Integrated Rate Equations of Chemical Reaction

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

The half-life period of a first order reaction at $298 \mathrm{K}$ is $20$ minutes. The time (in min.) required for $99.9\%$ completion of the reaction at the same temperature is.

Graph of half life of first-order reaction and initial concentration of reactant is a:

Graph of half life of zero-order reaction and initial concentration of reactant is a:

The consecutive reaction $\mathrm{X}⟶\mathrm{Y}⟶\mathrm{Z}$ takes place in a closed container. Initially, the container has ${\mathrm{A}}_0$ moles of $\mathrm{X}$ (and no $\mathrm{Y}$ and $\mathrm{Z}$). The plot of total moles of the constituents in the container as a function of time will be

Which among the following represents the expression for $(3/4{)}^{\mathrm{th}}$ life of $1^{\mathrm{st} }$ order reaction?

If the rate constant of a first order reaction is $4.606\times {10}^{-3}{ \mathrm{s}}^{-1}$, then find the time required for $400 \mathrm{g}$ of the reactant to reduce to $50 \mathrm{g}$.

If the decomposition reaction ${\mathrm{A}}_{\left(\mathrm{g}\right)}⟶{\mathrm{B}}_{\left(\mathrm{g}\right)}$ follows first order kinetics, then the graph of rate of formation of $\mathrm{B},$ denoted by $\mathrm{R},$ against time $\text{'}t\text{'}$ will be

If the rate constant for a first order reaction is $\mathrm{k},$ then find the time required for completion of $80\%$ of the reaction.

Reactant $R$ gives $n$ different products $\left(P_r:r=1,2,3,\cdots ,n\right)$ in $n$ parallel first order reactions. Rate constant for the formation of any produet $P_r$ is $rk$ where $r=1,2,3,\cdots ,n.$ For the decay of $R,$ what is the overall rate constant in terms of $k?$

The rate constant for the first-order reaction is $60\mathrm{ }{\mathrm{s}}^{-1}$. How much time will it take to reduce the concentration of the reactant to $1/16$ of initial value?

Which of the following curve represent zero order reaction of $\mathrm{A}\mathrm{ }\to \mathrm{ }$products?

The inactivation of a viral preparation in a chemical bath is found to be a first order reaction. Calculate the rate constant for the viral inactivation if in the beginning $1.5\mathrm{ }\mathrm{\%}$ of the virus is inactivated per minute.

 $\left(\mathrm{Given}:\ln \frac{100}{98.5}=0.01511\right)$

Addition of a catalyst at $300 \mathrm{K}$ increases the rate of a chemical reaction by a factor of $36$. By how many $\mathrm{kJ}$, the activation energy of the catalysed pathway is less than the activation energy of the original pathway approximately $\left(\log \left(6\right)=0.78 \mathrm{and} \mathrm{R}=8.3 \mathrm{J} {\mathrm{k}}^{-1}{\mathrm{mol}}^{-1}\right)$.

Two first-order reactions have half times in the ratio of $8 : 1.$ The ratio of time intervals ${\mathrm{t}}_1:{\mathrm{t}}_2$ is:

Here, the time ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ are time period for ${\left(\frac{1}{4}\right)}^{\mathrm{th}}$ and ${\left(\frac{3}{4}\right)}^{\mathrm{th}}$ completion.

Which of the following equations represent integrated rate equation of zero order reaction?

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

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.