Fundamentals E Question 35 [ENDORSED]

[Amanda Mac 1C]

The decay of teeth can be slowed by the use of fluoridated toothpaste. The fluoride ions convert the hydroxyapatite, Ca5(PO4)3OH, in tooth enamel into fluorapatite, Ca5(PO4)3F. If all the hydroxyapatite is converted into fluorapatite, by what percentage does this conversion increase the mass of the enamel?

This is question 35 in the Fundamentals E section. I began by finding the molar masses of both substances and got 440.374 g*mol^-1 for hydroxyapatite and 504.31 g*mol^-1 for fluorapatite. I thought the next step was subtracting 440.374 from 504.31 to find the difference and then dividing by one of the molar masses to find the mass percentage increase. The answer is 0.39%. Can someone please tell me what the proper steps are?

[Shanmitha Arun 1L]

The reason you may be getting the wrong answer is because the molar mass you calculated is wrong. The molar mass of Ca5(PO4)3F is 504.3, which is what you got, but the molar mass of Ca5(PO4)3OH is actually 502.31. Now if you subtract 502.31 from 504.3 and divide that overall by 504.3, you will get 0.0039 or 0.39%.

[Julie Steklof 1A]

I thought percent change was always (final-intial)/initial x100%? This would make the equation (504.3-502.31)/502.31 x100% which gives you .396% and rounds to .40%. However the solutions manual shows dividing by 504.3. Does anyone know why this is?