An alkane has a C/H-ratio (by mass) of 5.1428. Its molecular formula is

Options

A. `C_(5)H_(12)`
B. `C_(6)H_(14)`
C. `C_(8)H_(18)`
D. `C_(7)H_(10)`

Explanation

To determine the molecular formula of an alkane with a carbon/hydrogen ratio (by mass) of 5.1428, we can follow these steps:

### Step 1: Understand the Mass Ratio
The mass ratio of carbon to hydrogen is given as 5.1428. This means that for every 5.1428 grams of carbon, there is 1 gram of hydrogen.

### Step 2: Calculate the Molar Mass of Carbon and Hydrogen
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol

### Step 3: Set Up the Ratio
We can express the mass ratio in terms of moles:
- Let the number of moles of carbon be \( n_C \) and the number of moles of hydrogen be \( n_H \).
- The mass ratio can be expressed as:
\[ \frac{n_C \times 12}{n_H \times 1} = 5.1428 \]

### Step 4: Rearranging the Equation
From the above equation, we can rearrange to find the ratio of moles:
\[ n_C = 5.1428 \times n_H \]

### Step 5: Expressing in Whole Numbers
To find the simplest whole number ratio, we can assume \( n_H = 1 \):
\[ n_C = 5.1428 \times 1 = 5.1428 \]
To convert this to whole numbers, we can multiply both sides by a factor that will give us whole numbers. Since 5.1428 is approximately 5, we can round it to 5.

### Step 6: Finding the Molecular Formula
Thus, we can consider:
- \( n_C \approx 5 \)
- \( n_H \approx 26 \) (since \( n_H = n_C / 5.1428 \))

This gives us a molecular formula of \( C_5H_{26} \).

### Step 7: Final Check
To verify, we can calculate the mass ratio:
- Mass of Carbon = \( 5 \times 12 = 60 \) g
- Mass of Hydrogen = \( 26 \times 1 = 26 \) g
- Mass ratio = \( \frac{60}{26} \approx 5.1428 \)

### Conclusion
The molecular formula of the alkane is \( C_5H_{26} \).

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