Integrated Rate Equations of Chemical Reaction

The half life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be

In a first-order reaction, the concentration of reactant decreases from $\text{800}{\text{ mol/dm }}^3{\text{ to 50 mol/dm }}^3$ in$2 \times {10}^2 \mathrm{s}$. The rate constant of reaction in ${\mathrm{s}}^{-1}$ is

In a first order reaction the concentration of reactant decreases from $800 \mathrm{mol}/{\mathrm{dm}}^{\mathrm{3}}$ to  $50 \mathrm{mol}/{\mathrm{dm}}^{\mathrm{3}}$ in $200 \sec$. The rate constant of reaction in ${\mathrm{s}}^{-\mathrm{1}}$ is

The reaction $\mathrm{A}\to \mathrm{B}+\mathrm{C}$ is found to be zero order reaction. If it takes $3.3\times {10}^2$ seconds for an initial concentration of $\mathrm{A}$ to go from $0.50 \mathrm{M} \mathrm{to} 0.25\mathrm{M}$, what is the rate constant for the reaction.

The rate constant for a first order reaction is $2.54\times {10}^{-3} {\mathrm{s}}^{-1}$. Calculate its  $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\mathrm{th}$ life time.

For a parallel first order reaction ${\mathrm{E}}_{\mathrm{a}}\left(\mathrm{kJ}/\mathrm{mol}\right)$ is:

If reaction starts with pure $\mathrm{A}$, then at any stage of reaction, mole $\%$ of $\mathrm{B}$ in product is $40\%$. Then activation energy for overall reaction is:

If an optically active compound 'A' decompose through given parallel 1st order kinetics.

Initial mole of $\mathrm{A}$ is $2\left({\mathrm{k}}_1=0.0693{\sec }^{-1}, {\mathrm{k}}_2=0.1386{\sec }^{-1}\right)$. If only $\mathrm{A},\mathrm{B}$ & $\mathrm{D}$ are optically active compounds and their angle of rotation per mole are $60°,30°,-90°$ respectively, then which of the following is/are correct -

The kinetic data for the given reaction $\mathrm{A}\left(\mathrm{g}\right)+2\mathrm{B}\left(\mathrm{g}\right)⟶\mathrm{C}\left(\mathrm{g}\right)$ is provided in the following table for three experiments at $300 \mathrm{K}$.

In another experiment starting with initial concentration of $0.5$ and $1\mathrm{M}$ respectively for $\mathrm{A}$ and $\mathrm{B}$ at $300 \mathrm{K}$. Find the rate of reaction after 50 minutes from start of experiment (in $\mathrm{m}/\sec$)?

Consider a reaction $\mathrm{A}\left(\mathrm{g}\right)\stackrel{\mathrm{k}=0.1\mathrm{M} {\min }^{-1}}{\to }2\mathrm{B}\left(\mathrm{g}\right)$. If initial concentration of $\mathrm{A}$ is $0.5\mathrm{M}$ then select correct graph.

For a zero-order reaction, with the initial reactant concentration $\mathrm{a}$, the time for completion of the reaction is:

The rate of the haemoglobin $\left(\mathrm{Hb}\right)$-carbon monoxide reaction, 

$4\mathrm{Hb}+3\mathrm{CO}\to {\mathrm{Hb}}_4(\mathrm{CO}{)}_3$

has been studied at $20°\mathrm{C}$. The Concentration of reactants are expressed in $\mathrm{\mu } \mathrm{mole}/\mathrm{L}.$ 

The rate constant for the reaction is $7\times {10}^{-\mathrm{x}} \mathrm{L} {\mathrm{\mu mol}}^{-1}.{\sec }^{-1}$. The value of $\mathrm{x}$ is
 

The reaction $\mathrm{A}\to \mathrm{C}+\mathrm{D}$ was found to be second order in $\mathrm{A}$. The rate constant for the reaction was determined to be $2.42 \mathrm{L}/\mathrm{mol}/\mathrm{s}$. If the initial concentration is $0.5 \mathrm{mole}/\mathrm{L},$ what is the value of $t_{\frac{1}{2}}$in sec?

