Write down the reactions involved in the preparation of the following using the reagents indicated against it in parenthesis: Propionic anhydride from propionaldehyde \left[ AgNO _3 / NH _4 OH , P _2 O _5\right]
\begin{matrix} \\ && CH _3 CH _2 CO\\ &&& \diagdown \\ CH _3 CH _2 COOH & \overset{P _2 O_5}{\underset{\text {Heat}}{\xrightarrow {\hspace{2 cm}} }} &&& O &+&H_2O \\ + &&&\diagup \\ CH _3 CH _2 COOH && CH _3 CH _2 CO \\ &&\text {Propionic anhydride} \end{matrix}