1) Washing Soda from Baking Soda
Step 1: Thermal decomposition of baking soda (sodium hydrogen carbonate)
\[ \mathrm{2\,NaHCO_3 \xrightarrow{\Delta} Na_2CO_3 + CO_2 + H_2O} \] (Soda ash, \(\mathrm{Na_2CO_3}\), is formed.)
Step 2: Hydration to washing soda (decahydrate)
\[ \mathrm{Na_2CO_3 + 10\,H_2O \longrightarrow Na_2CO_3\cdot 10H_2O} \] (Washing soda crystals.)
2) Plaster of Paris from Gypsum
Controlled heating (about \(373\,\text{K}\)) of gypsum
\[ \mathrm{CaSO_4\cdot 2H_2O \xrightarrow{373\,K} CaSO_4\cdot \tfrac{1}{2}H_2O + \tfrac{3}{2}H_2O} \] \(\mathrm{CaSO_4\cdot \tfrac{1}{2}H_2O}\) is
Plaster of Paris (POP).
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.