10L mixture of${\mathrm{C}}_2{\mathrm{H}}_6 \mathrm{and} {\mathrm{C}}_3{\mathrm{H}}_8$ at STP on complete combustion give 22L of ${\mathrm{CO}}_2$ at STP. The molar concentration of the mixture in mole ratio ___?

$$\begin{gathered} \text{ Let the volume of }{\mathrm{C}}_2{\mathrm{H}}_6\text{ be }\mathrm{VL} \\ \text{ Volume of }{\mathrm{C}}_3{\mathrm{H}}_8=(10-\mathrm{V})\mathrm{L} \\ \begin{array}{l}{\mathrm{C}}_2{\mathrm{H}}_6+\frac{7}{2}{\mathrm{O}}_2\to 2{\mathrm{CO}}_2+3{\mathrm{H}}_2\mathrm{O}\\ {\mathrm{C}}_3{\mathrm{H}}_8+5{\mathrm{O}}_2\to 3{\mathrm{CO}}_2+4{\mathrm{H}}_2\mathrm{O}\end{array} \\ \text{ Since }\mathrm{V}\propto \text{ Number of moles of gas and }{\mathrm{V}}_{{\mathrm{CO}}_2}=22 \mathrm{L}={\left[{\mathrm{V}}_{{\mathrm{CO}}_2}\right]}_{{\mathrm{C}}_2{\mathrm{H}}_6}+{\left[{\mathrm{V}}_{{\mathrm{CO}}_2}\right]}_{{\mathrm{C}}_3{\mathrm{H}}_8}=2\mathrm{V}+3(10-\mathrm{V})=22 \\ \begin{array}{l}\therefore -\mathrm{V}=-8\\ \mathrm{V}=8\mathrm{L}\\ \therefore \frac{{\mathrm{V}}_{{\mathrm{C}}_2{\mathrm{H}}_6}}{{\mathrm{V}}_{{\mathrm{C}}_3{\mathrm{H}}_8}}=\frac{{\mathrm{n}}_{{\mathrm{C}}_2{\mathrm{H}}_6}}{{\mathrm{n}}_{{\mathrm{C}}_3{\mathrm{H}}_8}}=\frac{8}{2}=4:1\end{array} \end{gathered}$$