An organic compound with C =40 % and H= 6.7% will have the empirical formula

Options

A. `CH_(4)`
B. `CH_(2)O`
C. `C_(2)H_(4)O_(2)`
D. `C_(2)H_(4)`

Answer

To find the empirical formula of the organic compound with the given percentages of carbon and hydrogen, we can follow these steps:

### Step 1: Determine the percentage of oxygen
Given:
- Carbon (C) = 40%
- Hydrogen (H) = 6.7%

To find the percentage of oxygen (O), we can subtract the sum of the percentages of carbon and hydrogen from 100%.

\[ \text{Percentage of Oxygen} = 100\% - (40\% + 6.7\%) = 100\% - 46.7\% = 53.3\% \]

### Step 2: Create a table for elements, their percentages, atomic masses, and mole ratios
We will create a table with the following columns: Element, Percentage Composition, Atomic Mass, Moles, and Simple Ratio.

| Element | Percentage Composition | Atomic Mass | Moles Calculation | Moles |
|---------|-----------------------|-------------|-------------------|-------|
| C | 40% | 12 | \( \frac{40}{12} \) | 3.33 |
| H | 6.7% | 1 | \( \frac{6.7}{1} \) | 6.7 |
| O | 53.3% | 16 | \( \frac{53.3}{16} \) | 3.33 |

### Step 3: Calculate the moles for each element
- For Carbon:
\[ \text{Moles of C} = \frac{40}{12} \approx 3.33 \]
- For Hydrogen:
\[ \text{Moles of H} = \frac{6.7}{1} = 6.7 \]
- For Oxygen:
\[ \text{Moles of O} = \frac{53.3}{16} \approx 3.33 \]

### Step 4: Find the smallest mole ratio
The smallest mole ratio among the calculated moles is for Hydrogen (6.7). We will divide all mole values by this smallest value.

### Step 5: Calculate the simple ratio
- For Carbon:
\[ \text{Simple Ratio of C} = \frac{3.33}{6.7} \approx 0.5 \quad \text{(or 1 when multiplied by 2)} \]
- For Hydrogen:
\[ \text{Simple Ratio of H} = \frac{6.7}{6.7} = 1 \]
- For Oxygen:
\[ \text{Simple Ratio of O} = \frac{3.33}{6.7} \approx 0.5 \quad \text{(or 1 when multiplied by 2)} \]

### Step 6: Adjust ratios to whole numbers
To express the ratios as whole numbers, we can multiply all ratios by 2:
- C: \(0.5 \times 2 = 1\)
- H: \(1 \times 2 = 2\)
- O: \(0.5 \times 2 = 1\)

### Step 7: Write the empirical formula
The empirical formula based on the simple ratio is:
\[ \text{Empirical Formula} = C_1H_2O_1 \quad \text{or simply} \quad CH_2O \]

### Final Answer
The empirical formula of the organic compound is **CH₂O**.

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