Answer:
Choice A: [tex]\rm 1\; C_2H_4 O_2 + 1\;NaHCO_3 \to 1\;NaC_2H_3O_2 + 1\;H_2O + 1\;CO_2[/tex].
Explanation:
Indeed it is possible to balance this equation by the conservation of atoms in a chemical reaction. However, knowing what's actually going on in this process will likely make this problem easier to solve.
Vinegar contains acetic acid [tex]\rm C_2H_4 O_2[/tex]. Acetic acid is a monoprotic acid. In other words, each [tex]\rm C_2H_4 O_2[/tex] can dissociate to produce up to one hydrogen ion [tex]\rm H^{+}[/tex]. That is:
[tex]\rm C_2H_4 O_2 \rightleftharpoons {C_2H_3 O_2}^{-} + H^{+}[/tex].
Baking soda is a common name for sodium bicarbonate [tex]\rm NaHCO_3[/tex]. Each formula unit of [tex]\rm NaHCO_3[/tex] contains one bicarbonate ion: [tex]\rm {HCO_3}^{-}[/tex]. Each bicarbonate ion will consume one hydrogen ion to produce water and carbon dioxide:
[tex]\rm {HCO_3}^{-} + H^{+} \to H_2O + CO_2[/tex].
For this chemical equation to balance, the number of hydrogen ions that [tex]\rm C_2H_4 O_2[/tex] supplies shall be the same as the number of these ions that [tex]\rm NaHCO_3[/tex] consumes. Each unit of [tex]\rm C_2H_4 O_2[/tex] supplies one unit of hydrogen ions while each unit of [tex]\rm NaHCO_3[/tex] consumes one unit of hydrogen ions. Reacting the two at a one-to-one ratio will make sure that this reaction neither run short of hydrogen ions or produce more hydrogen ions than it need.
Hence the coefficient in front of [tex]\rm C_2H_4 O_2[/tex] and [tex]\rm NaHCO_3[/tex] shall be the same. Let their coefficients be one.
[tex]\rm 1\; C_2H_4 O_2 + 1\;NaHCO_3 \to ?\;NaC_2H_3O_2 + ?\;H_2O + ?\;CO_2[/tex].
Now, balance this equation with reference to the number of atoms:
- One Na atom;
- Five H atoms;
- Five O atoms;
- Three C atoms.
[tex]\rm 1\; C_2H_4 O_2 + 1\;NaHCO_3 \to 1\;NaC_2H_3O_2 + 1\;H_2O + 1\;CO_2[/tex].
