Question

A \[{\mathbf{2500cc}}\] of oxygen was burned with \[{\mathbf{600cc}}\] ethane\[\left[ {{{\mathbf{C}}_2}{{\mathbf{H}}_6}} \right]\]. Calculate the volume of unused oxygen and the volume of carbon dioxide formed.

Answer 1

Hint: A chemical reaction occurs in a balanced stoichiometric ratio. By balancing out the reaction, we can confirm how much volume each compound is being used. And therefore, if we know about one, we can calculate the other reactants and products.

Complete step by step answer:
The chemical equation is a symbolic way to represent and show what is happening in the reaction. It is shown by writing the symbols of the atoms and the coefficient shows how much time that Atom or molecule has been used.
The arrow between the reactant products differentiate between both of them. The reactants are mentioned on the left hand side of the arrow and products are mentioned at the right hand side of the arrow. Now to find out the answer to the above question, we will first try to balance the equation given in the question.
In the question we are given that Oxygen and Ethane are reacted with each other. Which will result in a decomposition of ethane and will form carbon dioxide and water.
Balanced equation:
\[2{C_2}{H_6} + 7{O_2} \to 4C{O_2} + 6{H_2}O\]
\[{C_2}{H_6} = 2V\]
\[{O_2} = 7V\]
$C{O_2} = 4V$
\[{H_2}O = 6V\]
$V$ stands for volumes.
Total amount of ethane;
\[ = 600cc\]
\[ = 2V\]
From above we get that;
 \[1V\left[ {{C_2}{H_6}} \right] = \left( {\dfrac{600}{2}} \right)cc\]
 $ \Rightarrow $ \[1V\left[ {{C_2}{H_6}} \right] = 300cc\]
Now we know that 7 volumes of oxygen is needed;
\[1V = 300cc\]
$ \Rightarrow $ \[7V = \left( {300 \times 7} \right)cc\]
$ \Rightarrow $ \[7V = 2100cc\]
Since, total amount of oxygen is;
\[ = 2500cc\]
The residue amount of oxygen is;
\[ = \left( {2500 - 2100} \right)cc\]
\[ = 400cc\]
Now, the carbon dioxide formed in equation is;
\[ = 4V\]
Since, \[1V = 300cc\]
$ \Rightarrow $ \[4V = \left( {4 \times 300} \right)cc\]
$ \Rightarrow $ \[4V = 1200cc\]

Therefore, the volume of unused oxygen is \[{\mathbf{400cc}}\] and the volume of carbon dioxide formed is $1200cc$ .

Note:
To completely understand a chemical reaction, one must have a balanced chemical equation. To find the balanced chemical equation you should try to add an equal amount of atoms on both sides of the reaction.