Question

When the equation ${{{C}}_2}{{{H}}_6} + {{{O}}_2} \to {{C}}{{{O}}_2} + {{{H}}_2}{{O}}$ is completely balanced using the lowest whole number coefficients, the sum of the coefficients will be:
A. $4$
B. $9.5$
C. $19$
D. $15.5$
E. $11$

Answer 1

The given reaction is a combustion reaction since the reactant is a hydrocarbon and it is burnt in the presence of oxygen. This produces carbon dioxide and water molecules. Based on the law of conservation of mass, the chemical equation is balanced.

Complete answer:
Law of conservation of mass states that both the reactants and products have the same mass. And in a chemical reaction, new mass cannot be created or it cannot be destroyed.
Initially, we have to check the formula whether the reactants and products are correct or not. The coefficients are used to balance the elements. They are placed before each element or compounds. It is important to note that the subscripts near each element cannot be changed, since it is fixed. Moreover, the number of elements in reactants and products should be equal. Mass will be transferred from one substance to another.
Now let’s focus on reactants first. The number of carbons is not the same as that in products. In the reactant side, there are two carbon atoms and in the product side, there is only one carbon atom. To balance, we have to multiply with $2$. There are six hydrogen atoms in LHS, while there are two hydrogen atoms in RHS. Thus multiplying with $3$, we can balance the hydrogen atoms. Now the equation becomes:
${{{C}}_2}{{{H}}_6} + {{{O}}_2} \to 2{{C}}{{{O}}_2} + 3{{{H}}_2}{{O}}$
There are two oxygen atoms in LHS and seven oxygen atoms in RHS. So we can multiply with $\dfrac{7}{2}$ to balance the oxygen atom. Now the equation is:
${{{C}}_2}{{{H}}_6} + \dfrac{7}{2}{{{O}}_2} \to 2{{C}}{{{O}}_2} + 3{{{H}}_2}{{O}}$
But it is given that coefficients are whole numbers. So multiply the whole equation with $2$, we get the balanced chemical equation.
i.e. ${{2}}{{{C}}_2}{{{H}}_6} + 7{{{O}}_2} \to 4{{C}}{{{O}}_2} + 6{{{H}}_2}{{O}}$
Now all the elements are balanced. When we add the coefficients, we get $2 + 7 + 4 + 6 = 19$

Hence, the correct option is C.

Note:
The chemical equation can also be in ionic form. But, it has to be balanced by balancing mass and charge on the reactant and product side. We have to follow the law of conservation of charge also. Since the given chemical equation does not have any charge, we followed only the law of conservation of mass.