Question

Cortisone is a molecular substance containing 21 atoms of carbon per molecule. The mass percentage of carbon in cortisone is 69.98%. What is the molecular mass of cortisone?

Answer 1

Hint: We know that mass percentage is a way of expressing the concentration of components in a mixture. So, from the mass percentage definition we can easily find the molar mass of compound or mixture.

Complete Step by step answer:
- We have given that cortisone is a molecular substance which has 21 atoms of carbons per molecule, also the mass percentage of carbon in cortisone is 69.98%.
- Now, let us understand what mass percentage is. Mass percentage can be defined as the mass of an element present in 100g of its compound or mixture.
- So here let us consider we have 100g of cortisone that means that 100g of cortisone 69.98g is carbon, this is the information we get from the mass percentage of carbon.
- Therefore, we can say in 1g of carbon we will have $\dfrac{{100}}{{69.98}}g$of cortisone. Also the mass of carbon is 12g, then the mass of 21 atoms of carbon will be $21 \times 12 = 252g$
Hence 252g of carbon will have $\dfrac{{100}}{{69.98}} \times 256g$
Molecular mass of cortisone = $\dfrac{{100}}{{69.98}} \times 256g$
$\Rightarrow$ Molecular mass of cortisone = 360.10g

Approximately we can say the molecular mass of cortisone is 360g.

Note: Apart from using the definition we can also find the molecular mass of cortisone by mathematical equation. Bye definition of mass percentage,
$Mass\;percentage = \dfrac{{mass\;of\;solute}}{{mass\;of\;solution}} \times 100$
Here, we can consider solute as the carbon atom and the solution is cortisone.
$Molar\;mas\;of\;carbon = 12g$
$Total\;mass\;of\;carbon = 21 \times 21 = 252g$
Also given that the mass percentage of carbon is 69.98.
Substituting this into the equation, we get
$69.98 = \dfrac{{252}}{{molar\;mass\;of\;cortisone}} \times 100$
$\Rightarrow molecular\;mass\;of\;cortisone = \dfrac{{252 \times 100}}{{69.98}}g$
Therefore, the molecular mass of cortisone is 360.10g.