Chapter 18

The reaction, \(\boldsymbol{A} \rightarrow\) Product, follows first order kinetics. In 40 minutes the concentration of \(\boldsymbol{A}\) changes from \(0.1\) to \(0.025 \mathrm{M}\). The rate of reaction, when concentration of \(\boldsymbol{A}\) is \(0.01 \mathrm{M}\) is [2004S] (a) \(1.73 \times 10^{-4} \mathrm{M} \min ^{-1}\) (b) \(3.47 \times 10^{-5} \mathrm{M} \mathrm{min}^{-1}\) (c) \(3.47 \times 10^{-4} \mathrm{M} \min ^{-1}\) (d) \(1.73 \times 10^{-5} \mathrm{M} \mathrm{min}^{-1}\)

Assertion : Nuclide \(\frac{30}{13} \mathrm{Al}\) is less stable than \({ }_{20}^{40} \mathrm{Ca}\) Reason : Nuclides having odd number of protons and neutrons are generally unstable. (a) If both assertion and reason are correct, and reason is the correct explanation of the assertion. (b) If both assertion and reason are correct, but reason is not the correct explanation of the assertion. (c) If assertion is correct but reason is incorrect. (d) If assertion is incorrect but reason is correct.

In a first order reaction the concentration of reactant decreases from \(800 \mathrm{~mol} / \mathrm{dm}^{3}\) to \(50 \mathrm{~mol} / \mathrm{dm}^{3}\) in \(2 \times 10^{4} \mathrm{sec}\). The rate constant of reaction in \(\mathrm{sec}^{-1}\) is: [2003S](a) \(2 \times 10^{4}\) (b) \(3.45 \times 10^{-5}\) (c) \(1.386 \times 10^{-4}\) (d) \(2 \times 10^{-4}\)

In a bimolecular reaction, the steric factor \(P\) was experimentally determined to be 4.5. The correct option(s) among the following is(are) (a) The activation energy of the reaction is unaffected by the value of the steric factor (b) Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation (c) Since \(P=4.5\), the reaction will not proceed unless an effective catalyst is used (d) The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally

Complete and balance the following reactions. \({ }_{92} \mathrm{Th}^{234} \longrightarrow \ldots \ldots \ldots . .+7{ }_{2} \mathrm{He}^{4}+6_{-1}^{(i)} \beta^{0}\) (ii) \({ }_{92} \mathrm{U}^{235}+{ }_{0} \mathrm{n}^{1} \longrightarrow \ldots \ldots \ldots .+{ }_{52} \mathrm{Te}^{137}+{ }_{40} \mathrm{Zr}^{92}\) (iii) \({ }_{34} \mathrm{Se}^{86} \longrightarrow 2_{-1} \mathrm{e}^{0}+\ldots \ldots \ldots \ldots .\)

Consider the chemical reaction, \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) .\) The rate of this reaction can be expressed in terms of time derivative of concentration of \(\mathrm{N}_{2}(\mathrm{~g}), \mathrm{H}_{2}(\mathrm{~g})\) or \(\mathrm{NH}_{3}(\mathrm{~g})\). Identify the correct relationship amongst the rate expressions. [2002S](a) Rate \(=-\mathrm{d}\left[\mathrm{N}_{2}\right] / \mathrm{d} t=-1 / 3 \mathrm{~d}\left[\mathrm{H}_{2}\right] / \mathrm{d} t=1 / 2 \mathrm{~d}\left[\mathrm{NH}_{3}\right] / \mathrm{d} t\) (b) Rate \(=-\mathrm{d}\left[\mathrm{N}_{2}\right] / \mathrm{d} t=-3 \mathrm{~d}\left[\mathrm{H}_{2}\right] / \mathrm{d} t=2 \mathrm{~d}\left[\mathrm{NH}_{3}\right] / \mathrm{d} t\) (c) Rate \(=\mathrm{d}\left[\mathrm{N}_{2}\right] / \mathrm{d} t=1 / 3 \mathrm{~d}\left[\mathrm{H}_{2}\right] / \mathrm{d} t=1 / 2 \mathrm{~d}\left[\mathrm{NH}_{3}\right] / \mathrm{d} t\) (d) Rate \(=-\mathrm{d}\left[\mathrm{N}_{2}\right] / \mathrm{d} t=-\mathrm{d}\left[\mathrm{H}_{2}\right] / \mathrm{d} t=\mathrm{d}\left[\mathrm{NH}_{3}\right] / \mathrm{d} t\)

According to the Arrhenius equation, (a) a high activation energy usually implies a fast reaction. (b) rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy. (c) higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant. (d) the pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.

