An organic compound contains `C,H` and `O`. If `C (%):H^(%) = 6:1`, what is the simplest formula of the compound, given that one mole of the compound contains half as much oxygen as would be required to burn all the `C` and `H` atoms in it to `CO_(2)` and `H_(2)O`?

Options

A. `CH_(2) O`
B. `C_(2)H_(2)O_(3)`
C. `C_(3)H_(6)O`
D. `C_(3)H_(6) O_(2)`

Explanation

To find the simplest formula of the organic compound containing carbon (C), hydrogen (H), and oxygen (O), we can follow these steps:

### Step 1: Determine the Masses of Carbon and Hydrogen
Given the ratio of carbon to hydrogen is 6:1, we can assume a total mass for simplicity. Let's take the total mass of carbon and hydrogen to be 700 grams (this is an arbitrary choice to make calculations easier).

- Mass of Carbon (C) = (6/7) * 700 g = 600 g
- Mass of Hydrogen (H) = (1/7) * 700 g = 100 g

### Step 2: Calculate the Moles of Carbon and Hydrogen
Next, we calculate the number of moles of carbon and hydrogen using their respective molar masses.

- Moles of Carbon = Mass of Carbon / Molar Mass of Carbon = 600 g / 12 g/mol = 50 moles
- Moles of Hydrogen = Mass of Hydrogen / Molar Mass of Hydrogen = 100 g / 1 g/mol = 100 moles

### Step 3: Find the Ratio of Moles of Carbon to Hydrogen
Now, we can find the ratio of the number of moles of carbon to hydrogen.

- Ratio of moles of C to H = 50 moles C : 100 moles H = 1 : 2

### Step 4: Write the Empirical Formula
From the mole ratio, we can write the empirical formula of the compound as:

- Empirical Formula = C₁H₂ = CH₂

### Step 5: Determine the Amount of Oxygen Required for Combustion
The problem states that one mole of the compound contains half as much oxygen as would be required to burn all the carbon and hydrogen atoms in it to CO₂ and H₂O.

For complete combustion of CH₂:
- 1 mole of C produces 1 mole of CO₂
- 2 moles of H produce 1 mole of H₂O

Thus, for 1 mole of CH₂:
- Total O₂ required = 1 mole of CO₂ requires 2 moles of O₂ + 1 mole of H₂O requires 0.5 moles of O₂ = 2 + 0.5 = 2.5 moles of O₂.

Since the compound contains half as much oxygen as required:
- Oxygen in the compound = 2.5 moles O₂ / 2 = 1.25 moles O₂.

### Step 6: Write the Molecular Formula
Since we have established that the empirical formula is CH₂ and we need to account for oxygen, we can express the molecular formula as:

- Molecular Formula = CH₂O (since we need one oxygen atom).

### Conclusion
Thus, the simplest formula of the compound is **CH₂O**.

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