Calculate the rate constant of first order reaction if the concentration of the reactant decreases by $$90 \%$$ in 30 minutes.

The rate law for the reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ product is given by rate $$=k[A][B]$$ Calculate $$[A]$$ if rate of reaction and rate constant are $$0.25 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$$ and $$6.25 \mathrm{~mol}^{-1} \mathrm{dm}^3 \mathrm{~s}^{-1}$$ respectively $$\left[[\mathrm{B}]=0.25 \mathrm{~mol} \mathrm{dm}^{-3}\right]$$

Find the average rate of formation $$\mathrm{O}_{2(\mathrm{~g})}$$ in the following reaction.

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

Which from following is the slope of the graph of rate versus concentration of the reactant for first order reaction?