How do I prepare 50 mL of a .10M sodium bicarbonate/sodium carbonate buffer by weighing out and dissolving equimolar amounts of sodium bicarbonate and sodium carbonate in order to measure their pH?

many times you are interested in making a buffer system with a specific pH... typically one with a pH near the pKa of the acid, since the buffer system is most effective here. There are several ways to make a buffer system for this purpose... from the acid and adding HO-, from the pKa with calculations of the concentrations at the desired pH, from two solutions containing the two components... some are easier methods than others.

but here it sound like you are doing a different thing. Seems like you are just asking how to make a 50 mL solution with 0.1M concentration, that is, the amount of bicarb and carbonate total is 0.1M... if that's the case you simply need to do two things:

since 0.1M means 0.1moles/L... but you don't want a liter, you need to use this conversion ratio and the amount desired (50mL =? L) to get the total number of moles needed for your 50mL solution. This is a conversion you should be able to do.

then, once you know the number of moles required... you divide by two. That gives you the moles of each component... then convert to grams using the molecular formula.

one hint... when making the solution do not measure out 50mL of water and add the solids in. you'd typically start with maybe something like 35-40 mL water, add the components in, dissolve, and then dilute up to the 50mL mark. Adding the solids to 50mL will give you a solution greater than 50mL and not accurate... unless this lab is being run sloppily, which it might be... you could still see some trends if the teacher disregarded this prep technique.

good luck.