Cortisone consists of molecules, each of which contains 21 atoms of carbon (plus other atoms). The mass percentage of carbon in cortisone is 69.98%. What is the molar mass of cortisone?

Question

Quizplus · Accepted Answer

Since the mass percentage of carbon in cortisone is 69.98%, the remaining percentage of other atoms is 30.02%. We can assume 100 g of cortisone and calculate the mass of carbon and the mass of the other atoms. 
Mass of carbon = 69.98 g 
Mass of other atoms = 30.02 g 
We can then convert these masses to moles using the atomic masses of carbon and other atoms: 
Moles of carbon = 69.98 g / 12.011 g/mol = 5.822 
Moles of other atoms = 30.02 g / (molar mass of other atoms) 
To find the molar mass of cortisone, we need to add up the atomic masses of all the atoms in one molecule: 
Molar mass = (21 x atomic mass of carbon) + (other atoms) 
We can substitute the value of moles of carbon into the equation: 
Molar mass = (5.822 x 12.011 g/mol) + (moles of other atoms x molar mass of other atoms) 
We know that the total molar mass of cortisone is the sum of the molar masses of carbon and other atoms: 
Molar mass = (5.822 x 12.011 g/mol) + (moles of other atoms x molar mass of other atoms) = (100 g / molar mass) 
Solving for molar mass of cortisone: 
Molar mass = 360.4 g/mol

Cortisone Consists of Molecules, Each of Which Contains 21 Atoms