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 coefficients will be:
[A] 4
[B] 9.5
[C] 19
[D] 15.5
[E] 11

Answer 1

Hint: To solve this, follow the law of conservation of mass. Identify the number of each of the elements on both the sides. Balance the side which has a lower number of atoms by multiplying it with a number.

Complete step by step answer:
 We know that balancing a reaction equation means that the number of elements will be the same on the reactant as well as the product side. For this question we have to follow conservation of mass.
We know that the law of conservation of mass states that for a closed system, where transfer of mass and energy takes place, the mass of the system is always constant at any time as the mass of the system cannot change. Thus, mass can neither be added nor removed but only transfers from one form to another. In the question, the equation given to us is:
${{C}_{2}}{{H}_{6}}+{{O}_{2}}\to C{{O}_{2}}+{{H}_{2}}O$

Now, to balance this equation let us start by identifying the elements on the reactant i.e. the left hand side. We know that the elements will be the same on the product side too as they are formed from these reactants only.
In the reactant side, we have hydrogen, carbon and oxygen.
Now let us find the number of atoms of these elements on the reactant side.
In the left hand side we have 2 carbon atoms and on the product side we have 1. To balance the carbon atoms we will multiply the carbon on the product side by 2.
In the reactant side we have a total 6 hydrogen atoms and in the product side we have 2. To balance the hydrogen atoms we will multiply the hydrogen atom on the product side by 3.
Let us write the hydrogen and carbon balanced equation and then figure out how to balance oxygen atoms.
${{C}_{2}}{{H}_{6}}+{{O}_{2}}\to 2C{{O}_{2}}+3{{H}_{2}}O$

Now we have 2 oxygen atoms in the reactant side and 7 on the product side therefore, to balance this we will have to multiply the oxygen on the reactant side by $\dfrac{7}{2}$ . So, the equation becomes-
${{C}_{2}}{{H}_{6}}+\dfrac{7}{2}{{O}_{2}}\to 2C{{O}_{2}}+3{{H}_{2}}O$

To get a whole number we will multiply this by 2. So, the final balanced equation is-
$2{{C}_{2}}{{H}_{6}}+7{{O}_{2}}\to 4C{{O}_{2}}+6{{H}_{2}}O$
Therefore, the sum of the coefficients is 2 + 7 + 4 + 6 = 19.
So, the correct answer is “Option C”.

Note: If we had the equation in ionic form instead of the elemental form, we would have to balance mass as well as the charge on both the sides. We have to follow the law of conservation of mass as well as charge while writing a balanced equation. In the above equation, there was no overall charge on any of the reactant or product species and thus are neutral so we just followed the conservation of mass.