Half-life

$t_{100\%}$ is the time required for the 100% completion of the reaction while $t_{1/2}$ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first order reactions respectively ?

Consider the reaction $\ce{aX -> bY}$, for which the rate constant at 30 °C is $1\times10^{-3}$ mol$^{-1}$ L s$^{-1}$. Which of the following statements are true ?

A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times.

B. The reaction is a second order reaction.

C. The half-life period is independent of the concentration of X.

D. Decomposition of $\ce{N2O5}$ is an example of the above reaction.

E. The graph of $\ln\dfrac{[R_0]}{[R]}$ against time shown is valid for the above reaction.

Choose the correct answer from the options given below :

If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be ________ minutes .

(Given : $\log 2 = 0.3010$)

For a reaction $\ce{A -> P}$ at T K, the half life ($t_{1/2}$) is plotted as a function of initial concentration $[\mathrm A]_o$ of A as given below.

The value of $x$ in the given figure is ________ s (Nearest integer)

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2}=3$ hour. The percentage of sucrose remaining after 6 hours is ________. (Nearest integer)

(Given : log 2 = 0.3010 and log 3 = 0.4771)

Given below are two statements :

R = 8.314 J K$^{-1}$ mol$^{-1}$ and 1 cal = 4.2 J

Statement I : When Ea = 12.6 kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K)

Statement II : For a first order reactions A → B, the plot of $t_{1/2}$ against $[\mathrm A]_o$ is as shown. Here $[\mathrm A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction.

In the light of the above statements, choose the correct answer from the options given below :

Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $\mathrm X_s$ and k are constants having appropriate units.

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is

(Given: $\ln10=2.303$ and $\log2=0.3010$)

At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ______. [integer answer]

A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ______ s.

(Given : $\ln2=0.693$)

For a first order reaction A $\rightarrow$ B, the rate constant, k = $5.5\times10^{-14}$ s$^{-1}$. The time required for 67% completion of reaction is $x\times10^{-1}$ times the half life of reaction. The value of $x$ is ______ (Nearest integer)

(Given : log 3 = 0.4771)

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ______. (Nearest integer)

(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

The half life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 Torr initially. When the pressure was 250 Torr, the half life was found to be 4.0 min. The order of the reaction is ______. (Nearest integer)

For the decomposition of azomethane, $\mathrm{CH_3N_2CH_3(g)\rightarrow CH_3CH_3(g)+N_2(g)}$, a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is ______ $\times10^{-5}$ s. [Nearest integer]

For a reaction A → 2B + C the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L$^{-1}$ respectively. The order of the reaction is ______. (Nearest Integer)

At 30°C, the half life for the decomposition of $\mathrm{AB_2}$ is 200 s and is independent of the initial concentration of $\mathrm{AB_2}$. The time required for 80% of the $\mathrm{AB_2}$ to decompose is

Given: log 2 = 0.30, log 3 = 0.48

$$\underset{\text{Reactant}}{[A]}\rightarrow\underset{\text{Product}}{[B]}$$

If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half of its initial concentration. Then the rate constant of the reaction is $x\times10^{-6}$ s$^{-1}$. The value of $x$ is ______. (Nearest Integer)

For the given first order reaction

A → B

the half life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ______. (Nearest integer)

Assuming 1 μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is _______ $\times10^{-1}$ μg.

[Given: ln 10 = 2.303; log 2 = 0.30]

X → Y + Z

X decomposes at 700 K to give Y and Z. The results of two measurements are :

Initial concentration of X / (mol/L)	6.0	12.0
Half life / s	1.0	2.0

The rate constant for the reaction is _______ (in appropriate unit)