Chemical Kinetics and Nuclear ChemistryHard

Question

The rate of a reaction A + 2B → P is 2 × 10−2 M/ min, when concentrations of each A and B are 1.0 M. If the rate of reaction r = K[A]2[B], the rate of reaction when half of the B has reacted should be

Options

A.5.625 × 10−3 M/min
B.3.75 × 10−3 M/min
C.9.375 M/min
D.2.5 × 10−3 M/min

Solution

A + 2B ? P

t1 1.0 M 1.0 M

t2 1.0 – 0.25 1.0 – 0.5

= 0.75 M = 0.5 M

Now, $\frac{r_{2}}{r_{1}} = \frac{K\left\lbrack A_{2} \right\rbrack^{2}\left\lbrack B_{2} \right\rbrack}{K\left\lbrack A_{1} \right\rbrack^{2}\left\lbrack B_{1} \right\rbrack} \Rightarrow \frac{r_{2}}{2 \times 10^{- 2}} = \frac{(0.75)^{2} \times 0.5}{(1.0)^{2} \times 1.0}$

$\therefore r_{2} = 5.625 \times 10^{- 3}\text{ M/min}$

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