Question

For the irreversible process, $A + B \to$ products, the rate is first-order w.r.t. $A$ and second-order w.r.t. $B.$ If $1.0\, mol$ each of $A$ and $B$ introduced into a $1.0\, L$ vessel, and the initial rate was $1.0 \times 10^{-2} mol L^{-1} s^{-1}$ rate when half reactants have been turned into products is:

• A. $1.25 \times 10^{-3} mol L^{-1} s^{-}$
• B. $1.0 \times 10^{-3} mol L^{-1} s^{-}$
• C. $2.50 \times 10^{-3} mol L^{-1} s^{-}$
• D. $2.0 \times 10^{-3} mol L^{-1} s^{-}$

Answer 1

Answer: (A)

$A+B\to$ product
$r=K\left[A\right]^{1}\left[B\right]^{2}$
$r_{1}=K\left[1\right]^{1}\left[1\right]^{1}=1\times10^{-2} \left(K=1\times10^{-2}\right)$
$r_{1}=K\left[\frac{1}{2}\right]\left[\frac{1}{2}\right]^{2}=1\times10^{-2}\times\frac{1}{8}$
$=1.25\times10^{-3}mol L^{-1}S^{-1}$