\({ }^{64} \mathrm{Cu}\) (half-life \(=12.8 \mathrm{~h}\) ) decays by \(\beta\) - emission \((38 \%), \beta^{+}\)emission \((19 \%)\) and electron capture (43\%). Write the decay products and calculate partial half-lives for each of the decay processes.

If ' \(I\) ' is the intensity of absorbed light and ' \(C\) is the concentration of \(A B\) for the photochemical process, \(A B+h v \longrightarrow A B^{*}\), the rate of formation of \(A B^{*}\) is directly proportional to [2001S] (a) \(\mathrm{C}\)(b) I (c) \(\mathrm{I}^{2}\) (d) C.I

A catalyst: (a) increases the average kinetic energy of reacting molecules (b) decreases the activation energy (c) alters the reaction mechanism (d) increases the frequency of collisions of reacting species

\({ }_{92}^{238} \mathrm{U}\) is radioactive and it emits \(\alpha\) and \(\beta\) particles to form \({ }_{82}^{206} \mathrm{~Pb}\). Calculate the number of \(\alpha\) and \(\beta\) particles emitted in this conversion. An ore of \({ }_{92}^{238} \mathrm{U}\) is found to contain \({ }_{92}^{238} \mathrm{U}\) and \({ }_{82}^{206} \mathrm{~Pb}\) in the weight ratio of \(1: 0.1\). The half-life period of \({ }_{92}^{238} \mathrm{U}\) is \(4.5 \times 10^{9}\) years. Calculate the age of the ore.

The rate constant for the reaction, \(2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\), is \(3.0 \times 10^{-5}\) \(\mathrm{sec}^{-1}\). If the rate is \(2.40 \times 10^{-5}\) mol litre \(^{-1} \mathrm{sec}^{-1}\), then the concentration of \(\mathrm{N}_{2} \mathrm{O}_{5}\) (in mol litre \(^{-1}\) ) is [2000S] (a) \(1.4\) (b) \(1.2\) (c) \(0.04\) (d) \(0.8\)

Read the following assertion and statement and answer as per the options given below: Assertion : For each ten degree rise of temperature the specific rate constant is nearly doubled. Statement : Energy-wise distribution of molecules in a gas is an experimental function of temperature. (a) If both assertion and statement are correct and statement is an explanation of assertion. (b) If assertion is correct and statement is wrong, statement is not an explanation of assertion. (c) If assertion is wrong and statement is correct, statement is not an explanation of assertion. (d) If both assertion and statement are wrong and statement is not explanation of assertion.

Write a balanced equation for the reaction of \({ }^{14} \mathrm{~N}\) with \(\alpha\)-particle.

The specific rate constant of a first order reaction depends on the [1983-1 Mark](a) concentration of the reactant (b) concentration of the product (c) time (d) temperature

The rate constant of a reaction is \(1.5 \times 10^{7} \mathrm{~s}^{-1}\) at \(50^{\circ} \mathrm{C}\) and \(4.5 \times 10^{7} \mathrm{~s}^{-1}\) at \(100^{\circ} \mathrm{C}\). Evaluate the Arrhenius parameters \(A\) and \(E_{a}\).

\({ }^{227}\) Ac has a half-life of \(21.8\) years with respect to radioactive decay. The decay follows two parallel paths, one leading to \({ }^{27} \mathrm{Th}\) and the other to \({ }^{223} \mathrm{Fr}\). The percentage yields of these two daughter nuclides are \(1.2\) and \(98.8\) respectively. What are the decay constants \((\lambda)\) for each of the separate paths?

