Integrated Rate Law for Zero and First Order Reactions

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

Select whether the following statement is true or false:

The graph that can be plotted between the rate of the reaction and time, for a zero-order reaction, will have a negative slope.

Select whether the following statement/graph is true or false:

 The graph between the rate of the reaction and time for a zero-order reaction is:

The graph that can be plotted between the rate of the reaction and time for a zero-order reaction will have a slope of _____ value. (negative/ zero/ positive)

Explain the graph that can be plotted between the rate of the reaction and time for a zero-order reaction.

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

The accompanying figure depicts the change in concentration of species $\mathrm{X}$ and $\mathrm{Y}$ for the elementary reaction $\mathrm{X}\to \mathrm{Y}$ as a function of time. The point of intersection of two curves represents:

The order of a reaction for which a linear line (with a negative slope) is obtained in a graph of $\log (\mathrm{a}-\mathrm{x})$ vs $\mathrm{t}$ is:

Two-third life for a first-order reaction is $55$ minutes. The value of its velocity constant is nearly

Consider a reaction that is first order in both directions

$\mathrm{A}\underset{{\mathrm{k}}_{\mathrm{b}}}{\overset{{\mathrm{k}}_{\mathrm{f}}}{\rightleftharpoons }}\mathrm{B}$

Initially only $\mathrm{A}$ is present, and its concentration is ${\mathrm{A}}_0.$ Assume ${\mathrm{A}}_{\mathrm{t}}$ and ${\mathrm{A}}_{\mathrm{eq}}$ are the concentrations of $\mathrm{A}$ at time $"\mathrm{t}"$ and at equilibrium, respectively. The time $"\mathrm{t}"$ at which ${\mathrm{A}}_{\mathrm{t}}=\left({\mathrm{A}}_0+{\mathrm{A}}_{\mathrm{eq}}\right)/2$ is:

For a first order reaction $\mathrm{R}\to \mathrm{P}$, the rate constant is $\mathrm{k}$. If the initial concentration of $\mathrm{R}$ is ${\left[\mathrm{R}\right]}_0$, the concentration of $\mathrm{R}$ at any time $\text{'}\mathrm{t}\text{'}$ is given by the expression:

The time taken for the completion of three-fourths of a first-order reaction is

The half-life period for a zero order reaction is equal to:

 Show that, In a first order reaction, time required for completion of $99.9\%$ is _____ times of half life. ($\log 10 = 1$).

The half-life period of a zero order reaction $\mathrm{A} \to$ product is given by:

A first order reaction has reaction constant, $\mathrm{k}=5.5\times {10}^{-14}{\mathrm{s}}^{-1}$. The half-life of the reaction in seconds is: _____ $\times {10}^{14}$

The half life of first order reaction is $6.0$ hours. Time  take (in hours) for the concentration of reactant to decrease from $0.8 \mathrm{M}$ to $0.25 \mathrm{M}$ is:

A first order reaction takes $40$ minutes for $20\%$ decomposition. Calculate half life?

What is the mathematical relation between half life of zero order reaction and its rate constant.