A saturated hydrocarbon contains 82.66% carbon. Its molecular formula is

Options

A. `C_(2)H_(6)`
B. `C_(3)H_(18)`
C. `C_4H_(10)`
D. `C_(2)H_(5)`

Explanation

To determine the molecular formula of a saturated hydrocarbon that contains 82.66% carbon, we can follow these steps:

### Step 1: Assume a Sample Size
Assume a sample size of 100 grams of the hydrocarbon. This makes calculations easier since the percentages can be directly converted to grams.

### Step 2: Calculate the Mass of Carbon and Hydrogen
From the given percentage:
- Mass of Carbon = 82.66 grams
- Mass of Hydrogen = 100 grams - 82.66 grams = 17.34 grams

### Step 3: Convert Mass to Moles
Next, we convert the masses of carbon and hydrogen to moles using their respective molar masses:
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol

Calculating the number of moles:
- Moles of Carbon = 82.66 g / 12 g/mol = 6.8883 moles
- Moles of Hydrogen = 17.34 g / 1 g/mol = 17.34 moles

### Step 4: Determine the Simplest Mole Ratio
To find the simplest ratio, divide the number of moles of each element by the smallest number of moles calculated:
- Ratio of Carbon = 6.8883 / 6.8883 = 1
- Ratio of Hydrogen = 17.34 / 6.8883 ≈ 2.52

### Step 5: Convert to Whole Numbers
Since we need whole numbers for the empirical formula, we can multiply both ratios by 2 to eliminate the decimal:
- Carbon: 1 × 2 = 2
- Hydrogen: 2.52 × 2 ≈ 5

Thus, the empirical formula is C2H5.

### Step 6: Determine the Molecular Formula
For a saturated hydrocarbon (alkane), the general formula is CnH2n+2. Here, n = 2:
- C2H5 is not a saturated hydrocarbon because it does not fit the formula CnH2n+2 (which would give C2H6).

Now, let's check for n = 4:
- C4H10 (where n = 4) fits the formula CnH2n+2 (C4H10 = C4H2(4)+2).

### Conclusion
The molecular formula of the saturated hydrocarbon is C4H10.

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