The percent composition of the high explosive HNS is:`{: (C,H,N,O),(37.35%, 1.34%, 18.67%, 42.65%):}`
The molar mass of HNS is 450.22. What is the molecular formular of HNS?

Options

A. `C_(13)H_(4)N_(7)O_(12)`
B. `C_(14)H_(6)N_(6)O_(12)`
C. `C_(15)H_(10)N_(6)O_(11)`
D. `C_(16)H_(12)N_(5)O_(11)`

Answer

To determine the molecular formula of HNS from its percent composition and molar mass, we can follow these steps:

### Step 1: Convert Percent Composition to Mass
Assuming we have 100 g of the compound, the mass of each element can be calculated directly from the percent composition:
- Carbon (C): 37.35 g
- Hydrogen (H): 1.34 g
- Nitrogen (N): 18.67 g
- Oxygen (O): 42.65 g

### Step 2: Convert Mass to Moles
Next, we convert the mass of each element to moles using their respective molar masses:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol
- Molar mass of Nitrogen (N) = 14 g/mol
- Molar mass of Oxygen (O) = 16 g/mol

Calculating the moles for each element:
- Moles of C = 37.35 g / 12 g/mol = 3.1125 moles
- Moles of H = 1.34 g / 1 g/mol = 1.34 moles
- Moles of N = 18.67 g / 14 g/mol = 1.3343 moles
- Moles of O = 42.65 g / 16 g/mol = 2.6641 moles

### Step 3: Find the Simplest Mole Ratio
Now, we divide each of the mole values by the smallest number of moles calculated:
- C: 3.1125 / 1.3343 ≈ 2.33
- H: 1.34 / 1.3343 ≈ 1
- N: 1.3343 / 1.3343 = 1
- O: 2.6641 / 1.3343 ≈ 2

### Step 4: Convert to Whole Numbers
To convert the ratios into whole numbers, we can multiply each by a common factor. In this case, multiplying by 3 gives:
- C: 2.33 * 3 ≈ 7
- H: 1 * 3 = 3
- N: 1 * 3 = 3
- O: 2 * 3 = 6

Thus, the empirical formula is approximately C7H3N3O6.

### Step 5: Determine the Molecular Formula
Next, we need to find the molar mass of the empirical formula:
- Molar mass of C7H3N3O6 = (7*12) + (3*1) + (3*14) + (6*16) = 84 + 3 + 42 + 96 = 225 g/mol

Now, we can find the ratio of the molar mass of the compound to the empirical formula mass:
- Ratio = Molar mass of HNS / Molar mass of empirical formula = 450.22 g/mol / 225 g/mol ≈ 2

### Step 6: Calculate the Molecular Formula
Finally, we multiply the subscripts in the empirical formula by this ratio:
- C: 7 * 2 = 14
- H: 3 * 2 = 6
- N: 3 * 2 = 6
- O: 6 * 2 = 12

Thus, the molecular formula of HNS is C14H6N6O12.

### Final Answer
The molecular formula of HNS is **C14H6N6O12**.