Observe the following reactions at T ( K ). I. A → products. II. 5 Br^-( aq )+ BrO_3^-( aq )+6 H^+( aq ) → 3 Br_2( aq )+3 H_2 O ( l ) Both the…

Observe the following reactions at $\displaystyle \mathrm{T}(\mathrm{K})$. I. A → products. II. $\displaystyle 5 \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{BrO}_3{ }^{-}(\mathrm{aq})+6 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow 3 \mathrm{Br}_2(\mathrm{aq})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ Both the reactions are started at $\displaystyle 10.00$ am . The rates of these reactions at $\displaystyle 10.10$ am are same. The value of $\displaystyle -\frac{\Delta\left[\mathrm{Br}^{-}\right]}{\Delta \mathrm{t}}$ at $\displaystyle 10.10$ am is $\displaystyle 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}$. The concentration of A at $\displaystyle 10.10$ am is $\displaystyle 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$. What is the first order rate constant (in $\displaystyle \min ^{-1}$ ) of reaction I?