Integrated rate equations

For a reversible reaction $\mathbf R\rightleftharpoons\mathbf P$, at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants $k_f$ and $k_b$, respectively. At time zero, the concentration of $\mathbf R$ is $[\mathbf R]_0$ and the concentration of $\mathbf P$ is zero. At any given time, $[\mathbf R]$ and $[\mathbf P]$ are the concentrations of $\mathbf R$ and $\mathbf P$, respectively. If $k_b=4k_f$, the correct graphical representation of the reaction is

For a first-order reaction $\mathbf R\longrightarrow\mathbf P$ at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of $\mathbf R$ and $\mathbf P$ at a time $t$ are $[\mathbf R]$ and $[\mathbf P]$, respectively. The correct graphical representation(s) for this reaction is(are)

$t_{100\%}$ 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 first order reaction $\ce{R -> P}$.
The fraction of molecules decomposed in the given first order reaction can be expressed as

Consider the given graph showing variation of reactant concentration with time.

Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

For a first order reaction $\ce{A -> B}$

t/min	[A]/M
0	0.6500
$x$	0.0650
20	0.00065

$x$ = ________ min. (Nearest integer)

First order gas phase reaction
$$\ce{A -> B + C}$$
$p_i$ = initial pressure of gas A, $p_t$ = total pressure of the reaction mixture at time $t$

Expression of rate constant ($k$) is

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 : $\log 2 = 0.3010$)

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 $\log2=0.3010$)

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)

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]

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)

For the following reaction
$$2\mathbf X + \mathbf Y \xrightarrow{k} \mathbf P$$
the rate of reaction is $\dfrac{d[\mathbf P]}{dt} = k[\mathbf X]$. Two moles of $\mathbf X$ are mixed with one mole of $\mathbf Y$ to make 1.0 L of solution. At 50 s, 0.5 mole of $\mathbf Y$ is left in the reaction mixture. The correct statement(s) about the reaction is(are)

(Use: $\ln 2 = 0.693$)

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of $3.3\times10^{-4}$ s$^{-1}$ at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is _______. (Rounded off to the nearest integer)

Which of the following plots is(are) correct for the given reaction?

($[\mathbf P]_0$ is the initial concentration of P)

The decomposition reaction $\ce{2N2O5(g) ->[\Delta] 2N2O4(g) + O2(g)}$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After $Y\times10^3$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is $5\times10^{-4}\ \mathrm{s^{-1}}$, assuming ideal gas behavior, the value of $Y$ is ______