First Order Reaction

Q. 26.Copper 63 and copper 65 has average atomic mass of 63.546u. % nature abundance of lighter isotope of copper will be

Q. The kinetics of the reaction, $2N_2{O}_5\to 4N{O}_2+O_2$, in liquid bromine medium was measured independently for three different initial concentrations of $N_2{O}_5$, which are $0.11,0.07$ and $0.05{\text{mol L}}^{-1}$ respectively. The half life of the reaction was found to be $4.5\text{hours}$ for all these concentrations. The order of the reaction is:

1. $0$
2. $1$
3. $2$
4. Can't be predicted

Q. cl 35 and cl 37 are two isotopes of chlorine . if average atomic mass is 35.5 then the ratio of these two isotopes is

Q. 30 The isotopes of chlorine with mass number 35 and 37 exist in ratio if its average atomic mass is 35.5 of

Q. 7. Two isotopes of Boron have atomic mass 10 and 11.Calculate percentage abundance of lighter isotope in a sample of Boron having average atomic mass 10.8.

Q. 26. An element (x) exist in two isotopic forms x80 and x82. If the percentage abundance of the lighter isotope is 40% then the average atomic mass of x is?

Q. The reaction, $Sucrose\to Fructose+Glucose$, takes place at a certain temperature while the volume of the solution is maintained at 1 L. At t = 0, the initial rotation of the mixture is ${34}^{\circ }$. After 30 minutes the total rotation is ${19}^{\circ }$and after a very long time, the total rotation is $-{11}^{\circ }$. Find the time when solution was optically inactive.

1. 135 minutes
2. 103.7 minutes
3. 38.7 minutes
4. 45 minutes

Q. 60. If the average atomic mass of chlorine is 35.5, then find the percentage abundance of the two isotopes of chlorine which have the mass number 35 and 37

Q. The rate constant for a first order reaction is $k=7\times {10}^{-4}{s}^{-1}$. The time taken for the reactant to be reduced to $\frac{1}{4}$ of the initial concentration is

1. 990 s
2. 1980 s
3. 445 s
4. 2970 s

Q. Mole of electrons present in 9 g of aluminium is a)0.33 b)4.33 c)1.33 d)2.6

Q. For zero order reaction, the relationship between first half life and second half life

Q. The ratio of average speed of an O2 molecule to the RMS speed of N2 molecule at the same temperature is

Q. 6. There are two isotopes of an element of average mass x .The isotope with heavier atomic mass x+2 and lighter one has x-1 , then the abundance of heavier one is?

Q.

This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : The decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction at low pressure.
A : गर्म प्लेटिनम पृष्ठ पर गैसीय अमोनिया का अपघटन निम्न दाब पर शून्य कोटि अभिक्रिया है।

R : Hydrogenation of ethene is an example of first order reaction.
R : एथीन का हाइड्रोजनीकरण एक प्रथम कोटि अभिक्रिया का उदाहरण है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. The kinetic study of hydrolysis of ethyl acetate is catalysed by an acid, and is followed by titrating a fixed volume of a reaction mixture with a standard alkali solution, at different intervals of time. The ester hydrolysis is acid catalysed. $V_0,V_t$ and $V_{\infty }$ are the volumes of alkali required at t = 0, t = t and $t=\infty$ respectively. Then, match the statements given in Column I with those in Column II.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ a)V_0\text{is proportional to}& \text{p) Total concentrations of acid initially}\\ & \text{present and concentration of acid}\\ & \text{formed at time t.}\\ b)V_t\text{is proportional to}& \text{q) Concentration of acid initially}\\ & \text{present as the catalyst}\\ c\left)\right(V_{\infty }-V_t)\text{is proportional to}& \text{r) Concentration of acid formed after}\\ & \text{the completion of reaction}\\ d\left)\right(V_{\infty }-V_0)\text{is proportional to}& \text{s) Concentration of ester remaining}\\ & \text{at time t.}\end{array}$

1. (a-q, b-p, c-s, d-r)
2. (a-p, b-p, c-s, d-r)
3. (a-q, b-q, c-s, d-r)
4. (a-q, b-q, c-r, d-s)

Q.

A first order reaction has a specific reaction rate of 10^-2 s^-1. How much time will it take for 20 g of the reactant to reduce to 5 g?

1. 238.6 s

2. 138.6s

3. 346.6s

4. 693.0s

Q. A first order reaction has a rate constant $23\times {10}^{-3}{s}^{-1}$. How long will it take to reduce $5.0\text{g}$ of the reactant to $3.0\text{g}$?

(Given: $log2=0.3,log3=0.5,log5=0.7$)

1. 20 seconds
2. 30 seconds
3. 40 seconds
4. 50 seconds

Q. In a 1st order reaction A $\to$products, the concentration of the reactant decreases to 6.25$\%$ of its initial value in 80 minutes. What is (i) the rate constant and (ii) the rate of reaction, 100 minutes after the start, if the initial concentration is 0.2 mole/litre?

