H2O(l) equilibrium reaction arrow H3O+(aq) + PO43−(aq)
Ka3 = 4.8 ✕ 10−13
Questions:
What is the molarity needed for the acid component of the buffer?
What is the molarity needed for the base component of the buffer?
How many moles of acid are needed for the buffer?
How many moles of base are needed for the buffer?
How many grams of acid are needed for the buffer?
How many grams of base are needed for the buffer?
How do I do this and what are the answers?
See your problem below. It's quite similar. Use HH equation to solve for (acid)/(base)
pH = pK2 + log (base/acid) ......(base/acid) = b/a
Plug in the values and solve for b/a. That's equation 1.
Equation 2 is a + b = 0.25M
Solve for (a) and (b). That gives you the molarity needed for the acid and the base.
Using M = mols/L, convert moles needed for acid or base convert to moles need for acid and base. You have M and you have L, solve for mols needed for acid and base. Remember acid is mols H2PO4^2- and base is HPO4^-.
After you have moles needed for base and acid, then
grams need = moles x molar mass of the salt.
Post your work if you get stuck.
To create the buffer solution, you need to calculate the molarity (M) of the acid and base components based on the desired pH and known pKa values. Here's how you can do it:
1. Calculate the pKa for the acid component (Ka1) using the given Ka value:
pKa1 = -log10(Ka1)
pKa1 = -log10(6.9 ✕ 10−3)
pKa1 = 2.16
2. Calculate the pKa for the base component (Ka2) using the given Ka value:
pKa2 = -log10(Ka2)
pKa2 = -log10(6.2 ✕ 10−8)
pKa2 = 7.21
3. Determine the acid form that corresponds to the desired pH (7.7). The pH should be between pKa1 and pKa2 for effective buffering. Since the desired pH is closer to pKa2, the base component will be Na2HPO4 (pKa2 = 7.21).
4. To determine the molarity needed for the acid component, you can use the Henderson-Hasselbalch equation, which relates pH, pKa, and the ratio of the conjugate base to acid. The equation is given as:
pH = pKa + log([Base]/[Acid])
Rearranging the equation gives:
[Acid] = [Base] * (10^(pH - pKa))
Substituting the values:
[Acid] = [Base] * (10^(7.7 - pKa1))
Calculate [Base] component:
[Base] = 0.25 M (as given)
Calculate [Acid]:
[Acid] = 0.25 * (10^(7.7 - 2.16))
[Acid] = 0.25 * (10^5.54)
[Acid] = 285,000 M
Therefore, the molarity needed for the acid component of the buffer is 285,000 M.
5. The molarity needed for the base component of the buffer is given as 0.25 M (as provided in the question).
6. To calculate the number of moles needed for each component, you need to multiply the molarity by the volume of the buffer solution (500 mL = 0.5 L):
Moles of acid = [Acid] * Volume
Moles of base = [Base] * Volume
Moles of acid = 285,000 M * 0.5 L
Moles of acid = 142,500 moles
Moles of base = 0.25 M * 0.5 L
Moles of base = 0.125 moles
Therefore, you need 142,500 moles of the acid component and 0.125 moles of the base component for the buffer solution.
7. To calculate the mass of each component, you need to use their molar masses (grams per mole):
Molar mass of acid (H3PO4) = 98.0 g/mol
Molar mass of base (Na2HPO4) = 141.96 g/mol
Mass of acid = Moles of acid * Molar mass of acid
Mass of base = Moles of base * Molar mass of base
Mass of acid = 142,500 moles * 98.0 g/mol
Mass of acid = 13,965,000 g
Mass of base = 0.125 moles * 141.96 g/mol
Mass of base = 17.74 g
Therefore, you need 13,965,000 grams of acid and 17.74 grams of base for the buffer solution.
To summarize, the answers are as follows:
- Molarity needed for the acid component of the buffer: 285,000 M
- Molarity needed for the base component of the buffer: 0.25 M
- Moles of acid needed for the buffer: 142,500 moles
- Moles of base needed for the buffer: 0.125 moles
- Grams of acid needed for the buffer: 13,965,000 g
- Grams of base needed for the buffer: 17.74 g