To balance the chemical reaction:
[tex]\[ CO \rightarrow C + O_2 \][/tex]
we need to ensure that the number of each type of atom on the reactant side matches the number on the product side.
Let's denote the coefficients for each compound in the balanced equation as follows:
[tex]\[ a \cdot CO \rightarrow b \cdot C + c \cdot O_2 \][/tex]
We need to balance both carbon (C) and oxygen (O) atoms:
1. Carbon atoms:
- On the reactant side, we have [tex]\( a \)[/tex] carbon atoms in [tex]\( a \cdot CO \)[/tex].
- On the product side, we have [tex]\( b \)[/tex] carbon atoms in [tex]\( b \cdot C \)[/tex].
Thus, the equation for carbon atoms is:
[tex]\[ a = b \][/tex]
2. Oxygen atoms:
- On the reactant side, we have [tex]\( a \)[/tex] oxygen atoms in [tex]\( a \cdot CO \)[/tex].
- On the product side, we have [tex]\( 2c \)[/tex] oxygen atoms in [tex]\( c \cdot O_2 \)[/tex].
Thus, the equation for oxygen atoms is:
[tex]\[ a = 2c \][/tex]
To find the coefficients, we solve this system of equations.
From the first equation, we have:
[tex]\[ a = b \][/tex]
From the second equation, we have:
[tex]\[ a = 2c \][/tex]
To ensure all coefficients are whole numbers, we can set [tex]\( a = 2 \)[/tex]. Then:
[tex]\[ b = a = 2 \][/tex]
[tex]\[ c = \frac{a}{2} = \frac{2}{2} = 1 \][/tex]
So the balanced reaction is:
[tex]\[ 2 \cdot CO \rightarrow 2 \cdot C + 1 \cdot O_2 \][/tex]
Therefore, the coefficients that balance the reaction are [tex]\( a = 2 \)[/tex], [tex]\( b = 2 \)[/tex], and [tex]\( c = 1 \)[/tex]. The balanced chemical equation is:
[tex]\[ 2CO \rightarrow 2C + O_2 \][/tex]
