A compound has `20%` of nitrogen by weight. If one molecule of the compound contains two nitrogen atoms, the molecular weight of the compound is

Options

A. 35
B. 70
C. 140
D. 280

Explanation

To find the molecular weight of the compound, we can follow these steps:

### Step 1: Understand the weight percentage of nitrogen
The problem states that the compound contains 20% nitrogen by weight. This means that in a 100 g sample of the compound, there are 20 g of nitrogen.

### Step 2: Determine the amount of nitrogen in moles
The atomic weight of nitrogen (N) is approximately 14 g/mol. Since there are 20 g of nitrogen in the compound, we can calculate the number of moles of nitrogen:

\[ \text{Moles of nitrogen} = \frac{\text{mass of nitrogen}}{\text{molar mass of nitrogen}} = \frac{20 \text{ g}}{14 \text{ g/mol}} \approx 1.43 \text{ moles of N} \]

### Step 3: Relate moles of nitrogen to moles of the compound
The problem states that one molecule of the compound contains two nitrogen atoms. Therefore, one mole of the compound contains two moles of nitrogen. This means:

\[ \text{Moles of compound} = \frac{\text{Moles of nitrogen}}{2} = \frac{1.43 \text{ moles of N}}{2} \approx 0.715 \text{ moles of compound} \]

### Step 4: Calculate the molecular weight of the compound
We know that the total mass of the compound is 100 g (from our initial assumption). Therefore, we can calculate the molecular weight of the compound using the number of moles we just calculated:

\[ \text{Molecular weight of the compound} = \frac{\text{mass of compound}}{\text{moles of compound}} = \frac{100 \text{ g}}{0.715 \text{ moles}} \approx 139.5 \text{ g/mol} \]

### Step 5: Round to the nearest whole number
Since molecular weights are typically expressed as whole numbers, we round 139.5 g/mol to 140 g/mol.

### Final Answer
The molecular weight of the compound is approximately **140 g/mol**.

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