The rate constant of a reaction depends on (a) temperature [1981-1 Mark] (b) initial concentration of the reactants (c) time of reaction (d) extent of reaction

An experiment requires minimum beta activity product at the rate of 346 beta particles per minute. The half life period of \({ }_{42}^{99} \mathrm{Mo}\), which is a beta emitter is \(66.6\) hours. Find the minimum amount of \({ }_{42}^{99}\) Mo required to carry out the experiment in \(6.909\) hours.

An experiment requires minimum beta activity product at the rate of 346 beta particles per minute. The half life period of \({ }_{42}^{99} \mathrm{Mo}\), which is a beta emitter is \(66.6\) hours. Find the minimum amount of \({ }_{42}^{99} \mathrm{Mo}\) required to carry out the experiment in \(6.909\) hours.

An organic compound undergoes first-order decomposition. The time taken for its decomposition to \(1 / 8\) and \(1 / 10\) of its initial concentration are \(t_{1 / 8}\) and \(t_{1 / 10}\) respectively. What is the value of \(\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right] \times 10\) ? \(\left(\log _{10} 2=0.3\right)\)

\({ }_{90}^{234}\) Th disintegrates to give \({ }_{82}^{206} \mathrm{~Pb}\) as the final product. How many alpha and beta particles are emitted during this process?

Two reactions (i) \(A \rightarrow\) products, (ii) \(B \rightarrow\) products, follows first order kinetics. The rate of the reaction: \((i)\) is doubled when the temperature is raised from \(300 \mathrm{~K}\) to \(310 \mathrm{~K}\). The half life for this reaction at \(310 \mathrm{~K}\) is 30 minutes. At the same temperature \(B\) decomposes twice as fast as \(A\). If the energy of activation for the reaction, (ii) is half that of reaction (i), calculate the rate constant of the reaction (ii) at \(300 \mathrm{~K}\).

Radioactive decay is a first order process. Radioactive carbon in wood sample decays with a half life of 5770 years. What is the rate constant (in years \(^{-1}\) ) for the decay? What fraction would remain after 11540 years?

If \(75 \%\) of a first order reaction was completed in 90 minutes, \(60 \%\) of the same reaction would be completed in approximately (in minutes) (Take : \(\log 2=0.30 ; \log 2.5=0.40\) )

A first order reaction is \(50 \%\) complete in 30 minutes at \(27^{\circ} \mathrm{C}\) and in 10 minutes at \(47^{\circ} \mathrm{C}\). Calculate the reaction rate constant at \(27^{\circ} \mathrm{C}\) and the energy of activation of the reaction in \(\mathrm{kJ} / \mathrm{mole}\).

During the nuclear explosion, one of the products is \({ }^{90} \mathrm{Sr}\) with half life of \(6.93\) years. If \(1 \square \mathrm{g}\) of \({ }^{90} \mathrm{Sr}\) was absorbed in the bones of a newly born baby in place of \(\mathrm{Ca}\), how much time, in years, is required to reduce it by \(90 \%\) if it is not lost metabolically. [Main Jan. 07, 2020 (I)]

The decomposition reaction\(2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \stackrel{\Delta}{\longrightarrow} 2 \mathrm{~N}_{2} \mathrm{O}_{4}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After \(Y \times 10^{3} \mathrm{~s}\), the pressure inside the cylinder is found to be \(1.45 \mathrm{~atm}\). If the rate constant of the reaction is \(5 \times 10^{-4} \mathrm{~s}^{-1}\), assuming ideal gas behaviour, the value of \(Y\) is [Adv. 2019]

The rate of a first-order reaction is \(0.04\) mol litre \(^{-1} \mathrm{~s}^{-1}\) at 10 minutes and \(0.03\) mol litre \(^{-1} \mathrm{~s}^{-1}\) at 20 minutes after initiation. Find the half-life of the reaction. [2001 - 5 Marks]

The gas phase decomposition of dimethyl ether follows first order kinetics. $$ \mathrm{CH}_{3}-\mathrm{O}-\mathrm{CH}_{3}(\mathrm{~g}) \rightarrow \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}(\mathrm{g}) $$ The reaction is carried out in a constant volume container at \(500^{\circ} \mathrm{C}\) and has a half life of \(14.5\) minutes. Initially, only dimethyl ether is present at a pressure of \(0.40\) atmosphere. What is the total pressure of the system after 12 minutes? Assume ideal gas behaviour. [1993 - 4 Marks]

