How would you prepare a 150.0mL of a 3.50 pH buffer solution using .500M NaOH and .500M HCOOH. I've gotten the base/acid ratio for the Henderson-H. equation. But now I'm not sure how to figure out the balance of solutions of HCOOH and NaOH to get both 150mL total and still have the ratio between COOH- and HCOOH

I would do this. First, note that the concns of acid and base are equal which means we can dispense with the molarity and just use volume of 150 mL.

..........HCOOH + OH^- ==>HCOO^- + H2O
We must take some quantity of HCOOH and add NaOH to it so volume NaOH = X.
Since the total volume is to be 150 mL, then we know HCOOH must be 150-x to start. What will it be at the end
.........HCOOH + OH^- ==> HCOO^- + H2O
begin....150-x....0.........0.......0
add...............x..................
react.....-x......-x........+x....+x
final...150-2x....0..........x.....x

3.5 = 3.75 + log[x/(150-2x)]
Solve for x (I get about 40 mL)
Then 150-x is about 110 mL HCOOH to begin and it will be 110-x = about 70 after reaction with the NaOH. So in the end we will have
pH = 3.75 + log(40/70) = close to 3.5
You need to do it more accurately than I've done.
I like to substitute these amounts, multiplied by the molarity or course, react them, and substitute the final mmoles into the HH equation and see if it gives me 3.5. If not we have trouble, if so we're ok. I tried it and it looks ok to me.

To prepare a buffer solution, you need to determine the appropriate amounts of NaOH and HCOOH to add to achieve the desired pH and maintain a specific ratio of COOH- to HCOOH. Here are the steps to calculate the quantities:

Step 1: Calculate the required moles of NaOH and HCOOH.
The volume of the buffer solution is given as 150.0 mL. Since we want to have equal molar concentrations of NaOH and HCOOH, we can assume we need an initial volume of 75.0 mL for both solutions.

To calculate the moles of NaOH needed, use the formula:
moles of NaOH = volume (in L) × concentration (in mol/L)

moles of NaOH = (75.0 mL / 1000 mL/L) × 0.500 mol/L

Similarly, to calculate the moles of HCOOH needed, use the same formula with the concentration of HCOOH:
moles of HCOOH = (75.0 mL / 1000 mL/L) × 0.500 mol/L

Step 2: Calculate the moles of COOH- and HCOOH required to achieve the desired ratio.
The Henderson-Hasselbalch equation gives you the ratio of COOH- to HCOOH needed to achieve the desired pH. Let's assume the ratio is x:1, where x is the number we need to determine.

pH = pKa + log(COOH- / HCOOH)

From your calculations, you already have the ratio at this step.

Step 3: Calculate the moles of COOH- and HCOOH required based on the ratio.
Since you have the ratio of COOH- to HCOOH from the Henderson-Hasselbalch equation, multiply the moles of HCOOH and COOH- by their respective ratios to obtain the final moles:

moles of HCOOH_final = moles of HCOOH × 1
moles of COOH-_final = moles of HCOOH × x

Step 4: Calculate the volume required to achieve the desired concentration.
To determine the volume needed for each solution to reach the final moles calculated in step 3, use the formula:
volume (in L) = moles / concentration (in mol/L)

volume of HCOOH = moles of HCOOH_final / concentration of HCOOH
volume of COOH- = moles of COOH-_final / concentration of NaOH

Convert the volumes to mL by multiplying by 1000.

Step 5: Prepare the buffer solution.
Now that you have the required volumes, mix the determined volumes of HCOOH and NaOH together in a container to make the final buffer solution.

It is essential to rinse the glassware before preparing the solution to ensure accurate measurements. Always wear appropriate safety equipment and follow lab protocols while handling chemicals.

Hope this helps! Let me know if you have further questions.