Initial rates for A + B -> products (concentrations in mol L^-1, rates in mol L^-1 s^-1): (i) [A]=0.10, [B]=0.10, rate =2.50x10^-4; (ii) [A]=0.20, [B]=0.10, rate =1.00x10^-3; (iii) [A]=0.20, [B]=0.30, rate =3.00x10^-3. The initial rate for [A]=0.30 and [B]=0.40 is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ck100

Initial rates for $A + B products$ (concentrations in $mol L^{- 1}$ , rates in $mol L^{- 1} s^{- 1}$ ): (i) $[A] = 0.10$ , $[B] = 0.10$ , rate $= 2.50 \times 1 0^{- 4}$ ; (ii) $[A] = 0.20$ , $[B] = 0.10$ , rate $= 1.00 \times 1 0^{- 3}$ ; (iii) $[A] = 0.20$ , $[B] = 0.30$ , rate $= 3.00 \times 1 0^{- 3}$ . The initial rate for $[A] = 0.30$ and $[B] = 0.40$ is

(i) to (ii):

[A]

doubles and the rate rises 4-fold, so order 2 in

A

. (ii) to (iii):

[B]

triples and the rate triples, so order 1 in

B

. Thus rate

= k [A]^{2} [B]

and

k = 2.50 \times 1 0^{- 4} / (0.1 0^{2} \times 0.10) = 0.25 L^{2} mo l^{- 2} s^{- 1}

. The new rate is

0.25 \times 0.3 0^{2} \times 0.40 = 9.00 \times 1 0^{- 3} mol L^{- 1} s^{- 1}