First Order Reaction

Q. For a first order reaction $A\to$ Products, initial concentration of $A$ is $0.1M$, which becomes $0.001M$ after $5$ minutes. Rate constant for the reaction in ${\text{min}}^{–1}$ is

Q. A first order reaction has a rate constant of $2.303\times {10}^{-3}{s}^{-1}$. The time required for 40 g of this reactant to reduce to 10 g will be:
(Given that log2 =0.3010)

1. 230.3 s
2. 301 s
3. 602 s
4. 2000 s

Q.

For a first order reaction, show that time required for $99\%$ completion is twice the time required for the completion of $90\%$ of reaction.

Q.

A radioactive nucleus decays by two different processes. The half-life for the first process is $10s$ and that for the second is $100s$. The effective half-life of the nucleus is close to:

1. $55sec$

2. $6sec$

3. $12sec$

4. $9sec$

Q.

A first order reaction takes 40 min for $30\%$ decomposition. Calculate $t_{\frac{1}{2}}$

Q. $t_{1/4}$ can be taken as the time taken for the concentration of a reactant to drop to 3/4 of its value. If the rate constant for a first order reaction is k, the $t_{1/4}$ can be written as [ln2 = 0.695, ln = 1.1]

1. 0.69 / k
2. 0.75 / k
3. 0.10 / k
4. 0.29 / k

Q.

Which of the following graphs is correct for a first order reaction ?

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. The distillation of phenol with zinc dust gives:

1. $C_6{H}_6$
2. $C_6{H}_5-C_6{H}_5$
3. $C_6{H}_{12}$
4. $C_6{H}_5-O-C_6{H}_5$

Q.

Consider a first order gas phase decomposition reaction given below

$A\left(g\right)\to B\left(g\right)+C\left(g\right)$ The initial prssure of the system before decomposition of A was $p_i$. After lapse of time 't' total pressure of the system increased by x units and became '$p_t$'. The rate constant k for the reaction is given as ...... .

$\left(a\right)k=\frac{2.303}{t}log\frac{p_i}{p_i-x}\left(b\right)k=\frac{2.303}{t}log\frac{p_i}{2p_i-p_t}\left(c\right)k=\frac{2.303}{t}log\frac{p_i}{2p_i+p_t}\left(d\right)k=\frac{2.303}{t}log\frac{p_i}{p_i-x}$

Q. The rate constant for a first order reaction is $6.93\times {10}^{-3}{\text{s}}^{-1}$. The Half-life period of the reaction is:

1. $10\text{s}$
2. $10000\text{s}$
3. $1000\text{s}$
4. $100\text{s}$

Q.

What is the rate law for a first-order reaction?

Q.

A first order reaction is 50% completed in $1.26\times {10}^{14}s.$ How much time would it take for 100% completion ?

$\left(a\right)1.26\times {10}^{15}s\left(b\right)2.52\times {10}^{14}s\left(c\right)2.52\times {10}^{28}s\left(d\right)Infinite$

Q.

If 60% of a first order reaction was completed in 60 minutes, 50% of the same reaction would be completed in approximately

1. 40 min
2. 50 min
3. 60 min
4. 45 min

Q. For a first order reaction, $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$, the rate constant in terms of initial pressure $P_0$ and pressure at time $t\left(P_t\right)$, is given by:

1. $\frac{1}{t}ln\frac{P_0}{P_t-P_0}$
2. $\frac{1}{t}ln\frac{3P_0}{P_t-P_0}$
3. $\frac{1}{t}ln\frac{3P_0}{3P_t-P_0}$
4. $\frac{1}{t}ln\frac{2P_0}{3P_0-P_t}$

Q.

The atomic mass of silver found in nature is $\mathrm{Ar}\left(\mathrm{Ag}\right)=107.983$. This silver is made of $107\mathrm{Ag}$ and $109\mathrm{Ag}$ Isotopes. Calculate the proportion of the mass of $107\mathrm{Ag}$ isotope which is in natural silver atoms.

Q.

Give the unit of Rate Constant of a Reaction.

Q.

Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with $t_{\frac{1}{2}}=3.00h$. What fraction of sample of sucrose remains after 8h?

Q.

The results given in the below table were obtained during kinetic studies of the following reaction: 2A + B → C + D

X and Y in the given table are respectively :

1. 0.4, 0.4

2. 0.3, 0.4

3. 0.4, 0.3

4. 0.3, 0.3

Q. One atmosphere is numerically equal to approximately

1. 10⁶ dynes cm^-2

2. 10² dynes cm^-2

3. 10⁴ dynes cm^-2

4. 10⁸ dynes cm^-2

Q. Thermal decomposition of a compound is of first order. If 50% of a sample of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose ?

1. 120 min
2. 299 min
3. 399 min
4. 320 min

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.

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. 0
2. 1

3. 2

4. 3

Q.

Consider a certain reaction; A $\to$ products with $k=2.0\times {10}^{-2}{s}^{-1}$. Calculate the concentration of A remaining after 100 s, if the initial concentration of A is $1.0mol{L}^{-1}$.

Q. The rate constant of a first order reaction is $6.93\times {10}^{-3}mi{n}^{-1}.$ If we start with 10 mol/L, it is reduced to 1.25 mol/L in:

1. 100 minutes
2. 200 minutes
3. 300 minutes
4. 30 minutes

Q.

Calculate the following:
Number of molecules of ${\mathrm{CH}}_4$ in 80.0 g of it.

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

Q. Given that for a reaction of order , the integrated form of the rate equation is $k=\frac{1}{t(n-1)}\left|\begin{array}{c}\frac{1}{C^{n-1}-\frac{1}{C_0^{n-1}}}\end{array}\right|$
where $C_0$ and C are the values of the reactant concentration at the start and after time t . What is the relationship between $t_{3/4}$ and $t_{1/2}$where $t_{3/4}$ is the time required for to become $\frac{1}{4}{C}_0$?

1. $t_{3/4}=t_{1/2}[2^{n-1}+1]$
2. $t_{3/4}=t_{1/2}[2^{n-1}-1]$
3. $t_{3/4}=t_{1/2}[2^{n+1}-1]$
4. $t_{3/4}=t_{1/2}[2^{n+1}+1]$

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. ${10}^{-6}$

Q. In the following reaction
$A\to B+C,$ rate constant is $0.001\text{M/s}$. If we start with $1$ $M$ of A, the concentration of $A$ and $B$ after 10 min are respectively:

1. $0.5\text{M},0.5\text{M}$
2. $0.4\text{M},0.6\text{M}$
3. $0.6\text{M},0.4\text{M}$
4. None of these