Integrated rate equations for zero and first order; half-life — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For a first-order reaction, the integrated rate equation is

• A. $\ln([A]_0/[A])=kt$
• B. $[A]=[A]_0-kt$ always
• C. $1/[A]-1/[A]_0=kt$
• D. $[A]=kt$

Question 2 · difficulty L2 · understanding

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 $\log 3=0.4771$ )

Question 3 · difficulty L2 · understanding

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 $: \log 2=0.3010$ )

Question 4 · difficulty L2 · understanding

$$\text { For a first order reaction } \mathrm{A} \rightarrow \mathrm{~B}$$ $$\begin{array}{|l|l|} \hline \mathrm{t} / \min & {[\mathrm{A}] / \mathrm{M}} \\ \hline 0 & 0.6500 \\ \hline x & 0.0650 \\ \hline 20 & 0.00065 \\ \hline \end{array}$$ $x=$ $\_\_\_\_$ min. (Nearest integer)

Question 5 · difficulty L2 · understanding

Time required for completion of $$99.9 \%$$ of a First order reaction is ________ times of half life $$\left(t_{1 / 2}\right)$$ of the reaction.

Question 6 · difficulty L2 · understanding

$$\mathrm{A}$$ $$\rightarrow \mathrm{B}$$ The above reaction is of zero order. Half life of this reaction is $$50 \mathrm{~min}$$. The time taken for the concentration of $$\mathrm{A}$$ to reduce to one-fourth of its initial value is ____________ min. (Nearest integer)

Question 7 · difficulty L2 · understanding

The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is _______ $\times 10^{-2} \mathrm{~min}$. (Nearest integer) (Given : $\ln 10=2.303$ and $$\log 2=0.3010 \text { )}$$

Question 8 · difficulty L2 · understanding

If compound A reacts with B following first order kinetics with rate constant $$2.011 \times 10^{-3} \mathrm{~s}^{-1}$$. The time taken by $$\mathrm{A}$$ (in seconds) to reduce from $$7 \mathrm{~g}$$ to $$2 \mathrm{~g}$$ will be ___________. (Nearest Integer) $$[\log 5=0.698, \log 7=0.845, \log 2=0.301]$$

Question 9 · difficulty L2 · understanding

For the first order reaction A $$\to$$ B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest integer) Given : log 2 = 0.3010 log 3 = 0.4771 log 5 = 0.6989

Question 10 · difficulty L2 · understanding

For the given first order reaction $$\mathrm{A} \rightarrow \mathrm{B}$$ the half life of the reaction is $$0.3010 \mathrm{~min}$$. The ratio of the initial concentration of reactant to the concentration of reactant at time $$2.0 \mathrm{~min}$$ will be equal to ___________. (Nearest integer)