Question

For the decomposition of ${\text{HI}}$ at ${\text{1000K}}$, ${\text{2HI}} \to {{\text{H}}_{\text{2}}}{\text{ + }}{{\text{I}}_{\text{2}}}$ the following data were obtained

HI(M)	Rate of decomposition of ${\text{HI(mol}}\,{{\text{l}}^{{\text{ - 1}}}}{\text{se}}{{\text{c}}^{{\text{ - 1}}}})$
0.1	${\text{2.75}}{{ \times 1}}{{\text{0}}^{{\text{ - 8}}}}$
0.2	${\text{11}}\times {{\text{10}}^{{\text{ - 8}}}}$
0.3	${\text{24}}{\text{.75}}\times {{\text{10}}^{{\text{ - 8}}}}$

The order of reaction is
A) 1
B) 2
C) 0
D) 1.5

Answer 1

Hint:The rate of reaction is the rate of change of concentration of reactants with time.
OR
The rate of reaction is the rate of formation of products with time.
Order of reaction: Order of reaction is the sum of powers of concentration terms of reactants in the rate equation. It can be determined experimentally and it does not depend on the stoichiometry of the reaction or it does not depend on the stoichiometric coefficients of the reactants in the equation representing the reaction

Complete step by step answer:
Rate = $k{[HI]^n}$
$\Rightarrow {\text{11}}\times {{\text{10}}^{{\text{ - 8}}}}{\text{ = k[0}}{\text{.2}}{{\text{]}}^{\text{n}}}$ --(I)
$\Rightarrow {\text{2}}{\text{.75}}\times {{\text{10}}^{{\text{ - 8}}}}{\text{ = k[0}}{\text{.1}}{{\text{]}}^{\text{n}}}$ --(II)
Dividing equation (I) by equation (II)
$\Rightarrow {\text{4 = [2}}{{\text{]}}^{\text{n}}}$
$\Rightarrow {\text{n = 2}}$
Therefore, Order of the reaction is 2

Option “B” is correct

Note:
The reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution.
For a reaction of the type
${\text{aA + bB}} \to {\text{cC}}$
The reaction rate is often found to have the form
 ${\text{r = kT[A}}{{\text{]}}^{\text{m}}}{{\text{[B]}}^{\text{n}}}$
M and n are the partial orders of the reaction and are not dependent on the stoichiometric coefficients of the reactants (a and b) .they can be found experimentally and they depend on the reaction mechanism.