Assignment: Rate Law and Order of Reaction - Chemical Kinetics - Class 12 NEET JEE A...

Ques 1. The decomposition of $\ce{N2O5}$, in carbon tetrachloride solution has been investigated.

        $\ce{N2O5 (solution) -> 2NO2 (solution) + 1/2 O2(g)}$

        The reaction has been found to be of first order in $\ce{N2O5}$ with a first order rate constant \(6.2 \times 10^{-4} sec^{-1} \). Calculate the rate of the reaction when

        (a) $\ce{ [N2O5] = 1.25 mol \quad L^{-1}}$

        (b) $\ce{ [N2O5] = 0.25 mol \quad L^{-1}}$

    What concentration of $\ce {N2O5 }$ would give a rate of \(2.4 \times 10^{-3} \quad mol L^{-1} sec^{-1} \) ?

... Answer (a) \(7.75 \times 10^{-4} mol L^{-1} sec^{-1} \), (b) \(3.8 mol L^{-1} \)
(a) Rate o reaction = $\ce{k[N2O5]}$ = \( 6.2 \times 10^{-4} sec^{-1} \times 1.25 mol L^{-1} \) = \(7.75 \times 10^{-4} mol L^{-1} sec^{-1} \)
(b) Rate o reaction = $\ce{k[N2O5]}$ = \( 6.2 \times 10^{-4} sec^{-1} \times 0.25 mol L^{-1} \) = \(1.55 \times 10^{-4} mol L^{-1} sec^{-1} \) Concentration of $\ce{N2O5}$ when the rate is \( 2.4 \times 10^{-3} mol L^{-1} sec^{-1} \)
$\ce{ [N2O5]= \frac{Rate \quad of \quad reaction}{k}}$
=\( {2.4 \times 10^{-3} mol L^{-1} sec^{-1}} \over {6.2 \times 10^{-4} sec^{-1}}\) \( = 3.8 mol L^{-1}\)

Ques 2. For the following reaction

        $\ce{ 2A + B + C -> A2B + C }$

        the rate law has been determined to be rate = \(k [A] [B]^2 \) with

        \( k= 2.0 \times 10^{-6} mol^{-2}L^2 sec^{-1} \)

        For this reaction (i) determine the initial rate of reaction with \([A] = 0.1 mol L^{-1} , [B] = 0.2 mol L^{-1} \) of A has reacted.

... Answer
(i) \( 8 \times 10^{-9} mol L^{-1}sec^{-1} \) (ii) \( 3.9 \times 10^{-9} mol^{-2} L^{-1} sec^{-1} \)

Ques 3. For a reaction $\ce{ A + B -> Product }$, the rate law is given by, \( r=k[A]^{1\over 2} [B]^2 \). What is the order of reaction?

... Answer
2.5

Ques 4. The conversion of molecules X to Y follows second order kinetics. If the concentration of X is increased three times, how will it affect the rate of formation of Y?

... Answer
(a) 2, (b) 1/2

Ques 5. Calculate the overall order of reaction which has the rate expression: 

        (a) \( Rate = k [A]^1/2 [B]^3/2 \)

        (b) \( Rate = k [A]^3/2 [B]^{-1} \)

... Answer
Rate of formation of Y increase 9 times.

Ques 6. Identify the reaction order from each of the following rate constants:

        (i) \( k= 2.3 \times 10^{-5} L mol^{-1} sec^{-1} \)

        (ii) \( k = 3 \times 10^{-4} sec^{-1} \)

... Answer
(i) second order, (ii) First order