Cortisone is a molecular substance substance containing `21` atoms of carbon per molecule. The mas percentage of carbon in cortisone is `69.98%`. Its molar mass is :

Options

A. `176.5`
B. `252.2`
C. `287.6`
D. `360.1`

Explanation

To find the molar mass of cortisone, we can follow these steps:

### Step 1: Understand the Given Information
Cortisone contains 21 atoms of carbon per molecule, and the mass percentage of carbon in cortisone is 69.98%.

### Step 2: Set Up the Equation for Carbon Mass
Since the mass percentage of carbon in cortisone is given as 69.98%, we can say that in 100 grams of cortisone, there are 69.98 grams of carbon.

### Step 3: Calculate the Molar Mass of Carbon
The molar mass of carbon (C) is approximately 12 g/mol. Therefore, for 21 carbon atoms, the total mass of carbon in one mole of cortisone can be calculated as:
\[ \text{Mass of carbon in cortisone} = 21 \text{ atoms} \times 12 \text{ g/mol} = 252 \text{ g/mol} \]

### Step 4: Relate the Mass of Carbon to Molar Mass of Cortisone
From the mass percentage, we can set up a relationship:
\[ \text{Mass of carbon} = \frac{69.98}{100} \times \text{Molar mass of cortisone} \]

### Step 5: Set Up the Equation
We know that the mass of carbon in one mole of cortisone is 252 g. Therefore, we can equate:
\[ 252 = \frac{69.98}{100} \times \text{Molar mass of cortisone} \]

### Step 6: Solve for Molar Mass of Cortisone
Rearranging the equation gives us:
\[ \text{Molar mass of cortisone} = \frac{252 \times 100}{69.98} \]

### Step 7: Calculate the Molar Mass
Now, performing the calculation:
\[ \text{Molar mass of cortisone} = \frac{25200}{69.98} \approx 360.1 \text{ g/mol} \]

### Final Answer
The molar mass of cortisone is approximately **360.1 g/mol**.

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