25 g of an unknown hydrocarbon contains 24 g of carbon. 25 g of this hydrocarbon on burning produces x gm of `H_(2)O`. The numerical value of x is_____.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the mass of hydrogen in the hydrocarbon
Given that the total mass of the hydrocarbon is 25 g and it contains 24 g of carbon, we can find the mass of hydrogen in the hydrocarbon.

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

### Step 2: Write the general formula for the combustion of a hydrocarbon
The general formula for the combustion of a hydrocarbon (CxHy) can be written as:

\[ \text{CxHy} + O_2 \rightarrow CO_2 + H_2O \]

### Step 3: Determine the moles of carbon and hydrogen
- The molar mass of carbon (C) is 12 g/mol.
- The molar mass of hydrogen (H) is 1 g/mol.

Calculating the moles of carbon:

\[ \text{Moles of Carbon} = \frac{\text{Mass of Carbon}}{\text{Molar Mass of Carbon}} = \frac{24 \, \text{g}}{12 \, \text{g/mol}} = 2 \, \text{mol} \]

Calculating the moles of hydrogen:

\[ \text{Moles of Hydrogen} = \frac{\text{Mass of Hydrogen}}{\text{Molar Mass of Hydrogen}} = \frac{1 \, \text{g}}{1 \, \text{g/mol}} = 1 \, \text{mol} \]

### Step 4: Determine the moles of water produced
From the combustion reaction, we know that:
- 1 mole of C produces 1 mole of CO2.
- 2 moles of H produces 1 mole of H2O.

Thus, for 2 moles of carbon, we will produce 2 moles of CO2 and for 1 mole of hydrogen, we will produce:

\[ \text{Moles of H2O} = \frac{\text{Moles of H}}{2} = \frac{1 \, \text{mol}}{2} = 0.5 \, \text{mol} \]

### Step 5: Calculate the mass of water produced
The molar mass of water (H2O) is:

\[ \text{Molar Mass of H2O} = 2 \times 1 + 16 = 18 \, \text{g/mol} \]

Now, we can calculate the mass of water produced:

\[ \text{Mass of H2O} = \text{Moles of H2O} \times \text{Molar Mass of H2O} = 0.5 \, \text{mol} \times 18 \, \text{g/mol} = 9 \, \text{g} \]

### Final Answer
The numerical value of \( x \) (the mass of water produced) is:

\[ \boxed{9} \, \text{g} \]