[asianburger]

My highschool science experiment is testing to see if there are differences in growth of algae if they are grown in growth mediums with different pH levels. The problem is that I am very confused on how to to calculate how many mL of phosphate buffer solutions I should add to change the growth medium to the desired pH. For example,
 
How many mL of a .1 M phosphate buffer solution (pH 5) should I add to 15 mL of a growth medium (pH 7. 8) to lower the growth medium's pH to the desired pH level of 5? I believe that I need the Henderson Hasselbalch equation but I am very confused with the math. If it is not possible then what further information do I need to calculate? Any help would be much appreciated. If math is shown then I will be able to calculate the mL of buffer solution needed for my other levels of pH.

[Borek]

You won't be able to calculate exact pH after buffer addition without knowing the original composition of the solution. But the idea is - don't care. Add enough buffer so that initial pH becomes irrelevant and the solution pH is that of the buffer, but not more, to not kill your algae with high osmotic pressure.

This approach is based on the assumption there are no strong buffering agents in the original sample.

[asianburger]

If it helps, the buffer solution was made by mixing 1 M Na2HPO4 and 1 M NaH2PO4 with distilled water. With the pH of 6 buffer, it was 12 mL Na2HPO4 and 88 mL of NaH2PO4. Then it was diluted to 1 L. Would that be considered the original composition? If so, how can I calculate how many mL of the pH of 6 buffer I should add to the growth medium so that it changes to a pH of 7.8 to a pH of 6?

If that does not work, do you have a suggestion with how much mL of the buffer solution I should add to the 15 mL of the growth medium so that the pH is irrelevant? Thanks for the help.

[Borek]

I would start with 1 mL and test the effect with the pH meter, or even pH strips. Experimental confirmation is often the easiest and the fastest approach.