For the reaction $\mathrm{A}\to \mathrm{B}+\mathrm{C}$ the following data were obtained: 

$\begin{array}{lccr}t\left(\mathrm{s}\right)& 0& 900& 1800\\ \left[\mathrm{A}\right]& 50.8& 19.7& 7.62\end{array}$

What is the order of the reaction?

From the following data calculate the order with respect to each reactant $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. Report the order with respect to $\mathrm{A}$.

$\begin{array}{|cccc|}\hline \begin{array}{c}\left[\mathrm{A}\right]\\ (\mathrm{mole}/\mathrm{L})\end{array}& \begin{array}{c}\left[\mathrm{B}\right]\\ (\mathrm{mole}/\mathrm{L})\end{array}& \begin{array}{c}\left[\mathrm{C}\right]\\ (\mathrm{mole}/\mathrm{L})\end{array}& \begin{array}{c}d\left[\mathrm{B}\right]/dt\times {10}^{-5}\\ (\mathrm{mole}/\mathrm{L}/\mathrm{s})\end{array}\\ 0.010& 0.005& 0.010& 5.0\\ 0.015& 0.005& 0.010& 5.0\\ 0.010& 0.010& 0.010& 2.5\\ 0.010& 0.005& 0.020& 14.1\\ \hline\end{array}$

The half-life period of a gaseous substance undergoing thermal decomposition was measured for various initial pressures $\left(\mathrm{p}\right)$ with the following results: $\begin{array}{lllll}\mathrm{p} \left(\mathrm{mm}\right)& 250& 300& 400& 450\\ {\mathrm{t}}_{\frac{1}{2}} \left(\min \right)& 136& 112.5& 85& 75.5\end{array}$

Calculate the order of the reaction.

For the non-equilibrium process: $\mathrm{A}+\mathrm{B}\to \mathrm{P}$, the reaction is of the first order with respect to $\mathrm{A}$ and of the second order with respect to $\mathrm{B}$. If $1$ mole each of $\mathrm{A}$ and $\mathrm{B}$ are introduced into a $1 \mathrm{litre}$ flask, and the initial rates were $1\times {10}^{-2} \mathrm{mole}/\mathrm{litres},$ calculate the rate when half the reactants have converted to the product.

If the answer is of type $\mathrm{y}\times {10}^{-3} \mathrm{M} {\sec }^{-1}$, report the value of $\mathrm{y}$.

For a gas reaction at $\mathrm{T} \left(\mathrm{K}\right)$, the rate is given by $-\frac{{\mathrm{dP}}_{\mathrm{A}}}{\mathrm{dt}}={\mathrm{k}}^{\text{'}}{\mathrm{P}}_{\mathrm{A}}^2 \mathrm{atm} {\mathrm{hr}}^{-1}$. If the rate equation is expressed as $-{\mathrm{r}}_{\mathrm{A}}=-\frac{1}{\mathrm{V}}\frac{{\mathrm{dn}}_{\mathrm{A}}}{\mathrm{dt}}={\mathrm{kC}}_{\mathrm{A}}^2$,$\mathrm{mol} {\mathrm{L}}^{-1} {\mathrm{hr}}^{-1}$, the rate constant $\mathrm{k}$ is given by

(where, $\mathrm{R}=$ ideal gas law constant, $\mathrm{cal} {\mathrm{g}}^{-1} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

${}^{227}\mathrm{Ac}$ has a half-life of $22$ years with respect to radioactive decay. The decay follows two parallel paths:

${}^{227}\mathrm{Ac}\to {}^{227}\mathrm{Th}$ and ${}^{227}\mathrm{Ac}\to {}^{223}\mathrm{Fr}$. If the percentage of the two daughter nuclides are $2.0$ and $98.0$, respectively, the decay constant (in ${\mathrm{year}}^{-1}$) for ${}^{227}\mathrm{Ac}{\to }^{227}\mathrm{Th}$ path is closest to: