$$ [ C _ { 2 } H _ { 2 } + \ldots O _ { 2 } \rightarrow \_ CO _ { 2 } + \ldots H _ { 2 } O $$

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It looks like you're trying to write a balanced chemical equation for the combustion of ethylene ($$C_2H_2$$). The general form of the combustion reaction for a hydrocarbon is:

$$
\text{Hydrocarbon} + O_2 \rightarrow CO_2 + H_2O
$$

For ethylene ($$C_2H_2$$), the balanced equation for its complete combustion in oxygen is:

$$
2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O
$$

Here's how we arrive at this balanced equation:

1. **Count the number of carbon (C) atoms**: There are 2 carbon atoms in $$C_2H_2$$. Therefore, we need 4 $$CO_2$$ to balance the carbon atoms (2 C from each of the 2 $$C_2H_2$$).
  
2. **Count the number of hydrogen (H) atoms**: There are 2 hydrogen atoms in $$C_2H_2$$. Therefore, we need 2 $$H_2O$$ to balance the hydrogen atoms (2 H from each of the 2 $$C_2H_2$$).

3. **Count the oxygen (O) atoms**: On the right side, we have 4 $$CO_2$$ contributing 8 oxygen atoms and 2 $$H_2O$$ contributing 2 oxygen atoms, totaling 10 oxygen atoms. Therefore, we need 5 $$O_2$$ on the left side (since each $$O_2$$ provides 2 oxygen atoms).

Putting it all together, the balanced equation is:

$$
2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O
$$
The balanced equation for the combustion of ethylene is $$2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O$$.

\( [ C _ { 2 } H _ { 2 } + \ldots O _ { 2 } \rightarrow \_ CO _ { 2 } + \ldots H _ { 2 } O \)

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