Aspartame an artificial sweetener contains `9.52 "wt". %` nitrogen. There are two nitrogen atoms per molecule. What is the molecular weight of aspartame ? .

Options

A. `147`
B. `294`
C. `588`
D. `266`

Explanation

To find the molecular weight of aspartame given that it contains 9.52 wt% nitrogen and has two nitrogen atoms per molecule, we can follow these steps:

### Step 1: Determine the weight of nitrogen in 100 grams of aspartame.
Since the problem states that aspartame contains 9.52 wt% nitrogen, in 100 grams of aspartame, the weight of nitrogen can be calculated as follows:
\[ \text{Weight of Nitrogen} = 9.52 \, \text{g} \]

### Step 2: Calculate the weight of two nitrogen atoms.
The atomic weight of nitrogen (N) is approximately 14 g/mol. Therefore, the weight of two nitrogen atoms is:
\[ \text{Weight of 2 Nitrogen Atoms} = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]

### Step 3: Set up the equation to find the molecular weight of aspartame.
If 9.52 grams of nitrogen corresponds to 28 grams of nitrogen in the molecular weight of aspartame, we can set up the following proportion:
\[ \frac{100 \, \text{g of aspartame}}{9.52 \, \text{g of nitrogen}} = \frac{M}{28 \, \text{g of nitrogen}} \]
Where \( M \) is the molecular weight of aspartame.

### Step 4: Solve for the molecular weight of aspartame.
Cross-multiplying gives:
\[ M \times 9.52 = 100 \times 28 \]
Now, solving for \( M \):
\[ M = \frac{100 \times 28}{9.52} \]
Calculating this gives:
\[ M = \frac{2800}{9.52} \approx 294.34 \, \text{g/mol} \]
Rounding this, we find:
\[ M \approx 294 \, \text{g/mol} \]

### Final Answer:
The molecular weight of aspartame is approximately **294 g/mol**.

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