A decongestant which is used to treat tough chest and clogged nose. Analysis shown that it contains 71.52% C, 8.61% H, 9.27% N, and the rest as O (all are % by mass). If the molecular weight is 151 g/mol, what is its molecular formula?

To determine the molecular formula of the compound, we follow these steps:

### Step 1: Find the empirical formula
First, we use the percentage composition to calculate the moles of each element in a 100 g sample.

- **Carbon (C)**: \( 71.52 \% \)
\[
\text{Moles of C} = \frac{71.52 \, \text{g}}{12.01 \, \text{g/mol}} = 5.955 \, \text{mol}
\]

- **Hydrogen (H)**: \( 8.61 \% \)
\[
\text{Moles of H} = \frac{8.61 \, \text{g}}{1.008 \, \text{g/mol}} = 8.543 \, \text{mol}
\]

- **Nitrogen (N)**: \( 9.27 \% \)
\[
\text{Moles of N} = \frac{9.27 \, \text{g}}{14.01 \, \text{g/mol}} = 0.662 \, \text{mol}
\]

- **Oxygen (O)**: The remainder will be for oxygen.
\[
100 \% - (71.52 \% + 8.61 \% + 9.27 \%) = 10.60 \%
\]
\[
\text{Moles of O} = \frac{10.60 \, \text{g}}{16.00 \, \text{g/mol}} = 0.662 \, \text{mol}
\]

### Step 2: Determine the mole ratio
Next, we divide the moles of each element by the smallest number of moles (which is 0.662 mol) to get the mole ratio.

- **C**: \( \frac{5.955}{0.662} = 9.0 \)
- **H**: \( \frac{8.543}{0.662} = 12.9 \approx 13 \)
- **N**: \( \frac{0.662}{0.662} = 1.0 \)
- **O**: \( \frac{0.662}{0.662} = 1.0 \)

So, the empirical formula is \( C_9H_{13}NO \).

### Step 3: Find the molecular formula
The empirical formula mass of \( C_9H_{13}NO \) is:
\[
(9 \times 12.01) + (13 \times 1.008) + (1 \times 14.01) + (1 \times 16.00) = 151.21 \, \text{g/mol}
\]

Since the molecular weight of the compound is given as 151 g/mol, the empirical formula and molecular formula are the same.

### Conclusion:
The molecular formula of the compound is \( C_9H_{13}NO \).

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Would you like more details on any of the steps or have any questions?

Here are 5 related questions you could explore:
1. How do empirical and molecular formulas differ in larger compounds?
2. What techniques are used in laboratories to determine the molecular weight of a compound?
3. How do decongestants function chemically in the body?
4. What is the significance of nitrogen in organic compounds?
5. Can oxygen percentage in a compound be more accurately determined through combustion analysis?

**Tip:** When calculating empirical formulas, always ensure to simplify the mole ratios to the smallest whole numbers possible.

Learn how to calculate the molecular formula of a decongestant based on percent composition (C: 71.52%, H: 8.61%, N: 9.27%, O: 10.60%) and a molecular weight of 151 g/mol. This step-by-step guide covers empirical and molecular formula calculations, ideal for high school chemistry students.

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