Slope of the graph between $$\log \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}$$ (y axis) and time ( $$x$$ axis) for first order reaction is equal to:

What is half life time of a first order reaction if initial conc. of reactant is $$0.01 \mathrm{~mol} \mathrm{~L}^{-1}$$ and rate of reaction is $$0.00352 \mathrm{~mol} \mathrm{~L}^{-1}$$ minute $$^{-1}$$ ?

Find the average rate of formation of $$\mathrm{NO}_{2(\mathrm{~g})}$$, in following reaction.

$$\begin{aligned} & 2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \\ & {\left[-\frac{\Delta\left[\mathrm{N}_2 \mathrm{O}_5\right]}{\Delta \mathrm{t}}\right]=x \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}} \end{aligned}$$

Calculate the rate constant for the first order reaction, $$\mathrm{A} \rightarrow \mathrm{B}$$ if the rate of reaction is $$5.4 \times 10^{-6} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$ and $$[\mathrm{A}]=0.3 \mathrm{M}$$.