Question

For the decomposition of AB at 600 K, the following data were obtained:

$[AB]\text{mol d}{{\text{m}}^{3}}$	Initial rate of decomposition of AB in $\text{mol d}{{\text{m}}^{-3}}{{s}^{-1}}$
0.20	$2.75\times {{10}^{-8}}$
0.40	$11\times {{10}^{-8}}$
0.60	$24.75\times {{10}^{-8}}$

The order of the decomposition of AB is:
(A)- 0
(B)- 1
(C)- 2
(D)- 1.5

Answer 1

Hint: The order of reaction gives the relationship between the rate of reaction and the concentration of reactants or products. The order of a reaction is the power to which a concentration is raised in the rate law equation.

Complete Step by step solution:
-The speed at which the products are formed from the reactants in a chemical equation is known as the rate of the reaction.
-In other words, we can say that the rate of reaction is the speed at which a reaction takes place.
-The rate of reaction depends on numerous out of which order of the reaction is one of the factors. How the reactant pressure or concentration affects the rate of reaction is managed by the order of the reaction.
-Let us consider the rate equation for the reaction be r.
$\text{Rate of reaction(r) = }k{{[AB]}^{n}}$
-Now let us find the values of rate constant (k) for all the three values-
For case I: $2.75\times {{10}^{-8}}=k{{[0.20]}^{n}}...(1)$
For case II: $11\times {{10}^{-8}}=k{{[0.40]}^{n}}...(2)$
For case III: $24.75\times {{10}^{-8}}=k{{[0.60]}^{n}}.....(3)$
-Dividing the equation (1) by equation (2)-
\[\dfrac{2.75\times {{10}^{-8}}}{11\times {{10}^{-8}}}=\dfrac{{{[0.20]}^{n}}}{{{[0.40]}^{n}}}\]
$=\dfrac{1}{4}={{(\dfrac{1}{2})}^{n}}$
$\Rightarrow n=2$

So, the correct answer is option C.

Additional information:
-The rate of reaction depends on numerous factors other than the order of reaction such as the nature of the reaction, effect of concentration on reaction rate, pressure factor, temperature, type of solvent, presence of electromagnetic radiation, the intensity of light, presence of a catalyst, and the surface area of the reactants.

(i) Nature of the reaction- The rate of reaction depends on the physical state of reactants, number of reactants, complexity of reaction, and the size of the reactant. The rate of reaction is slower when the reactants are in the liquid phase as compared to gases and slower in solids as compared to liquids. The rate of reaction increases if the size of the reactant is smaller.

(ii) Effect of concentration on reaction rate- The rate of reaction increases with the increase in the concentration of the reactants.

(iii) Pressure factor- As the pressure for a reaction increases, the concentration of gases also increases
which in turn increases the rate of reaction.

(iv) Temperature- The increase in temperature generates more energy for the reaction because colliding particles require the activation energy at high temperature and therefore, more successful collisions will take place.

(v) Type of solvent- The properties of the solvent and the ionic strength greatly affects the reaction rate.

(vi) Electromagnetic radiation- The presence of electromagnetic radiation increases the rate of reaction as it gives the particles of reactants more energy.

(vii) Intensity of light- With the increase in the intensity of light, particles absorb more energy and thereby increase the rate of reaction.

(viii) Presence of catalyst- The presence of a catalyst in a reaction increases the speed of reaction in both forward and reverse direction by providing an alternate pathway of lower activation energy.

(ix) Surface area of the reactants- Smaller the size of the particle, the more is the surface area for the reaction to take place, hence the speed of heterogeneous chemical reactions increases.

Note: The alternate way of finding the order of the reaction is given below-
Concentration Rate
$\dfrac{0.4}{0.2}=2\text{ times}$ $\dfrac{11\times {{10}^{-8}}}{2.72\times {{10}^{-8}}}=4\text{ times}$
$\dfrac{0.6}{0.2}=3\text{ times}$ $\dfrac{24.75\times {{10}^{-8}}}{2.75\times {{10}^{-8}}}=9\text{ times}$
$\Rightarrow {{2}^{2}}=4$