Determine the empirical formula of kelvar, used in making bullet proof vests, containing `70.6% C,4.2% H,11.8%N and 13.4%O`:

Options

A. `C_7H_5NO_2`
B. `C_7H_5N_2O
`
C. `C_7H_9NO`
D. `C_7H_5NO`

Answer

To determine the empirical formula of Kevlar, we will follow these steps:

### Step 1: Assume a Total Mass
Assume the total mass of the Kevlar is 100 grams. This makes the calculation straightforward since the percentages can be directly converted to grams.

### Step 2: Calculate the Mass of Each Element
From the percentages given, we can determine the mass of each element in 100 grams of Kevlar:
- Carbon (C): 70.6 grams
- Hydrogen (H): 4.2 grams
- Nitrogen (N): 11.8 grams
- Oxygen (O): 13.4 grams

### Step 3: Convert Mass to Moles
Next, we convert the mass of each element to moles using their respective atomic masses:
- Moles of Carbon = \( \frac{70.6 \text{ g}}{12 \text{ g/mol}} \) = 5.88 moles
- Moles of Hydrogen = \( \frac{4.2 \text{ g}}{1 \text{ g/mol}} \) = 4.2 moles
- Moles of Nitrogen = \( \frac{11.8 \text{ g}}{14 \text{ g/mol}} \) = 0.84 moles
- Moles of Oxygen = \( \frac{13.4 \text{ g}}{16 \text{ g/mol}} \) = 0.84 moles

### Step 4: Find the Simplest Mole Ratio
Now, we will find the simplest ratio of moles by dividing each value by the smallest number of moles calculated (which is 0.84):
- Ratio of Carbon = \( \frac{5.88}{0.84} \) ≈ 7
- Ratio of Hydrogen = \( \frac{4.2}{0.84} \) ≈ 5
- Ratio of Nitrogen = \( \frac{0.84}{0.84} \) = 1
- Ratio of Oxygen = \( \frac{0.84}{0.84} \) = 1

### Step 5: Write the Empirical Formula
Using the simplest mole ratios, we can write the empirical formula:
- Empirical formula = \( C_7H_5N_1O_1 \) or simply \( C_7H_5NO \)

### Final Answer
The empirical formula of Kevlar is \( C_7H_5NO \).

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