Question

Calculate the volume of oxygen required to burn \[12.00\;{\rm{L}}\] of ethane gas, \[{{\rm{C}}_2}{{\rm{H}}_6}\], to produce carbon dioxide and water, if the volumes of \[{{\rm{C}}_2}{{\rm{H}}_6}\]and \[{{\rm{O}}_2}\]are measured under the same conditions of temperature and pressure.

Short answer

Therefore, volume of \[42\;{\rm{L}}\]\[{{\rm{O}}_2}\] will be required to react with \[12\;{\rm{L}}\] of \[{{\rm{C}}_2}{{\rm{H}}_6}\].

Step-by-step solution

Definition of pressure

The sum of all gas particle/wall impact forces divided by the wall's surface area.

Calculate the volume of oxygen

Let us solve the given problem.

Gases combine, or react, in definite and simple proportions by volume, according to Avogadro's law, assuming that all gas volumes are measured at the same temperature and pressure.

The ratio of the volumes of \[{{\rm{C}}_2}{{\rm{H}}_6}\]and \[{{\rm{O}}_2}\]will be equal to the ratio of their coefficients in the balanced equation for the reaction:

Balanced equation:

\[2{{\rm{C}}_2}{{\rm{H}}_6}(\;{\rm{g}}) + 7{{\rm{O}}_2}(\;{\rm{g}}) \to 4{\rm{C}}{{\rm{O}}_2}(\;{\rm{g}}) + 6{{\rm{H}}_2}{\rm{O}}({\rm{g}})\]

\[2\]volumes \[ + 7\]volumes \[ - - 4\] volumes \[ + 6\] volumes From the balanced equation, we can see that two volumes of \[{{\rm{C}}_2}{{\rm{H}}_6}\] will react with seven volumes of \[{{\rm{O}}_2}\] :

\[12\;{\rm{L}}{{\rm{C}}_2}{{\rm{H}}_6} \times \frac{{7\;{\rm{L}}{{\rm{O}}_2}}}{{2\;{\rm{L}}{{\rm{C}}_2}{{\rm{H}}_6}}} = 42\;{\rm{L}}\,\,{{\rm{O}}_2}\]

Therefore, calculated volume of \[{{\rm{O}}_2}\] is \[42\;{\rm{L}}\,\].