Question

The following experimental rate data were obtained for a reaction carried out at 25°C:

\[\ce{A_{(g)} + B_{(g)} -> C_{(g)} + A_{(g)}}\]

Initial [A(g)]/mol dm−3	Initial [B(g)]/mol dm−3	Initial rate/mol dm−3s−1
3.0 × 10−2	2.0 × 10−2	1.89 × 10−4
3.0 × 10−2	4.0 × 10−2	1.89 × 10−4
6.0 × 10−2	4.0 × 10−2	7.56 × 10−4

What are the orders with respect to A_(g) and B_(g)?

Options

• Order with respect to A(g)	Order with respect to B(g)
  Zero	Second

• Order with respect to A(g)	Order with respect to B(g)
  First	Zero

• Order with respect to A(g)	Order with respect to B(g)
  Second	Zero

• Order with respect to A(g)	Order with respect to B(g)
  Second	First

Answer 1

Order with respect to A(g)	Order with respect to B(g)
Second	Zero

Explanation:

Rate of reaction R = k[A]ⁿ [B]^m

where n and m are the order of reaction w.r.t

A and B from the given table change A_(g), keeping B_(g) constant,

R₁ = k[3 × 10⁻²]ⁿ [4 × 10⁻²]^m = 1.89 × 10⁻⁴

R₂ = k[6 × 10⁻²]ⁿ [4 × 10⁻²]^m = 7.56 × 10⁻⁴

`(1/2)^"n" = 1/4` ⇒ n  = 2

Change B_(g), keeping A_(g) constant,

R₁ = k[3 × 10⁻²]ⁿ [2 × 10⁻²]^m = 1.89 × 10⁻⁴

R₂ = k[3 × 10⁻²]ⁿ [4 × 10⁻²]^m = 1.89 × 10⁻⁴

`(1/2)^"m"` = 1 ⇒ m  = 0

Therefore the order of reaction with respect to A_(g) and B_(g) will be second order and zero order, respectively.