For a first order reaction \(A(\mathrm{~g}) \rightarrow 2 B(\mathrm{~g})+C(\mathrm{~g})\) at constant volume and \(300 \mathrm{~K}\), the total pressure at the beginning \((t=0)\) and at time \(t\) are \(P_{0}\)and \(P_{p}\) respectively. Initially, only \(A\) is present with concentration \([A]_{0}\), and \(t_{1 / 3}\) is the time required for the partial pressure of \(A\) to reach \(1 / 3^{\text {rd }}\) of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases) [Adv. 2018]

For the first order reaction $$ 2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ (a) the concentration of the reactant decreases exponentially with time (b) the half-life of the reaction decreases with increasing temperature (c) the half-life of the reaction depends on the initial concentration of the reactant (d) the reaction proceeds to \(99.6 \%\) completion in eight half-life duration

The following statement(s) is (are) correct : [1999 - 3 Marks] (a) A plot of \(\log K_{p}\) versus \(1 / T\) is linear (b) A plot of \(\log [X]\) versus time is linear for a first order reaction, \(X \rightarrow P\) (c) A plot of \(P\) versus \(1 / T\) is linear at constant volume (d) A plot of \(P\) versus \(1 / V\) is linear at constant temperature

At constant temperature and volume, \(X\) decomposes as [2005 - 4 Marks] \(2 \mathrm{X}(\mathrm{g}) \rightarrow 3 \mathrm{Y}(\mathrm{g})+2 \mathrm{Z}(\mathrm{g}) ; P_{X}\) is the partial pressure of \(X\) \begin{tabular}{|c|c|c|} \hline Observation No. & Time (in minute) & \(P_{X}\) (in mm of \(\mathrm{Hg}\) ) \\\ \hline 1 & 0 & 800 \\ \hline 2 & 100 & 400 \\ \hline 3 & 200 & 200 \\ \hline \end{tabular} (i) What is the order of reaction with respect to \(X ?\) (ii) Find the rate constant. (iii) Find the time for \(75 \%\) completion of the reaction. (iv) Find the total pressure when pressure of \(X\) is \(700 \mathrm{~mm}\) of \(\mathrm{Hg}\).

The rate constant for an isomerisation reaction, \(A \rightarrow B\) is \(4.5 \times 10^{3}\) \(\min ^{1}\). If the initial concentration of \(A\) is \(1 \mathrm{M}\), calculate the rate of the reaction after \(1 \mathrm{~h}\). [1999-4 Marks]

The decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) according to the equation : \(2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) [1991 - 6 Marks] is a first order reaction. After \(30 \mathrm{~min}\). from the start of the decomposition in a closed vessel, the total pressure developed is found to be \(284.5\) \(\mathrm{mm}\) of \(\mathrm{Hg}\) and on complete decomposition, the total pressure is \(584.5\) \(\mathrm{mm}\) of \(\mathrm{Hg}\). Calculate the rate constant of the reaction.

A first order reaction has \(k=1.5 \times 10^{-6}\) per second at \(200^{\circ} \mathrm{C}\). If the reaction is allowed to run for 10 hours, what percentage of the initial concentration would have changed in the product? What is the half life of this reaction? [1987 - 5 Marks]

While studying the decomposition of gaseous \(\mathrm{N}_{2} \mathrm{O}_{5}\), it is observed that a plot of logarithm of its partial pressure versus time is linear. What kinetic parameters can be obtained from this observation? [1985-2 Marks|

Rate of a reaction \(A+B \rightarrow\) products, is given below as a function of different initial concentrations of \(A\) and \(B\) : [1982-4 Marks] 119 \(\begin{array}{lll}{[A](\operatorname{mol} / l)} & {[B](\mathrm{mol} / l)} & \text { Initial rate }(\mathrm{mol} / l / \mathrm{min}) \\ 0.01 & 0.01 & 0.005 \\ 0.02 & 0.01 & 0.010 \\ 0.01 & 0.02 & 0.005\end{array}\) 1