First Order Reaction

Q. The decomposition reaction $2N_2{O}_5\left(g\right)\stackrel{\Delta }{\to }2N_2{O}_4\left(g\right)+O_2\left(g\right)$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of $1atm$. After $Y\times {10}^{3}s$, the pressure inside the cylinder is found to be $1.45atm$. If the rate constant of the reaction is $5\times {10}^{-4}{s}^{-1}$, assuming ideal gas behaviour, the value of Y is

Q. For the reaction :
$2N_2{O}_5\to 4N{O}_2+O_2$
Rate and rate constant $1.02\times {10}^{-4}$ and $3.4\times {10}^{-5}{s}^{-1}$ respectively, then concentration of $N_2{O}_5$ at that time will be

1. $1.732$
2. $3$
3. $1.02\times {10}^{-4}$
4. $3.4\times {10}^5$

Q. Inversion of sucrose $\left(C_{12}{H}_{22}{O}_{11}\right)$ is a first order reaction and is studied by measuring angle of rotation at different intervals of time $\underset{\text{d-Sucrose}}{C_{12}{H}_{22}{O}_{11}}+H_{2}O\stackrel{H^{+}}{\to }\underset{\text{d -Glucose}}{C_6{H}_{12}{O}_6}+\underset{\text{l -Fructose}}{C_6{H}_{12}{O}_6}$
$r_0$ = angle of rotation at the start, $r_t$ = angle of rotation at time ti, and $r_{\infty }$ = angle of rotation at the complete reaction, if 50% of sucrose undergoes inversion, then

1. $r_0=r_t-2r_{\infty }$
2. $r_0=2r_t-r_{\infty }$
3. $r_0=r_t-r_{\infty }$
4. $r_0=r_t+r_{\infty }$

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. Inversion of sucrose $\left(C_{12}{H}_{22}{O}_{11}\right)$ is a first order reaction and is studied by measuring angle of rotation at different intervals of time $\underset{\text{d-Sucrose}}{C_{12}{H}_{22}{O}_{11}}+H_{2}O\stackrel{H^{+}}{\to }\underset{\text{d -Glucose}}{C_6{H}_{12}{O}_6}+\underset{\text{l -Fructose}}{C_6{H}_{12}{O}_6}$
$r_0$ = angle of rotation at the start, $r_t$ = angle of rotation at time ti, and $r_{\infty }$ = angle of rotation at the complete reaction, if 50% of sucrose undergoes inversion, then

1. $r_0=r_t-2r_{\infty }$
2. $r_0=2r_t-r_{\infty }$
3. $r_0=r_t+r_{\infty }$
4. $r_0=r_t-r_{\infty }$

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. A gas phase reaction $R\to A+B+C+D$ follows first order kinetics. The initial pressure was $x_o$, the pressure after 10 minutes was $y$. The correct expression for the rate constant $k$ is :

1. $k=\frac{2.303}{10}\log \frac{4x_0}{3x_0-y}$
2. $k=\frac{2.303}{10}\log \frac{2x_0}{3x_0-y}$
3. $k=\frac{2.303}{10}\log \frac{4x_0}{4x_0-y}$
4. $k=\frac{2.303}{10}\log \frac{3x_0}{4x_0-y}$

Q. Which of the following plot(s) is/are correct for a first order reaction?

1. I, II
2. II, I
3. I, II, III
4. I, III

Q.

A is one of the reactants. Which concentration plot is linear for a first-order equation?

1. [A] versus time

2. square root of [A] versus time

3. In [A] versus time

4. [A]² versus time

Q. The time required for 75% completion of a first order reaction is (k = 6.93 min^–1)

एक प्रथम कोटि अभिक्रिया के 75% पूर्णता के लिए आवश्यक समय है (k = 6.93 min^–1)

1. 0.5 min
2. 0.1 min
3. 0.2 min
4. 1.5 min

Q.

For a first order reaction $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$ at constant volume and 300 K, the total pressure at the beginning (t=0) and time t are $P_o$ and $P_t$ respectively. Initially, only $A$ is present with concentration $[A{]}_o$ and $t_{1/2}$ is the time required for the partial pressure of $A$ to reach a third of its initial value. The correct options are:
(Assume that all these gases behave as ideal gaes)

1. 
2. 
3. 
4. 

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

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

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

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.

What is the order for absorption of alcohol through the lining of the stomach and small intestine?

1. zero order

2. first order

3. second order

4. third order

Q. For a first order reaction $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$ at constant volume and 300 K, the total pressure at the beginning (t= 0) and at time t are $P_0$ and $P_t$, respectively. Initially, only A is present with concentration $\left[A_0\right]$, and $t_{\frac{1}{3}}$ is the time required for the partial pressure of A to reach ${\frac{1}{3}}^{rd}$ of its initial vlaue. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

1. 
2. 
3. 
4. 

