Consider the following reversible reaction, $$A\left( g \right) + B\left( g \right) \to AB\left( g \right).$$

The activation energy of the backward reaction exceeds that of the forward reaction by $$2RT$$ (in $$J\,mo{l^{ - 1}}$$). If the pre-exponential factor of the forward reaction is $$4$$ times that of the reverse reaction, the absolute value of $$\Delta {G^ \circ }$$ (in $$J\,mo{l^{ - 1}}$$ ) for the reaction at $$300$$ $$K$$ is ____________.

(Given; $$\ln \left( 2 \right) = 0.7,RT = 2500$$ $$J\,mo{l^{ - 1}}$$ at $$300$$ $$K$$ and $$G$$ is the Gibbs energy)

In dilute aqueous H₂SO₄, the complex diaquodioxalatoferrate(II) is oxidized by $$MnO_4^-$$. For this reaction, the ratio of the rate of change of [H⁺] to the rate of change of $$[MnO_4^-]$$ is

A closed vessel with rigid walls contains 1 mol of $${}_{92}^{238}U$$ and 1 mol of air at 298 K. Considering complete decay of $${}_{92}^{238}U$$ to $${}_{82}^{206}Pb$$, the ratio of the final pressure to the initial pressure of the system at 298 K is

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table?

$${}_{29}^{63}Cu$$ + $${}_1^1H$$ $$\to$$ $$6{}_0^1n$$ + $${}_2^4\alpha $$ + 2$${}_1^1H$$ + X