1. $2.17\times {10}^{-2}mi{n}^{-1},3.47\times {10}^{-4}mol.litr{e}^{-1}mi{n}^{-1}$
2. $3.465\times {10}^{-2}mi{n}^{-1},2.166\times {10}^{-4}mol.litr{e}^{-1}mi{n}^{-1}$
3. $3.465\times {10}^{-3}mi{n}^{-1},2.17\times {10}^{-3}mol.litr{e}^{-1}mi{n}^{-1}$
4. $2.166\times {10}^{-3}mi{n}^{-1},2.667\times {10}^{-4}mol.litr{e}^{-1}mi{n}^{-1}$

Q. The decomposition of $N_2{O}_5$ according to the equation $2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right)$
is a first order reaction. After 2 minutes from the start of decomposition in a closed vessel, the total pressure developed is found to be 500 mm Hg. On complete decomposition, the total pressure is 800 mm Hg. If the rate constant of the reaction is $ymi{n}^{-1}$ then, what is the value of y? (given log 2 = 0.3, log 3 = 0.5)

Q. The time required for 5% completion of a reaction at 300 K is equal to that required for its 20% completion at 320 K. If the pre -exponential factor for the reaction is $3.56\times {10}^9$ $se{c}^{-1}$. Then which of the following is correct.(given log95 = 1.98, log80 = 1.90, log5 =0.7, R=$\frac{25}{3}J{K}^{-1}mo{l}^{-1}$)

1. The reaction follows first order kinetics
2. The activation energy of the reaction is 64.48 kJ/mol
3. The activation energy for the reaction is 7.19 kJ/mol
4. The reaction follows second order kinetics

Q. If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed in approximately (in minutes)

(Take : log 2 = 0.30; log 2.5 = 0.40)

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> JEE MAINS 2020

Q.

Consider the chemical reaction

$N_2\left(g\right)+3H_2\left(g\right)⟶2N{H}_3\left(g\right)$

The rate of this reaction can be expressed in terms of time derivatives of the concentration of $N_2\left(g\right),H_2\left(g\right),orN{H}_3\left(g\right).$ Identify the correct relationship among the rate expressions.

1. Rate = $\frac{-d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$

2. Rate = $\frac{d\left[N_2\right]}{dt}=-3\frac{d\left[H_2\right]}{dt}=2\frac{d\left[N{H}_3\right]}{dt}$

3. Rate = $\frac{d\left[N_2\right]}{dt}=\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$

4. Rate = $\frac{d\left[N_2\right]}{dt}=\frac{d\left[H_2\right]}{dt}=\frac{d\left[N{H}_3\right]}{dt}$

Q.

Half - life of the reaction :$H_2{O}_{2\left(aq\right)}\to H_2{O}_{\ell }+\frac{1}{2}{O}_{2\left(g\right)}$ is independent of initial concentration of $H_2{O}_2$. Volume of $O_2$ gas after 20 minutes is 5L at 1 atm and ${27}^{\circ }C$, and after completion of the reaction 50 L. The rate constant is :

1. $\frac{1}{20}log10mi{n}^{-1}$

2. $\frac{2.303}{20}log10mi{n}^{-1}$

3. $\frac{2.303}{20}log\frac{50}{45}mi{n}^{-1}$

4. $\frac{2.303}{20}log\frac{45}{50}mi{n}^{-1}$

Q.

In a first order reaction the concentration of reactant decreases from $800mol/d{m}^3$ to $50mol/d{m}^3$ in $2\times {10}^{4}s$. The rate constant of reaction in $s^{-1}$ is:

1. $2\times {10}^4$

2. $3.45\times {10}^{-5}$

3. $1.386\times {10}^{-4}$

4. $2\times {10}^{-4}$

Q. In a first order reaction $x\to y$, the concentration of ‘$x$’ changes from 0.1 M to 0.025 M in 40 minutes. The rate of the reaction (mol/L min) when the concentration of $x$ is 0.01 M would be:

1. $3.47\times {10}^{-5}$
2. 
   $3.47\times {10}^{-4}$
3. $5.8\times {10}^{-4}$
4. $5.8\times {10}^{-6}$

Q. A first order reaction has a specific reaction rate of ${10}^{-2}{s}^{-1}$. How much time will take for 20 g of the reactant to reduce to 5 g?

1. 238.6 seconds
2. 138.6 seconds
3. 346.5 seconds
4. 693.0 seconds

Q.

(A) follows first order reaction, (A) $\to$ product.

The concentration of A changes from 0.1 to 0.025 M in 40 min.

Find the rate of reaction of A when the concentration of A is 0.01 M.

1. $3.47\times {10}^{-4}Mmi{n}^{-1}$

2. $3.47\times {10}^{-5}Mmi{n}^{-1}$

3. $1.73\times {10}^{-4}Mmi{n}^{-1}$

4. $1.73\times {10}^{-5}Mmi{n}^{-1}$

Q. The rate of a first order reaction has been found to be $2.45\times {10}^{-6}mol{L}^{-1}{s}^{-1}$at concentration $C_1$. The value of $C_1$ is (rate constant = $3.5\times {10}^{-5}$)

1. $7mol{L}^{-1}$
2. $0.7mol{L}^{-1}$
3. $0.07mol{L}^{-1}$
4. $2.1mol{L}^{-1}$

Q.

(A) follows first order reaction : $A\to$ Products; concentration of A changes from 0.1 M to 0.025 M in 40 minutes. Find the rate of reaction of A when its concentration is 0.01 M.

1. $1.73\times {10}^{-4}Mmi{n}^{-1}$

2. $1.73\times {10}^{-5}Mmi{n}^{-1}$

3. $3.47\times {10}^{-4}Mmi{n}^{-1}$

4. $3.47\times {10}^{-5}Mmi{n}^{-1}$

Q. The reaction, $Sucrose\to Fructose+Glucose$, takes place at a certain temperature while the volume of the solution is maintained at 1 L. At t = 0, the initial rotation of the mixture is ${34}^{\circ }$. After 30 minutes the total rotation is ${19}^{\circ }$and after a very long time, the total rotation is $-{11}^{\circ }$. Find the time when solution was optically inactive.

1. 135 minutes
2. 103.7 minutes
3. 38.7 minutes
4. 45 minutes