The rate equation for the reaction \(2 A+B \longrightarrow\) products is rate \(=k[A][B]^2\). If \(k\) at…

The rate equation for the reaction \(2 A+B \longrightarrow\) products is rate \(=k[A][B]^2\). If \(k\) at \(T(\mathrm{~K})\) is \(5.0 \times 10^{-6} \mathrm{~mol}^{-2} \mathrm{~L}^2 \mathrm{~s}^{-1}\), the initial rate of the reaction, when \([A]=0.05 \mathrm{~mol} \mathrm{~L}^{-1}\) and \([B]=0.1 \mathrm{~mol} \mathrm{~L}^{-1}\) is
  1. \(1.25 \times 10^{-9} \mathrm{~L} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
  2. \(1.25 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
  3. \(2.50 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
  4. \(2.50 \times 10^{-9} \mathrm{~L} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)

Solution

For the reaction, \(2 A+B \longrightarrow\) Products \(\text {Rate }=k[A][B]^2\) Given, Rate constant, \(k\) of reaction \(=5.0 \times 10^{-6} \mathrm{~mol}^{-2} \mathrm{~L}^2 \mathrm{~s}^{-1}\) \(\begin{aligned} {[A]=0.05 \mathrm{~mol} \mathrm{~L}^{-1} } \\ {[B]=0.1 \mathrm{~mol} \mathrm{~L}^{-1} } \end{aligned}\) \(\begin{aligned} \therefore \text { Rate of reaction } & =5.0 \times 10^{-6}[0.05][0.1]^2 \\ & =5 \times 10^{-6} \times 5 \times 10^{-4} \\ & =2.5 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \end{aligned}\)

Asked in: AP EAMCET 2019 (23 Apr Shift 1)

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