buffer problem

[devin alexander]

when we were going over answers to a homework in class today my teacher had a answer that was different from mine so i asked what i had done wrong. the question reads "the pH of a bicarbonate-carbonic acid bufer is 8.00. calculate the ratio of the concentration of carbonic acid (H2CO3) to that of the bicarbonate ion (HCO3-)" (see attached file for pic of the question and my work) . now our work was almost exactly the same but there was one difference which was that when he went to undo the log on the last step, he undid the log as if it was a negative log (EX: 10^-x). he claims that its the right way to do it, and even tho i have found a few other ways to solve the problem and have shown him he still thinks his is right and niether one of us know why. so i need a people with a good chem background to solve this so we can see if you get my answer or his. and i say a good chem background because my teacher has a very strong background in chem, so its gonna take more then a chem highschool chem student to prove him wrong.  (i dont know exactly what his degree is in but he has teached chem for 20 years at the college and highschool level).

pls let me know what you get for your answer

 

[hypervalent_iodine]

I believe your teacher is correct, and you have misread the question. The question has asked for the acid:conjugate base ratio, whereas the HH equation has the ratio the other way around. To correct for that, it can be rewritten so that it becomes pH = pKa - log([HA]/[A-]), or to simply inverse your answer (giving the same thing). Remembering that 1/a^x is the same as a^-x, you should be able to see that your teacher has given the right answer (I haven’t checked any of the arithmetic), he just missed a step of explanation.