Which among the following represents the correct reaction of general combustion?

Options

A. `C_(x)H_(y)+(x+(Y)/(4))O_(2)rarrxCO_(2)+(Y)/(2)H_(2)O`
B. `C_(x)H_(y)+(2x+(y)/(4))O_(2)rarrxCO_(2)+(Y)/(2)H_(2)O`
C. `C_(x)H_(y)+(x+(Y)/(2))O_(2)rarrxCO_(2)+(Y)/(2)H_(2)O`
D. `C_(x)Y_(y)+(x+(Y)/(4))O_(2)rarrxCO_(2)+(Y)/(4)H_(2)O`

Answer

To determine the correct reaction of general combustion for hydrocarbons, we can follow these steps:

### Step 1: Understand the General Combustion Reaction
The general combustion reaction for a hydrocarbon (represented as \( C_xH_y \)) involves its reaction with dioxygen (\( O_2 \)) to produce carbon dioxide (\( CO_2 \)) and water (\( H_2O \)). The general form of the reaction can be written as:
\[ C_xH_y + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Write the Unbalanced Equation
The unbalanced equation for the combustion of a hydrocarbon can be expressed as:
\[ C_xH_y + O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]

### Step 3: Balance the Carbon Atoms
To balance the carbon atoms, we note that there are \( x \) carbon atoms in the hydrocarbon, so we need \( x \) \( CO_2 \) molecules:
\[ C_xH_y + O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]

### Step 4: Balance the Hydrogen Atoms
Next, we balance the hydrogen atoms. There are \( y \) hydrogen atoms in the hydrocarbon, which means we need \( \frac{y}{2} \) \( H_2O \) molecules to have \( y \) hydrogen atoms on the product side:
\[ C_xH_y + O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]

### Step 5: Balance the Oxygen Atoms
Now we need to balance the oxygen atoms. On the product side, we have \( 2x \) oxygen atoms from \( x CO_2 \) and \( \frac{y}{2} \) oxygen atoms from \( \frac{y}{2} H_2O \). Thus, the total number of oxygen atoms on the product side is:
\[ 2x + \frac{y}{2} \]

On the reactant side, if we denote the coefficient of \( O_2 \) as \( a \), then we have \( 2a \) oxygen atoms. Therefore, we set up the equation:
\[ 2a = 2x + \frac{y}{2} \]

### Step 6: Solve for \( a \)
Solving for \( a \):
\[ a = \frac{2x + \frac{y}{2}}{2} = x + \frac{y}{4} \]

### Step 7: Write the Balanced Equation
Now we can write the balanced combustion equation:
\[ C_xH_y + \left( x + \frac{y}{4} \right) O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]

### Conclusion
The correct representation of the general combustion reaction for a hydrocarbon \( C_xH_y \) is:
\[ C_xH_y + \left( x + \frac{y}{4} \right) O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]