A carbon compound containing only carbon and oxygen has an approximate molecular weight of 290. On analysis it is found to contain 50% by weight of each element. What is the molecular formula of the compound ?

Explanation

To find the molecular formula of the carbon compound containing only carbon and oxygen, we can follow these steps:

### Step 1: Determine the Empirical Formula
Given that the compound contains 50% carbon and 50% oxygen by weight, we can assume we have 100 grams of the compound. This means we have:
- 50 grams of carbon
- 50 grams of oxygen

Next, we convert these masses to moles using the atomic masses:
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

Calculating the number of moles:
- Moles of Carbon = 50 g / 12 g/mol = 4.1667 mol
- Moles of Oxygen = 50 g / 16 g/mol = 3.125 mol

### Step 2: Find the Simplest Ratio
To find the simplest ratio of moles, we divide each by the smallest number of moles:
- Ratio of Carbon = 4.1667 / 3.125 = 1.3333
- Ratio of Oxygen = 3.125 / 3.125 = 1

This gives us a ratio of approximately 4:3 when multiplied by 3 to convert to whole numbers.

### Step 3: Write the Empirical Formula
From the simplest ratio, we can write the empirical formula:
- Empirical Formula = C4O3

### Step 4: Calculate the Mass of the Empirical Formula
Next, we calculate the molar mass of the empirical formula:
- Molar mass of C4O3 = (4 × 12) + (3 × 16) = 48 + 48 = 96 g/mol

### Step 5: Determine the Value of n
We know the molecular weight of the compound is approximately 290 g/mol. We can find n using the formula:
- n = Molecular weight / Mass of empirical formula
- n = 290 g/mol / 96 g/mol = 3.0208 (approximately 3)

### Step 6: Calculate the Molecular Formula
Now we can find the molecular formula by multiplying the subscripts in the empirical formula by n:
- Molecular Formula = n × Empirical Formula = 3 × C4O3 = C12O9

### Final Answer
The molecular formula of the compound is C12O9.

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