First Order Reaction

Q.

U with atomic number 92 and mass number 238 is radioactive and it emits alpha and beta particles to form Pb with atomic number 82 and mass number 206. Calculate the number of alpha and beta particles emitted in this conversation.

An ore of U with atomic number 92 and mass number 238 is found to contain U and Pb in the weight ratio of 1:0.1. The half-life period of U is $4.5\times {10}^9$ years. Calculate the age of the ore.

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.

When initial concentration of a reactant is doubled in a reaction, its half-life period is not affected. The order of the reaction is:

1. Zero

2. First

3. Second

4. More than zero but less than first

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.

${\mathrm{Mg}}^{2+}$ is isoelectronic with

1. ${\mathrm{Cu}}^{2+}$

2. ${\mathrm{Ca}}^{2+}$

3. ${\mathrm{Na}}^{+}$

4. ${\mathrm{Zn}}^{2+}$

Q. $N_2+3H_2\rightleftharpoons 2N{H}_3$
Which is correct statement if $N_2$ is added at equilibrium condition?

1. The equilibrium will shift to forward direction because according to IInd law of thermodynamics, the entropy must increases in the direction of spontaneous reaction
2. The condition for equilibrium is $G\left(N_2\right)+3G\left(H_2\right)=2G\left(N{H}_3\right)$ where, G is Gibbs free energy per mole fo the gaseous species measured at that partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent
3. The catalyst will increase the rate fo forward reaction by $\alpha$ and that of backward reaction by $\beta$
4. Catalyst will not alter the rate fo either fo the reaction

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

Q. 75$\%$ of a first order reaction was completed in 32 minutes. 50$\%$ of the reaction was complete in

1. 4 min
2. 16 min
3. 8 min
4. 24 min

Q.

Which of the following statements is/are correct?
(IIT-JEE, 1999)

1. A plot of log kp versus 1/T is linear.

2. A plot of log [X] versus time is linear for a first order reaction, x → p.

3. A plot of log p versus 1/T is linear at constant volume.
4. A plot of p versus 1/V is linear at constant temperature.

Q. A reaction $2A+B\stackrel{K}{\to }C+D$ is first order w.r.t. and second order w.r.t. . Initial conc. (t=0) of is $C_0$ while is $2C_0$. If at as 300 minutes the conc. of C is $\frac{C_0}{4}$ then rate expression at t = 300 minutes is

1. $R=49C_0^3\frac{k}{32}$
2. $R=7C_0^3\frac{k}{16}$
3. $R=27C_0^3\frac{k}{32}$
4. $R=247C_0^3\frac{k}{64}$

Q. This time Arun got first order reaction to set up in Laboratory. He observed for 16 min and noticed that reaction is $50\%$ completed. How much time will it take for the reaction to $75\%$ complete?

1. 24 min
2. 32 min
3. 28 min
4. 48 min

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

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.

For a first order reaction,
(IIT-JEE, 1998)

1. The degree of dissociation is equal to $(1–e^{-kt})$
2. A plot of reciprocal concentration of the reactant versus time gives a straight line.
3. The time taken for the completion of 75% of the reaction is thrice the time taken for ½ of the reaction.
4. The pre-exponential factor in the Arrhenius equation has the dimension of time $T^{-1}$.

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. The molar conductance of $N{H}_{4}OH$ at 0.01M concentration is 11.3 $oh{m}^{-1}c{m}^{2}mo{l}^{-1}$. The degree of dissociation
of $N{H}_{4}OH$ is
(molar conductance at infinite dilution is 271.1)

1. $4.2\%$
2. $1.3\%$
3. $12.6\%$
4. $41\%$

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. For a reaction $A\to B,\Delta C_B$ is 0.01 moles per litre in 20 seconds, what is the average rate of reaction?

1. $5\times {10}^{-4}mole{L}^{-1}se{c}^{-1}$
2. $0.5\times {10}^{-4}mole{L}^{-1}se{c}^{-1}$
3. $0.2\times {10}^{-4}mole{L}^{-1}se{c}^{-1}$
4. $2\times {10}^{-4}mole{L}^{-1}se{c}^{-1}$