(Express your answer by multiplying with 100 and rounding off to two significant figures)

A drop $(0.05 \mathrm{mL})$ of a solution contains $3.0\times {10}^{-6}$ moles of ${\mathrm{H}}^{+}$ Ions. If the rate constant of disappearance of ${\mathrm{H}}^{+}$ ion is $1.0\times {10}^7\mathrm{mol} {\mathrm{litre}}^{-1} {\sec }^{-1},$  the time taken for  ${\mathrm{H}}^{+}$ ions in the drop to disappear is $\mathrm{p}\times {10}^{-\mathrm{q}}. \text{Calculate the value of} \mathrm{q}-\mathrm{p}$.

Give the nearest integer as the answer.

For the reaction: ${\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right),$ It is found that a plot of $\ln \left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]$ Versus time is linear, and that in $240 \mathrm{s}$, the $\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]$ decreases from $0.4 \mathrm{M}$ to $0.28 \mathrm{M}$, If the rate constant is $\mathrm{A} \mathrm{X} {10}^{-3}$ in ${\mathrm{s}}^{-1}$, report the value of A by rounding it off to one decimal and multiplying with 2.

What is the half-life for the decomposition of $\mathrm{NOCl}$ when $\left[\mathrm{NOCl}\right]=0.15\mathrm{M}?$ Given that for $2\mathrm{NOCl}\to 2\mathrm{NO}+{\mathrm{Cl}}_2:-\frac{\mathrm{d}\left[\mathrm{NOCl}\right]}{\mathrm{dt}}=\left(8.0\times {10}^{-8}\mathrm{L}/\mathrm{mol}/\mathrm{s}\right) [\mathrm{NOCl}{]}^2$

(Express you answer up to one significant figures and in multiple of ${10}^7$)

A substance decomposes according to second order rate law. If the rate constant is $6·8\times {10}^{-4}\mathrm{L}$ mole ${}^{-1}\mathrm{s}^{-1},$ Calculate half-life of the substance, if the initial concentration is $0.05 \mathrm{mole}/\mathrm{L}$. 

If the value of half life is $\mathrm{Y} \mathrm{X}{10}^2$, Report the value of $\mathrm{Y}$ 

Catalytic decomposition of nitrous oxide by gold at $900 °\mathrm{C}$ at an initial pressure of $200 \mathrm{mm}$ was $50 \%$ in $53$ minutes and $73 \%$ in $100$minutes. Find the order of the reaction and report the value of how much percentage will it decompose in $100$ minutes at the same temperature, but at an initial pressure of $600 \mathrm{mm} ?$

The decomposition of arsine $\left({\mathrm{AsH}}_3\right)$ in to arsenic and hydrogen is a first order reaction. The decomposition was studied at constant volume and at constant temperature. The pressures at different times are as follows:

$\begin{array}{ccccc}\mathrm{t}\left(\mathrm{h}\right)& 0& 5.5& 6.5& 8\\ \mathrm{p}\left(\mathrm{atm}\right)& 0.9654& 1.06& 1.076& 1.1\end{array}$

If the velocity constant (in ${\mathrm{h}}^{-1}$) value is A h^-1, Report the answer by multiplying A with 100 and rounding off to the nearest integer value.

The gas-phase decomposition of $\mathrm{NOBr}$ is of second order in $\left[\mathrm{NOBr}\right],$ with $\mathrm{k}=0.81 {\mathrm{M}}^{-1}·{\mathrm{s}}^{-1}$ at $10°\mathrm{C}.$ The initial concentration of $\mathrm{NOBr}$ in the flask at $10°\mathrm{C}$ $=4.00\times {10}^{-3} \mathrm{M}.$ In how many seconds does it take up $1.50\times {10}^{-3} \mathrm{M}$ of this $\mathrm{NOBr}?$ 

$2\mathrm{NOBr}\to 2\mathrm{NO}+{\mathrm{Br}}_2$\

Give answer after rounding off to the nearest integer value.