At $727°\mathrm{C}$ and $1.23 \mathrm{atm}$ of total equilibrium pressure, ${\mathrm{SO}}_3$ is partially dissociated into ${\mathrm{SO}}_2$ and ${\mathrm{O}}_2$, according to the following reaction: ${\mathrm{SO}}_3 \left(\mathrm{g}\right)\rightleftharpoons {\mathrm{SO}}_2 \left(\mathrm{g}\right)+1/2{\mathrm{O}}_2 \left(\mathrm{g}\right).$ The density of the equilibrium mixture is $0.9 \mathrm{gm}/\mathrm{litre}$. The degree of dissociation is

${\mathrm{SO}}_3\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{SO}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$

If observed vapour density of mixture at equilibrium is $35$ then find out value of $\mathrm{\alpha }$.

For the reaction  ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right)$

${\mathrm{K}}_{\mathrm{c}}=66.9$ at $350°\mathrm{C}$ and ${\mathrm{K}}_{\mathrm{c}}=50.0$ at $448°\mathrm{C}$. The reaction has:

The value of $\mathrm{\Delta }$ G° for a reaction in aqueous phase having K_C = 1, would be: