Insulin contains 3.4% sulphur by mass. What will be the minimum molecular weight of insulin -

Options

A. 94.117
B. 1884
C. 941
D. 976

Answer

To determine the minimum molecular weight of insulin based on the given percentage of sulfur, we can follow these steps:

### Step 1: Understand the given data
We know that insulin contains 3.4% sulfur by mass. This means that in a sample of insulin, 3.4 grams out of every 100 grams of insulin is sulfur.

### Step 2: Use the mass percentage to find the mass of sulfur
Let’s denote the molecular weight of insulin as \( M \). According to the percentage by mass formula:

\[ \text{Mass of Sulfur} = \frac{\text{Mass of Sulfur in Insulin}}{\text{Total Mass of Insulin}} \times 100 \]

From the problem, we have:

\[ 3.4 = \frac{\text{Mass of Sulfur}}{M} \times 100 \]

### Step 3: Rearranging the equation
We can rearrange the equation to find the mass of sulfur:

\[ \text{Mass of Sulfur} = \frac{3.4}{100} \times M \]

### Step 4: Use the molecular mass of sulfur
The molecular mass of sulfur (S) is given as 32 g/mol. Therefore, we can set up the equation:

\[ \text{Mass of Sulfur} = n \times 32 \]

where \( n \) is the number of sulfur atoms in the insulin molecule.

### Step 5: Equate the two expressions for mass of sulfur
Now, we can equate the two expressions for the mass of sulfur:

\[ \frac{3.4}{100} \times M = n \times 32 \]

### Step 6: Solve for the minimum molecular weight of insulin
To find the minimum molecular weight of insulin, we can assume that there is 1 atom of sulfur in the insulin molecule (this gives us the minimum molecular weight). Thus, \( n = 1 \):

\[ \frac{3.4}{100} \times M = 1 \times 32 \]

Now, solving for \( M \):

\[ M = \frac{32 \times 100}{3.4} \]

Calculating this gives:

\[ M = \frac{3200}{3.4} \approx 941.18 \text{ g/mol} \]

### Step 7: Conclusion
Thus, the minimum molecular weight of insulin is approximately **941.18 g/mol**.

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