\(\text{CH}_3(\text{CH}_2)_5\text{COOC}_2\text{H}_5 \xrightarrow{\text{DIBAL-H, H}_2\text{O}} \text{CH}_3(\text{CH}_2)_5\text{CHO}\)
\(\text{C}_6\text{H}_5\text{COC}_6\text{H}_5 \xrightarrow{\text{Zn(Hg) \& conc. HCl}} \text{C}_6\text{H}_5\text{CH}_2\text{C}_6\text{H}_5\)
\(\text{C}_6\text{H}_5 \xrightarrow{\text{CH}_3\text{MgBr, H}_2\text{O}} \text{C}_6\text{H}_5\text{CH(OH)CH}_3\)
\(\text{CH}_3\text{COCH}_2\text{COOC}_2\text{H}_5 \xrightarrow{\text{NaBH}_4, \text{H}^+} \text{CH}_3\text{CH(OH)CH}_2\text{COOC}_2\text{H}_5\)
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____