Question

For the non-stoichiometric reaction, \[\ce{2A + B -> C + D}\], the following kinetic data were obtained in three separate experiments, all at 298 K.

Initial concentration (A)	Initial concentration (B)	Initial rate of formation of C (mol L−1 s−1)
0.1 M	0.1 M	1.2 × 10−3
0.1 M	0.2 M	1.2 × 10−3
0.2 M	0.1 M	2.4 × 10−3

The rate law for the formation of C is:

Options

• `(dc)/(dt) = k[A][B]`

• `(dc)/(dt) = k[A]^2[B]`

• `(dc)/(dt) = k[A][B]^2`

• `(dc)/(dt) = k[A]`

Answer 1

`bb((dc)/(dt) = k[A])`

Explanation:

The rate law expression is k[A]^x[B]^y

∴ `("d"["C"])/"dt"` = k[A]^x[B]^y

Substituting the given values in above equation for three separate experiments we get,

1.2 × 10⁻³ = k[0.1]^x[0.1]^y    ...(i)

1.2 × 10⁻³ = k[0.1]^x[0.2]^y    ...(ii)

2.4 × 10⁻³ = k[0.2]^x[0.1]^y    ...(iii)

Dividing equation (i) by (ii)

`(1.2 xx 10^-3)/(1.2 xx 10^-3) = (k[0.1]^x [0.1]y)/(k[0.1]^x [0.2]^y)`

1 = `[1/2]^y`    ...(∴ y = 0)

Now Dividing equation (i) by (iii)

`(1.2 xx 20^-3)/(2.4 xx 10^-3) = (k[0.1]^x [0.1]^y)/(k[0.2]^x [0.1]^y)`

`[1/2]^1 = [1/2]^x`

x = 1