For the process $R \rightarrow P$, the energy of the reactant is $50 \ kJ$ and the energy of the transition state is $170 \ kJ$. Determine the activation energy $(E_a)$ for the forward reaction in $kJ$.

According to the collision theory of chemical reactions:

For a complex reaction $A \xrightarrow{K} \text{products}$,where $Ea_1 = 180 \ kJ/mol$,$Ea_2 = 80 \ kJ/mol$,and $Ea_3 = 50 \ kJ/mol$,the overall rate constant $K$ is related to individual rate constants by the equation $K = (\frac{K_1 \cdot K_2}{K_3})^{2/3}$. The activation energy $(kJ/mol)$ for the overall reaction is:

Which statement is incorrect according to the Arrhenius equation?

The rate of a chemical reaction doubles with every $10^{\circ}C$ rise in temperature. If the reaction is carried out in the vicinity of $22^{\circ}C$,the activation energy of the reaction is (Given $R = 8.3 \ J \ K^{-1} \ mol^{-1}$,$\ln 2 = 0.69$ and $\ln 3 = 1.1$)

If for a hypothetical reaction,$E_a = 0$ at $273 \ K$,then find the ratio of the rate constants at $383 \ K$ and $273 \ K$.