how to prepare 500ml of a 0.75M Sodium Phosphate buffer solution at pH 7.5, how would you go about doing that?

I like to do these in millimoles. Although technically they are to be done with concentration in molarity, mmols works just as well and I think it is easier.

You have two equations. Let a = acid and b = base.
eqn 1 is a + b = 500 x 0.75 mmols.
eqn 2 is 7.5 = pKa2 + log (b/a)
where pKa2 is that of H3PO4.

Solve eqn 1 and eqn 2 simultaneously for a and b in millimoles.
Then convert mmols acid and mmols base to grams, weigh each and make the solution. The acid will be NaH2PO4 and the base will be Na2HPO4.

To prepare a 500ml of a 0.75M Sodium Phosphate buffer solution at pH 7.5, you would need to follow these steps:

Step 1: Calculate the amount of Sodium Phosphate needed
To determine the amount of Sodium Phosphate needed, you can use the formula:
m = M × V
Where:
m is the mass of Sodium Phosphate (in moles)
M is the desired molarity (0.75M)
V is the desired volume (500ml)

So, substitute the given values into the formula:
m = 0.75 × 0.5
m = 0.375 moles

Step 2: Convert moles to grams
Since the molar mass of Sodium Phosphate (Na3PO4) is approximately 163.94 g/mol, you can use the formula:
mass = moles × molar mass
Substitute the given values:
mass = 0.375 × 163.94
mass ≈ 61.48 grams

Therefore, you would need approximately 61.48 grams of Sodium Phosphate.

Step 3: Prepare the solution
To prepare the buffer solution, follow these steps:
1. Weigh out approximately 61.48 grams of Sodium Phosphate and add it to a container.
2. Add approximately 400ml of distilled water to the container and mix well until the Sodium Phosphate is dissolved.
3. Adjust the pH of the solution to 7.5 using pH adjusting agents (e.g., sodium hydroxide or phosphoric acid). Add small amounts at a time while stirring and check the pH using a pH meter until it reaches 7.5.
4. Once the pH is stable at 7.5, add distilled water to make the final volume up to 500ml.
5. Mix well to ensure uniformity.

Now, you have prepared a 500ml of a 0.75M Sodium Phosphate buffer solution at pH 7.5.