25 g of an unknown hydrocarbon upon burning produces 88 g of `CO_2` and 9 g of `H_2O` . This unknown hydrocarbon contains

Options

A. 18 g of carbon and 7 g of hydrogen
B. 20 g of carbon and 5 g of hydrogen
C. 22 g of carbon and 3 g of hydrogen
D. 24 g of carbon and 1 g of hydrogen.

Answer

To determine the composition of the unknown hydrocarbon, we will follow these steps:

### Step 1: Calculate the amount of Carbon in CO₂ produced

1. **Molar Mass of CO₂**: The molar mass of carbon dioxide (CO₂) is 44 g/mol (12 g/mol for Carbon + 32 g/mol for Oxygen).
2. **Carbon in CO₂**: Each mole of CO₂ contains 1 mole of Carbon. Therefore, the mass of Carbon in CO₂ can be calculated using the ratio of the molar masses.

\[ \text{Mass of Carbon} = \left(\frac{12 \, \text{g/mol}}{44 \, \text{g/mol}}\right) \times 88 \, \text{g} \]

\[ \text{Mass of Carbon} = \left(\frac{12}{44}\right) \times 88 = 24 \, \text{g} \]

### Step 2: Calculate the amount of Hydrogen in H₂O produced

1. **Molar Mass of H₂O**: The molar mass of water (H₂O) is 18 g/mol (2 g/mol for Hydrogen + 16 g/mol for Oxygen).
2. **Hydrogen in H₂O**: Each mole of H₂O contains 2 moles of Hydrogen. Therefore, the mass of Hydrogen in H₂O can be calculated similarly.

\[ \text{Mass of Hydrogen} = \left(\frac{2 \, \text{g/mol}}{18 \, \text{g/mol}}\right) \times 9 \, \text{g} \]

\[ \text{Mass of Hydrogen} = \left(\frac{2}{18}\right) \times 9 = 1 \, \text{g} \]

### Step 3: Total Mass of Hydrocarbon

Now, we can summarize the total mass of Carbon and Hydrogen in the unknown hydrocarbon:

- Mass of Carbon = 24 g
- Mass of Hydrogen = 1 g

### Step 4: Verify Total Mass

The total mass of the hydrocarbon can be verified by adding the masses of Carbon and Hydrogen:

\[ \text{Total Mass} = \text{Mass of Carbon} + \text{Mass of Hydrogen} = 24 \, \text{g} + 1 \, \text{g} = 25 \, \text{g} \]

This matches the initial mass of the unknown hydrocarbon.

### Conclusion

The unknown hydrocarbon contains:
- **24 g of Carbon**
- **1 g of Hydrogen**

### Final Answer

Thus, the unknown hydrocarbon contains 24 g of Carbon and 1 g of Hydrogen.

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