Half life

Q.

The rate constant for the first order decomposition of H₂O₂ is given by the following equation:

log k = 14.34 − 1.25 × 10⁴ K/T

Calculate E_a for this reaction and at what temperature will its half-period be 256 minutes?

Q.

The half - time period of a radioactive element is 140 days. After 560 days, one gram of the element will reduce to

1. $\frac{1}{2}g$

2. $\frac{1}{4}g$

3. $\frac{1}{16}g$

4. $\frac{1}{8}g$

Q.

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

1. 4.6 x 10^-2 sec

2. 5.1 x 10^-2 sec

3. 4.6 x 10^-4 sec

4. 4.6 x 10^-2 min

Q. In a first order reaction, the reactant has a half-life period of ten minutes. What fraction of the substance will be left after an hour of the reaction has occured?

1. $\frac{1}{64}$ of the initial the concentration
2. $\frac{1}{12}$ of the initial the concentration
3. $\frac{1}{32}$ of the initial the concentration
4. $\frac{1}{6}$ of the initial the concentration

Q.

Calculate the half-life of a first order reaction from their rate constants given below:

$200s^{-1}$

$2mi{n}^{-1}$

$4y{r}^{-1}$

Q.

The experimental data for decomposition of N₂O₅

in gas phase at 318K are given below:

t(s)	0	400	800	1200	1600	2000	2400	2800	3200
	1.63	1.36	1.14	0.93	0.78	0.64	0.53	0.43	0.35

(i) Plot [N₂O₅] against t.

(ii) Find the half-life period for the reaction.

(iii) Draw a graph between log [N₂O₅] and t.

(iv) What is the rate law?

(v) Calculate the rate constant.

(vi) Calculate the half-life period from k and compare it with (ii).

Q. What will be the order of reaction and rate constant for a chemical change having log t vs log concentration of (A) curves as:

1. 3, 1
2. 1, 1
3. $0,\frac{1}{2}$
4. 2, 2

Q. A first order reaction is half completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed?

1. 20 hours
2. 10 hours
3. 7.5 hours
4. 5 hours

Q. The half-life for the reaction, $N_2{O}_5\Rightarrow 2N{O}_2+\frac{1}{2}{O}_2$ is 12 minutes at ${30}^{\circ }C$. Starting with 100 g of $N_2{O}_5$ how many gram of $N_2{O}_5$ will remain after a period of 1 hour 36 minutes.

1. 1.25 g
2. 0.39 g
3. 1.77 g
4. 0.5 g

Q. The half life period for a first order reaction is 69.3s. Its rate constant is

1. ${10}^{-2}{s}^{-1}$
2. ${10}^{-4}{s}^{-1}$
3. $10s^{-1}$
4. ${10}^2{s}^{-1}$

Q. The half-life for a reaction is 50 minutes. If the initial concentration is halved, the half-life becomes 25 minutes. Then it is a order reaction.

1. zero
2. first
3. second

Q. The half life period of a radioactive element is 120 days. After 600 days, one gram of the element will reduced to

1. $\frac{1}{64}g$
2. $\frac{1}{16}g$
3. $\frac{1}{8}g$
4. $\frac{1}{32}g$

Q. The rate of a first order reaction is $1.5\times {10}^{-2}mol{L}^{-1}mi{n}^{-1}$ at 0.5 M concentration of the reactant. The half-life of the reaction is :

1. 23.1 min
2. 8.73 min
3. 0.383 min
4. 7.53 min

Q.

The rate of the chemical reaction doubles for an increase of 10 K in absolute temperature from 298 K. Calculate E_a.

Q. A certain zero order reaction has k = 0.025 M/S for the disappearance of A. What will be the concentration of A after 15 seconds if the initial concentration is 0.50 M?

1. 0.05M
2. 0.375M
3. 0.06M
4. 0.125M

Q. (a) For a reaction $A+B\to P$, the rate is given by Rate = $k\left[A\right][B{]}^2$
(i) How is the rate of reaction affected if the concentration of B is doubled?
(ii) What is the overall order of reaction if A is present in large excess?
(b) A first order reaction takes 23.1 minutes for 50% completion. Calculate the time required for 75% completion of this reaction. (log 2 =0.301, log 3 =0.4771, log 4 =0.6021)

Q. For a certain reaction of order ‘n’, the half-life $\left(t_{\frac{1}{2}}\right)$ is given by, $t_{\frac{1}{2}}=\frac{2-\sqrt{2}}{k}\times C_0^{\frac{1}{2}}$, where k is a constant and $C_0$ is the initial concentration. Find 'n'.

