Respuesta :
[tex]\text{C}_2\text{H}_6 \text{O} \; (g) + 3 \; \text{O}_2 \; (g) \to 2\; \text{CO}_2 \; (g) + 3\; \text{H}_2\text{O} \; (g)[/tex]
Start with an unbalanced chemical equation of this reaction. Express all species involved in their chemical formula.
Ethanol reacts with oxygen to produce carbon dioxide and water.
[tex]?\; \text{C}_2\text{H}_6 \text{O}+ ? \; \text{O}_2 \to ?\; \text{CO}_2 +?\; \text{H}_2\text{O}[/tex] (NOT BALANCED)
Assign a coefficient one to the species with the greatest number of elements. Ethanol [tex]\text{C}_2\text{H}_6 \text{O}[/tex] contains all three elements involved and shall suit the purpose.
[tex]1 \;\text{C}_2\text{H}_6\text{O}+ ?\; \text{O}_2 \to ?\; \text{CO}_2 +?\; \text{H}_2\text{O}[/tex] (NOT BALANCED)
The presence of one ethanol molecule on the left hand side of the equation indicates the presence of the following atoms on the right:
- Two carbon atoms,
- Six hydrogen atoms, and
- One oxygen atom.
Ethanol is the only reactant that contain carbon and hydrogen. Atoms conserve. All atoms it contains shall end up on the reactant side. No other species would contribute to the number of carbon or hydrogen atoms on the other side. It is thus clear that the there are two carbon atoms and six hydrogen atoms among the two products.
Carbon dioxide is the only product that contains carbon atoms. Both carbon atoms from ethanol would have thus ended up in carbon dioxide molecules. Each carbon dioxide molecule contains one carbon atoms. [tex]2 / 1 = 2[/tex]. There would therefore be two carbon dioxide molecules among the products.
Water is the only product that contains hydrogen atoms. Each water molecule contains two hydrogen atoms. [tex]6 / 2 = 3[/tex]. Similarly, there should be three water molecules on the reactant side.
Thus, assign coefficients 2 and 3 to carbon dioxide and water, respectively, in the previous equation.
[tex]1 \;\text{C}_2\text{H}_6\text{O}+ ? \; \text{O}_2 \to 2\; \text{CO}_2 + 3\; \text{H}_2\text{O}[/tex] (NOT BALANCED)
- Each carbon dioxide molecule contains two oxygen atoms;
- Each water molecule contains one oxygen atoms.
There are therefore [tex]2 \times 2 + 3 \times 1 = 7[/tex] oxygen atoms in the products. The reactants should also contain seven oxygen atoms.
Based on the initial assumption, one of the seven oxygen atoms originates from the ethanol molecule. [tex]7 - 1 \times 1 = 6[/tex]. The remaining six oxygen atoms all came from oxygen molecules. Each oxygen molecule [tex]\text{O}_2[/tex] contains two oxygen atoms. The reactants should therefore contain [tex]6 / 2 = 3[/tex] oxygen molecules.
The coefficient in front of oxygen should thus be three.
[tex]1 \;\text{C}_2\text{H}_6 \text{O}+ 3\; \text{O}_2 \to 2\; \text{CO}_2 + 3\; \text{H}_2\text{O}[/tex]. (balanced.)
The question states that ethanol, carbon dioxide, and water are in their gaseous states [tex](g)[/tex] during this reaction.
Combustion reactions tend to involve a high temperature. It is implied that oxygen is also in its gaseous state during the reaction process.
State symbols:
- [tex](s)[/tex]- solid;
- [tex](l)[/tex]- liquid;
- [tex]\bb{(g)}[/tex]- gaseous;
- [tex](aq)[/tex]- aqueous.
The state symbol indicates the phase of a chemical. It should be placed right after the chemical formula of each species.
It is not necessary to write [tex]1[/tex] in coefficients as it is implied.
Hence the balanced chemical equation.
[tex]\text{C}_2\text{H}_6 \text{O} \; (g) + 3 \; \text{O}_2 \; (g) \to 2\; \text{CO}_2 \; (g) + 3\; \text{H}_2\text{O} \; (g)[/tex]
