Empirical formula, molecular formula, and exact molar mass?

Question

Ursolic acid is a substance found in the protective wax-like coating of apples, pears, and other fruits. It has the following elemental analysis: C- 78.90%, H- 10.59%, and O- 10.51%, compute its empirical formula. If its molar mass is determined to be 460.g/mol, determine its molecular formula and exact molar mass (to 5 significant figures).

Answer 1

Try working it out this way

You have!

78.9C + 10.59H +10.51O =100 of the whole molecules which has 460 g

79.9 C + 10.59 H + 10.51 O =460

The atomic mass of Carbon is 12
The atomic mass of the Hydrogen is 1
The Atomic mass of Oxygen is 16
The above are approximates

460*0.789 = 363 of Carbon

460* 0.1059 = 48.7 Hydrogen

46* 0.1051= 48.346 Oxygen
Now divide each by the atomic mass of each element:

363/12 = 30 atoms of Carbon

48.7/1 = 49 atoms of Hydrogen

48.346/16 = 3 atoms Oxygen

The formula of the compound should then be { C30H49O3 }

The molar mass should be calculated as 30*12 + 49*1 + 3*16 = 457

This is the closest I could get. Double check the formula
Good luck!

Answer 2

This is the method.

Take the percentage of each element as given and divide by its molecular mass. Now you have molar ratios of each element. Divide each ratio by the smalles ones to get whole number ratios. If they are not whole numbers at this point, do the last step a second time.

Th ewhole numbers now give you the empirical formula. Add up the molecular mass of theis formula and compare to the real mass of 460.0 g/mol. See how many multiples of the EF you need to match the real molecular mass.

Although you ask for 5 sig. digits, the problem only uses 4 sig. digits in the given data, and it would not be proper to report an answer with more than 4.