Consider the following reaction,

$$ 2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) $$

which follows the mechanism given below :

$$ \begin{array}{ll} 2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g}) & \text { (fast equlibrium) } \\\\ \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (slow reaction) } \\\\ \mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (fast reaction) } \end{array} $$

The order of the reaction is __________.

$$_{92}^{238}U$$ is known to undergo radioactive decay to form $$_{82}^{206}Pb$$ by emitting alpha and beta particles. A rock initially contained 68 $$ \times $$ 10^$$-$$6 g of $$_{92}^{238}U$$. If the number of alpha particles that it would emit during its radioactive decay of $$_{92}^{238}U$$ to $$_{82}^{206}Pb$$ in three half-lives is Z $$ \times $$ 10¹⁸, then what is the value of Z?

The decomposition reaction

$$2{N_2}{O_5}(g)\buildrel \Delta \over \longrightarrow 2{N_2}{O_4}(g) + {O_2}(g)$$

is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y $$ \times $$ 10³ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5 $$ \times $$ 10^-4s^-1, assuming ideal gas behaviour, the value of Y is ...............

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 .................