Q. A substance '$A$' undergoes conversion by elementary step to '$B$' and '$C$' in aqueous phase as shown:
$A_{\left(aq\right)}+H_{2}O\to B_{\left(aq\right)}+C_{\left(aq\right)}$
If concentration of $A_{\left(aq\right)}$ initially and after $6.93$ minutes is $1\text{M}$ & $\frac{1}{4}\text{M}$ respectively then calculate rate constant in terms of $M^{-1}{\text{min}}^{-1}$.
(Given: $\log 2=0.3010$)

1. $\frac{1}{5}$
2. $\frac{1}{10}$
3. $3.6\times {10}^{-3}$
4. $1.8\times {10}^{-3}$

Q. When initial concentration of the reactant is doubled, the half-life period of a zero order reaction:

1. Is tripled
2. Is doubled
3. Is halved
4. Remains unchanged

Q. Choose the correct option(s) regarding first order reaction:

1. Half life period for a first order reaction depends directly on the concentration of the reactant(s).
2. Time of completion for first order reaction is infinity
3. Half life period for a first order reaction does not depend on the concentration of the reactant(s).
4. Average Life for First Order Reaction $\left(t_{av}\right)=\frac{1}{k}$
   

Q.

For the decomposition reaction $N{H}_{2}COON{H}_{4\left(s\right)}$$\leftrightharpoons$ $2N{H}_{3\left(g\right)}$ + $C{O}_{2\left(g\right)}$. The $K_p$= 2.9 $\times$ ${10}^{-5}$${atm}^2$. The partial pressure of $C{O}_2$ at equilibrium when 2 mole of $N{H}_{2}COON{H}_{4\left(s\right)}$ was taken to start with would be

1. 

2. 

3. 2 atm

4. 

Q. Rate law of a complex reaction can be determined by

1. Only experimental method
2. Only theoretical method
3. Both experimental and theoritical method
4. None of the above

Q. Concentration of the reactant in first order is reduced to ${\frac{1}{e}}^2$ after

1. three natural life time
2. two natural life time
3. one natural life time
4. four natural life time

Q. The half life of a first order reaction is

1. Independent of the initial concentration of the reactant
2. Directly proportional to the initial concentration of the reactant
3. Inversely proportional to the initial concentration of the reactant
4. Directly proportional to the square of the initial concentration of the reactant

Q.

What will be the effect of temperature on rate constant?

Q. For the reaction $3A\left(g\right)\stackrel{k}{\to }B\left(g\right)+C\left(g\right),k\text{is}{10}^{-14}\text{L/mol~min}$
if $\left[A\right]=0.5M$, then the value of $-\frac{d\left[A\right]}{dt}\left(inM{s}^{-1}\right)$ is :

1. 
   $7.5\times {10}^{-5}$
2. 
   $3\times {10}^{-4}$
3. 
   $2.5\times {10}^{-5}$
4. $1.25\times {10}^{-6}M{s}^{-1}$

Q. The correct difference between first and second order reactions is that:

1. A first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed
2. The half-life of a first-order reaction does not depend on $[A{]}_0$; the half-life of a second-order reaction depends on $[A{]}_0$
3. The rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction depends on reactant concentrations
4. The rate of a first-order reaction depends on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

Q. One of the hazards of nuclear explosion is the generation of ${}^{90}Sr$ and its subsequent incorporation in bones. This nuclide has a half-life of 28 years. Suppose one microgram was absorbed by a newborn child, how much ${}^{90}Sr$ will remain (in micrograms) in his bones on their ${14}^{th}$ birthday? (take $\sqrt{2}=1.4$)

Q. Which of the following relationship(s) is/are correct for a $1^{st}$ order reaction?

1. $t_{75\%}=2t_{1/2}$
2. $t_{87.5\%}=3t_{1/2}$
3. $t_{99.9\%}=9t_{1/2}$
4. $t_{96.87\%}=4t_{1/2}$

Q. Half-life period for a first order reaction is 10 s. The time required to reduce 2.0 g of the reactant to 0.25 g is:

1. 20 s
2. 50 s
3. 30 s
4. 15 s