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Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of \\( 3.33 \, \text{h} \\) at \\( 25^\circ \text{C} \\). After \\( 9 \, \text{h} \\), the fraction of sucrose remaining is \\( f \\). The value of \\( \log_{10}\!\left( \frac{1}{f} \right) \\) is _______ \\( \times 10^{-2} \\). (Rounded off to the nearest integer)
[Assume: \\( \ln 10 = 2.303 \\, \\ \ln 2 = 0.693 \\)]

For a reaction of order \( n \), the units of the rate constant is :

For the following graphs,

A reaction has a half life of \( 1 \) min. The time required for \( 99.9\% \) completion of the reaction is ___ min.
[Use : \( \ln 2 = 0.69 \); \( \ln 10 = 2.3 \)]

For a first order reaction, the ratio of the time for \( 75\% \) completion of a reaction to the time for \( 50\% \) completion is __________. (Integer answer)

For a certain first order reaction \( 32\% \) of the reactant is left after \( 570 \, \text{s} \). The rate constant of this reaction is _______ \( \times 10^{-3} \, \text{s}^{-1} \), (Round off to the Nearest Integer).
[Given : \( \log_{10} 2 = 0.301 \), \( \ln 10 = 2.303 \)]

\( \text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g) \)
In the above first order reaction the concentration of \( \text{PCl}_5 \) reduces from initial concentration \( 50 \, \text{mol L}^{-1} \) to \( 10 \, \text{mol L}^{-1} \) in \( 120 \) minutes at \( 300 \, \text{K} \). The rate constant for the reaction at \( 300 \, \text{K} \) is \( x \times 10^{-2} \, \text{min}^{-1} \). The value of \( x \) is __________ . [Given \( \log 5 = 0.6989 \) ]

The inactivation rate of viral preparation is proportional to the amount of virus. In the first minute after preparation, \( 10\% \) of the virus is inactivated. The rate constant for viral inactivation is ______ \( \times 10^{-3} \, \text{min}^{-1} \). (Nearest integer). [Use: \( \ln 10 = 2.303 \); \( \log_{10} 3 = 0.477 \); property of logarithm: \( \log x^{y} = y \log x \) ]

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is:
\( 2\mathrm{K_2Cr_2O_7} + 8\mathrm{H_2SO_4} + 3\mathrm{C_2H_6O} \rightarrow 2\mathrm{Cr_2(SO_4)_3} + 3\mathrm{C_2H_4O_2} + 2\mathrm{K_2SO_4} + 11\mathrm{H_2O} \)
If the rate of appearance of \( \mathrm{Cr_2(SO_4)_3} \) is \( 2.67 \, \text{mol} \, \text{min}^{-1} \) at a particular time, the rate of disappearance of \( \mathrm{C_2H_6O} \) at the same time is ____________ \( \text{mol} \, \text{min}^{-1} \). (Nearest integer)

$2\text{NO}\text{ (g)} + \text{Cl}_2\text{ (g)} \rightleftharpoons 2\text{NOCl}\text{(s)}$
This reaction was studied at \( -10^\circ \mathrm{C} \) and the following data was obtained.

\( [\mathrm{NO}]_0 \) and \( [\mathrm{Cl_2}]_0 \) are the initial concentrations and \( r_0 \) is the initial reaction rate.
The overall order of the reaction is ____________. (Round off to the Nearest Integer).

For a chemical reaction \( A \rightarrow B \), it was found that concentration of \( B \) is increased by \( 0.2 \, \mathrm{mol\,L^{-1}} \) in \( 30 \, \mathrm{min} \). The average rate of the reaction is _______ \( \times 10^{-1} \, \mathrm{mol\,L^{-1}\,h^{-1}} \). (in nearest integer)

The reaction \( 2A + B_2 \rightarrow 2AB \) is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of \( 3 \), the rate of the reaction increases by a factor of ________. (Round off to the Nearest Integer)

For the first order reaction \( \mathrm{A \rightarrow 2B} \), \( 1 \) mole of reactant \( \mathrm{A} \) gives \( 0.2 \) moles of \( \mathrm{B} \) after \( 100 \) minutes. The half life of the reaction is _______ min. (Round off to the Nearest Integer)
[Use: \( \ln 2 = 0.69 \), \( \ln 10 = 2.3 \) Properties of logarithms: \( \ln x^{y} = y \ln x \); \( \ln \left(\dfrac{x}{y}\right) = \ln x - \ln y] \)

\( \mathrm{N_2O_{5(g)}} \rightarrow 2\,\mathrm{NO_{2(g)}} + \dfrac{1}{2}\,\mathrm{O_{2(g)}} \)
In the above first order reaction the initial concentration of \( \mathrm{N_2O_5} \) is \( 2.40 \times 10^{-2} \,\mathrm{mol\,L^{-1}} \) at \( 318 \,\text{K} \). The concentration of \( \mathrm{N_2O_5} \) after \( 1 \) hour was \( 1.60 \times 10^{-2} \,\mathrm{mol\,L^{-1}} \). The rate constant of the reaction at \( 318 \,\text{K} \) is _______ \( \times 10^{-3} \,\mathrm{min^{-1}} \). (Nearest integer)
[Given: \( \log 3 = 0.477, \\ \log 5 = 0.699 \)]

The number of neutrons and electrons, respectively, present in the radioactive isotope of hydrogen is:

The first order rate constant for the decomposition of \( \mathrm{CaCO_3} \) at \( 700 \,\mathrm{K} \) is \( 6.36 \times 10^{-3} \,\mathrm{s^{-1}} \) and activation energy is \( 209 \,\mathrm{kJ\, mol^{-1}} \). Its rate constant (in \( \mathrm{s^{-1}} \)) at \( 600 \,\mathrm{K} \) is \( x \times 10^{-6} \). The value of \( x \) is _______. (Nearest integer)
[Given : \( R = 8.31 \,\mathrm{J\, K^{-1}\, mol^{-1}} \); \( \log 6.36 \times 10^{-3} = -2.19 \), \( 10^{-4.79} = 1.62 \times 10^{-5} \) ]

The following data was obtained for chemical reaction given below at 975 K.

The order of the reaction with respect to \( \mathrm{NO} \) is __________. [Integer answer]

For the reaction \( \mathrm{A} \to \mathrm{B} \), the rate constant \( k \) (in \( \text{s}^{-1} \)) is given by \( \log_{10} k = 20.35 - \frac{(2.47 \times 10^{3})}{T} \).
The energy of activation in \( \text{kJ mol}^{-1} \) is ________. (Nearest integer) [Given: \( R = 8.314 \, \text{J K}^{-1}\text{ mol}^{-1} \)]

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JEE Main 2021 18th March Evening Shift

A reaction has a half life of \( 1 \) min. The time required for \( 99.9\% \) completion of the reaction is ___ min.
[Use : \( \ln 2 = 0.69 \); \( \ln 10 = 2.3 \)]