For A + B -> P the initial rates at fixed temperature are: [A] = 0.10, [B] = 0.20 M, rate =1.0x10^-3; [A] = 0.30, [B] = 0.20 M, rate =3.0x10^-3; [A] = 0.10, [B] = 0.40 M, rate =4.0x10^-3 M s^-1. Choose the correct statements.

The reaction is first order in A.

Doubling both concentrations raises the rate eight-fold.

The reaction is first order in A.

Doubling both concentrations raises the rate eight-fold.

JEE Main levelOne or more correct optionsDifficulty 2 of 3ck022

For $A + B P$ the initial rates at fixed temperature are: $[A] = 0.10$ , $[B] = 0.20 M$ , rate $= 1.0 \times 1 0^{- 3}$ ; $[A] = 0.30$ , $[B] = 0.20 M$ , rate $= 3.0 \times 1 0^{- 3}$ ; $[A] = 0.10$ , $[B] = 0.40 M$ , rate $= 4.0 \times 1 0^{- 3} M s^{- 1}$ . Choose the correct statements.

Tripling [A] triples the rate (3x), so A is first order; doubling [B] gives 4x, so B is second order and the overall order is 3. Then

k = 1.0 \times 1 0^{- 3} / (0.10 \times 0.2 0^{2}) = 0.25

, not 2.5. Doubling both concentrations multiplies the rate by

2^{3} = 8