A hydrocarbon contains 91.3% carbon by mass. Find the empirical formula of hydrocarbon?

Options

A. CH
B. C_2H_3
C. C_7H_8
D. C_3H_5

Answer

To find the empirical formula of the hydrocarbon containing 91.3% carbon by mass, we can follow these steps:

### Step 1: Determine the mass percentages of carbon and hydrogen
Given that the hydrocarbon contains 91.3% carbon by mass, we can find the percentage of hydrogen by subtracting the percentage of carbon from 100%.

\[ \text{Percentage of Hydrogen} = 100\% - 91.3\% = 8.7\% \]

### Step 2: Assume a sample size
To simplify calculations, we can assume a sample size of 100 grams of the hydrocarbon. This means:
- Mass of Carbon = 91.3 grams
- Mass of Hydrogen = 8.7 grams

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

Calculating moles of Carbon:
\[ \text{Moles of Carbon} = \frac{\text{Mass of Carbon}}{\text{Molar Mass of Carbon}} = \frac{91.3 \text{ g}}{12 \text{ g/mol}} \approx 7.608 \text{ moles} \]

Calculating moles of Hydrogen:
\[ \text{Moles of Hydrogen} = \frac{\text{Mass of Hydrogen}}{\text{Molar Mass of Hydrogen}} = \frac{8.7 \text{ g}}{1 \text{ g/mol}} = 8.7 \text{ moles} \]

### Step 4: Determine the mole ratio
To find the simplest ratio of moles, we divide the number of moles of each element by the smallest number of moles calculated:

\[ \text{Ratio of Carbon} = \frac{7.608}{7.608} = 1 \]
\[ \text{Ratio of Hydrogen} = \frac{8.7}{7.608} \approx 1.143 \]

### Step 5: Simplify the ratio
To express the ratio in whole numbers, we can multiply both ratios by a common factor. In this case, multiplying both by 7 gives:

\[ \text{Carbon} : \text{Hydrogen} \approx 7 : 8 \]

### Step 6: Write the empirical formula
From the ratio of moles, we can write the empirical formula of the hydrocarbon as:

\[ \text{Empirical Formula} = C_7H_8 \]

### Conclusion
Thus, the empirical formula of the hydrocarbon is **C7H8**.

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