In a reaction between $A$ and $B$ , the initial rate of reaction $(r_{0})$ was measured for different initial concentrations of $A$ and $B$ as given below:

$A / m o l L^{- 1}$ $0.20$ $0.20$ $0.40$
$B / m o l L^{- 1}$ $0.30$ $0.10$ $0.05$
$r_{0} / m o l L^{- 1} s^{- 1}$ $5.07 \times 10^{- 5}$ $5.07 \times 10^{- 5}$ $1.43 \times 10^{- 4}$

What is the order of the reaction with respect to $A$ and $B$ ?

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Solution

Rate $= k [A]^{p} [B]^{q}$

Rate $_{1} = (0.20)^{p} (0.30)^{q} = 5.07 \times 10^{- 5}$ ......(i)
Rate $_{2} = (0.20)^{p} (0.10)^{q} = 5.07 \times 10^{- 5}$ ......(ii)
Divide equation (i) by equation (ii)
$\frac{R a t e_{1}}{R a t e_{2}} = \frac{(0.30)^{q}}{(0.10)^{q}} = 1$

$3^{q} = 1$ or $q = 0$

Hence, the reaction is zero order in $B$ .

Rate $_{3} = (0.40)^{p} (0.05)^{q} = 1.43 \times 10^{- 4}$ ......(iii)

Divide equation (iii) by (ii)
$\frac{R a t e_{3}}{R a t e_{2}} = \frac{(0.40)^{p}}{(0.20)^{p}} = \frac{1.43 \times 10^{- 4}}{5.07 \times 10^{- 5}}$

$2^{p} = 2.8$

$p = 1.5$

The reaction order with respect to $A$ is $1.5$ .

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Similar questions

In a reaction between A and B, the initial rate of reaction (r₀) was measured for different initial concentrations of A and B as given below:

A/ mol L⁻¹	0.20	0.20	0.40
B/ mol L⁻¹	0.30	0.10	0.05
r₀/ mol L⁻¹ s⁻¹	5.07 × 10⁻⁵	5.07 × 10⁻⁵	1.43 × 10⁻⁴

What is the order of the reaction with respect to A and B?

In a reaction between A and B the initial rate of reaction $(r_{0})$ was measured for different initial concentrations of A and B as given below.
$\begin{matrix} A / m o l L^{- 1} & 0.20 & 0.20 & 0.40 B / m o l L^{- 1} & 0.30 & 0.10 & 0.05 x_{0} / m o l L^{- 1} s^{- 1} & 5.07 \times 10^{- 5} & 5.07 \times 10^{- 5} & 1.43 \times 10^{- 4} \end{matrix}$
What is the order to the reaction with respect to A and B?

Q. In a reaction between

A

and

B

, initial rate of reaction was measured for different initial concentration

A

and

B

given as:

$[A]$ in mol $L^{- 1}$	$[B]$ in mol $L^{- 1}$	Initial rate in mole $L^{- 1} s^{- 1}$
0.2	0.3	$5.07 \times 10^{- 5}$
0.2	0.1	$5.07 \times 10^{- 5}$
0.4	0.05	$1.47 \times 10^{- 4}$

Order of reaction with respect to

A

and

B

is:

Q. Rate For the reaction

A + B \to p r o d u c t s

, what will be the order of reaction with respect of

A

and

B

Exp.	$[A] (m o l L^{- 1})$	$[B] (m o l L^{- 1})$	Initial rate $(m o l L^{- 1} s^{- 1})$
$1.$	$2.5 \times 10^{- 4}$	$3 \times 10^{- 5}$	$5 \times 10^{- 4}$
$2.$	$5 \times 10^{- 4}$	$6 \times 10^{- 5}$	$4 \times 10^{- 3}$
$3.$	$1 \times 10^{- 3}$	$6 \times 10^{- 5}$	$1.6 \times 10^{- 2}$

Q. What is the rate law expression for the reaction,

A + B \to C

?
The following data were collected from the experiments:

Expt. No.	Initial $[A]$ $(m o l L^{- 1})$	Initial $[B]$ $(m o l L^{- 1})$	Rate of formation of $C$
$1.$	$0.10$	$0.10$	$4.0 \times 10^{- 4}$
$2.$	$0.20$	$0.20$	$3.2 \times 10^{- 3}$
$3.$	$0.10$	$0.20$	$1.6 \times 10^{- 3}$

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$A / m o l L^{- 1}$	$0.20$	$0.20$	$0.40$
$B / m o l L^{- 1}$	$0.30$	$0.10$	$0.05$
$r_{0} / m o l L^{- 1} s^{- 1}$	$5.07 \times 10^{- 5}$	$5.07 \times 10^{- 5}$	$1.43 \times 10^{- 4}$

In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below:A/molL−10.200.200.40B/molL−10.300.100.05r0/molL−1s−15.07×10−55.07×10−51.43×10−4What is the order of the reaction with respect to A and B?