Consider the kinetic data given in the following table for the reaction A + B + C $$ \to $$ Product.


The rate of the reaction for [A] = 0.15 mol dm^-3, [B] = 0.25 mol dm^-3 and [C] = 0.15 mol dm^-3 is found to be Y $$ \times $$ 10^-5 mol dm^-3s^-1. The value of Y is .................

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)

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

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