Sure! Let's go through the process of determining the coefficient for [tex]\( O_2 \)[/tex] in the given chemical reaction.
Given the chemical reaction:
[tex]\[ C_4H_{10} + ? O_2 \rightarrow 4 CO_2 + 5 H_2O \][/tex]
First, analyze the number of oxygen atoms present in the products:
1. Carbon Dioxide ([tex]\( CO_2 \)[/tex]):
- Each [tex]\( CO_2 \)[/tex] molecule contains 2 oxygen atoms.
- We have 4 molecules of [tex]\( CO_2 \)[/tex].
- Therefore, the total number of oxygen atoms from [tex]\( CO_2 \)[/tex] is [tex]\( 4 \times 2 = 8 \)[/tex].
2. Water ([tex]\( H_2O \)[/tex]):
- Each [tex]\( H_2O \)[/tex] molecule contains 1 oxygen atom.
- We have 5 molecules of [tex]\( H_2O \)[/tex].
- Therefore, the total number of oxygen atoms from [tex]\( H_2O \)[/tex] is [tex]\( 5 \times 1 = 5 \)[/tex].
Now, sum the total number of oxygen atoms from both products:
[tex]\[ 8 + 5 = 13 \][/tex]
Next, determine the number of [tex]\( O_2 \)[/tex] molecules required. Each [tex]\( O_2 \)[/tex] molecule contains 2 oxygen atoms. To find the coefficient that satisfies the total of 13 oxygen atoms, we divide the total number of required oxygen atoms by the number of oxygen atoms in each [tex]\( O_2 \)[/tex] molecule:
[tex]\[ \frac{13}{2} = 6.5 \][/tex]
However, in standard chemical equation balancing, coefficients should be whole numbers. Therefore, to make it a whole number, we can multiply the entire reaction by 2:
[tex]\[ 2 \left( C_4H_{10} + 6.5 O_2 \rightarrow 4 CO_2 + 5 H_2O \right) \][/tex]
[tex]\[ 2 C_4H_{10} + 13 O_2 \rightarrow 8 CO_2 + 10 H_2O \][/tex]
Thus, the balanced equation for the reaction with whole number coefficients is:
[tex]\[ C_4H_{10} + 6.5 O_2 \rightarrow 4 CO_2 + 5 H_2O \][/tex]
Therefore, the coefficient in front of [tex]\( O_2 \)[/tex] in the original equation should be [tex]\(\mathbf{6.5}\)[/tex].
