A mixture of Na₂CO₃ and NaHCO₃  having a total weight of 100 gm on heating produced 11.2 lit of CO₂ under STP conditions. The percentage of Na₂CO₃ in the mixture is (X) .Find the value of $\frac{X}{8}$

${\text{W}}_{{\text{Na}}_{\text{2}}{\text{Co}}_{\text{3}}}{\text{ + W}}_{{\text{NaHCo}}_{\text{3}}}=100\text{ gm}$

$$\begin{gathered} \begin{array}{l}{\text{Na}}_{\text{2}}{\text{Co}}_{\text{3}}\text{ is thermally stable}\\ {\text{2NaHCo}}_{\text{3}}\stackrel{\Delta }{\to }{\text{Na}}_{\text{2}}{\text{Co}}_{\text{3}}+{\text{H}}_{\text{2}}{\text{o+Co}}_{\text{2}}\\ 2{\text{x84 gm NaHco}}_{\text{3}}\to 22.4{\text{ lit Co}}_{\text{2}}\text{ at STP}\\ \frac{\text{11.2}}{\text{22.4}}\text{X2X84 }\to {\text{ 11.2 lit Co}}_{\text{2}}\text{ at STP }\\ \text{=84 gm}\\ {\text{W}}_{{\text{Na}}_{\text{2}}{\text{Co}}_{\text{3}}}=84{\text{ gm, W}}_{{\text{NaHCo}}_{\text{3}}}\text{ = 100-84 = 16 gm}\end{array} \\ X=16g \\ \frac{X}{8}=\frac{16}{8}=2 \end{gathered}$$