You are instructed to create 400. mL of a 0.40 M phosphate buffer with a pH of 6.9. 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

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?

I really can't figure this out. I tried the ph=pka +log(a-/ha) but I'm really lost and if you could guide be that would be wondering. I'm really stressing out here.

Here is the hint you should need to work the problem. You have two equations and you solve them simultaneously (which I think is the easier way) but there are other ways to do it.

pH = pKa + log (base)/(acid)
Take the Ka of k1, k2, and k3. The closes one to 6.9 is the one you want and that is k2.
6.9 = pK2 + log b/a
b/a = ? . That's the first equation.
The second one is
a + b = 0.4M
Solve for a and b (in molarity). That will answer the first two. Convert to mols - M x L = ? and that gives the next two answers. The mols = grams/molar mass gives you the last two answers.

Don't worry, I'm here to help you! Let's break down the problem step by step.

1. Start by determining the acid and base components of the buffer. In this case, the acid component is phosphoric acid (H3PO4), and the base components are the sodium salts NaH2PO4, Na2HPO4, and Na3PO4.

2. Calculate the molarity needed for the acid component of the buffer. Since the pH is 6.9 and the pKa values are given for the acid dissociation reactions, you can use the Henderson-Hasselbalch equation:

pH = pKa + log ([A-]/[HA])

In this equation:
- pH is the desired pH (6.9)
- pKa is the pKa value for the acid (given as 6.9 for H3PO4)
- [A-] and [HA] are the concentrations of base and acid, respectively (in this case, [A-] refers to the concentration of HPO42- and [HA] refers to the concentration of H2PO4-)

Simplify the equation to solve for [HA]:

pH - pKa = log ([A-]/[HA])

Take the antilog of both sides:

10^(pH - pKa) = ([A-]/[HA])

Now, you know the pH, pKa, and the desired ratio of [A-]/[HA].

3. Calculate the molarity needed for the base component of the buffer. Since you have multiple base components, you need to consider the reactions and pKa values for each.

Use the Henderson-Hasselbalch equation again, but this time for the different base components:
- For H2PO4-/HPO42- use pKa2
- For HPO42-/PO43- use pKa3

4. Once you have the molarities for the acid and base components of the buffer, you can calculate the number of moles needed.

Remember, molarity (M) is defined as moles of solute per liter of solution.

So, to find the moles of acid and base, multiply the molarities by the volume of the buffer solution (given as 400 mL or 0.4 L).

5. Finally, to find the grams of acid and base needed, you'll need to convert moles to grams using the molar mass of each compound.

Phosphoric acid (H3PO4) has a molar mass of 98 g/mol.
The sodium salts (NaH2PO4, Na2HPO4, Na3PO4) will have different molar masses, so you'll need to calculate them individually using the atomic masses of the elements.

Let's go through these steps one by one to find the molarity and moles of the acid and base components, and the grams needed for the buffer.