This isn't homework. It's for my job. I'm supposed to be making a 50mM phosphate buffer to pH 7.2, 0.5 NaOH. I have access to salts, K_{2}HPO_{4} (dibasic), KH_{2}PO_{4} (monobasic), and NaCl. I've determined that I need two liters of buffer solution. I did the calculations but when I measured the pH after making the solution, it was more acidic than it should be. I adjusted the pH with strong base, so it's alright now. I'm just wondering if someone can verify my calculations. FW K_{2}HPO_{4} = 174.18 g/mol FW KH_{2}PO_{4} = 136.09 g/mol FW NaCl = 58.44 g/mol pH = pKa + log ([K_{2}HPO_{4}]/[KH_{2}PO_{4}]) Since pKa = 7.2 and pH =7.2, the HH equation reduces to [KH_{2}PO_{4}]=[K_{2}HPO_{4}] For two liters, I need 0.1 mol phosphate buffer 0.1 mol= [KH_{2}PO_{4}]+[K_{2}HPO_{4}] then 0.05 mol = [KH_{2}PO_{4}] 0.05 mol = [K_{2}HPO_{4}] then I weigh out 136.09 g/mol * 0.05 mol = 6.8045 g [KH_{2}PO_{4}] and 174.18 g/mol * 0.05 mol = 8.709 g [K_{2}HPO_{4}] and 58.44 g NaCl and fill the volume to 95% and adjust pH if necessary then fill to mark. Did I do something wrong? Some buffer calculators are showing something like 3 times the amount of base as acid and I don't know why. For example, http://www.biomol.net/en/tools/buffercalculator.htm
Without actually trying to go through your plan and calculations (which will require studying for a few days or more), just realize that your models will let you predict what quantities will give you the desired measured pH result, but the models are not the perfect reality for what you expect. Loosely speaking, if your result was close, then you did well. If your adjustment was small, then you did well.
Your calculations don't take ionic strength and activity coefficients into account. That's why you are a way off. See ionic strength & activity coefficients primer. Blatant ad, this is Buffer Maker at work: You wrote that your buffer should be 0.5M NaOH, yet you added NaCl. That further increased ionic strength - 0.5M solution has ionic strength around 0.5. That's too much for a reasonable calculations (that is, we are outside of the application range of the Debye-Huckel theory and Davies equation). I am not sure what the buffer recipe should be, as changing amounts of ions present you change ionic strength and osmolality of the solution, these can be important for the application. Using potassium phosphates AND sodium chloride you may be wrong. --