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

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

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

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

Q. Which of the following options cannot be represented by the plot given below?

1. $2^{\mathrm{nd}}orderreaction\to \frac{1}{\left[A\right]}\mathrm{vs}\mathrm{Time}$
2. $1^{\mathrm{st}}\mathrm{order}\mathrm{reaction}\to t_{\frac{1}{2}}\mathrm{vs}\mathrm{Concentration}$
3. $\mathrm{Zero}\mathrm{order}\mathrm{reaction}\to t_{\frac{1}{2}}\mathrm{vs}\mathrm{Concentration}$
4. $n^{\mathrm{th}}\mathrm{order}\mathrm{reaction}\to \mathrm{rate}\mathrm{vs}{\mathrm{Concentration}}^n$

Q. The rate of a first order reaction $R\to P$is $7.5\times {10}^{-4}mol{L}^{-1}{s}^{-1}$ when the concentration of R is 0.5 mol $L^{-1}$.

The rate constant is

1. $2.5\times {10}^{-5}{s}^{-1}$
2. $1.5\times {10}^{-3}{s}^{-1}$
3. $4.16\times {10}^{-7}{s}^{-1}$
4. $1.5\times {10}^{-5}{s}^{-1}$

Q. Two substances $A(t_{\frac{1}{2}}=5\text{min})$ and $B(t_{\frac{1}{2}}=15\text{min})$ are taken in such a way that initially $\left[A\right]=4\left[B\right]$. The time after which both the concentration will be equal is: (Assume that reaction is first order)

1. $5min$
2. $15min$
3. $20min$
4. Concentration can never be equal

Q. If on doubling the initial reactant concentration, half life of reaction becomes twice then order of this reaction will be

यदि प्रारम्भिक अभिकारक सांद्रता को दो गुना करने पर, एक अभिक्रिया की अर्ध-आयु दो गुना हो जाती है तो इस अभिक्रिया की कोटि होगी

1. Zero
   
   शून्य
2. First
   
   प्रथम
3. Second
   
   द्वितीय
4. Half
   
   आधी

Q. Decomposition of $H_2{O}_2$ follows first order kinetics. In fifty minutes, the concentration of $H_2{O}_2$ decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of $H_2{O}_2$ reaches 0.05 M, the rate of formation of $O_2$ will be:

1. $6.93\times {10}^{-4}$ mol ${\text{min}}^{-1}$
2. $2.66{\text{L min}}^{-1}$ at STP
3. $1.34\times {10}^{-2}$ mol ${\text{min}}^{-1}$
4. $6.93\times {10}^{-2}$ mol ${\text{min}}^{-1}$

Q.

In the reaction, P + Q ⟶ R + S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

1. 2

2. 3
3. \N
4. 1

Q. What will be the expression of $t_{1/2}$ half -life when reaction follows rate law, $\text{rate}=k[\text{concentration}{]}^2$
Here,
$k$ is the rate constant
$a$ is the initial concentration of the reactant

1. $\frac{3}{2k{a}^2}$
2. $\frac{1}{k{a}^2}$
3. $\frac{1}{ka}$
4. $k{a}^2$

Q. The rate for a first order reaction is $0.639\times {10}^{-2}mold{m}^{-1}mi{n}^{-1}$ and the initial concentration is 0.2 mol $d{m}^{-3}$. The half-life period is

1. 1200 s
2. 0.33 s
3. 20 s
4. 600 s

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

Q. $H_2{O}_2\to H_{2}O+O_2$
The rate constant of this reaction is $2\times {10}^{-2}mi{n}^{-1}$ (at certain temperature) and reaction is started with $0.5M$ concentration of $H_2{O}_2$, after $23.03min$ the reaction was suddenly stopped by lowering the temperature and remaining $H_2{O}_2$ was completely reacted with $NaOCl$, if number of moles of $O_2$ produced in second reaction is $\frac{1}{x}$. Find $x$.
(Given : $NaOCl+H_2{O}_2\to O_2+NaCl+H_{2}O$$log1.5=0.2$)

Q. Graph between concentration of the product ‘x’ and time ‘t’ for A $\to$B is given below:

The graph between $-\frac{d\left[A\right]}{dt}$ and time will be of the type:

1. 
2. 
3. 
4. 

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. $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$
Initially at t = 0 gas A was present along with some amount of gas C. At At t = 0, the mole fraction of gas C is $\frac{1}{3}$. After some time $t=t_1$, the total pressure is half of the final total pressure at $t=t_x$ (a very long time). Assume this decomposition to follow first order kinetics (at a constant temperature). It is also given at $t=t_x$, the final total pressure is 35 bar.

At $t=t_1$ pressure of gas B is.

1. 2.5 bar
2. 1.25 bar
3. 5.0 bar
4. Data is insufficient

Q. For a first order reaction, $t_{0.75}$ is 138.6 seconds. Its specific rate constant (in $s^{-1}$) is:

1. ${10}^{-2}$
2. ${10}^{-4}$
3. ${10}^{-5}$
4. ${10}^{-6}$