Maxwell–Boltzmann Distribution

Q.

In the graph showing Maxwell, Boltzmann distribution of energy ........ .
(a) area under the curve must not change with an increase in temperature
(b) area under the curve increases with increase in temperature
(c) area under the curve decreases with increase in temperature
(d) with an increase in temperature, curve broadens and shifts to the right-hand side

Q.

According to Maxwell, Boltzmann distribution of energy, ......... .
(a) the fraction of molecules with most probable kinetic energy decreases at higher temperatures
(b) the fraction of molecules with most probable kinetic energy increases at higher temperatures
(c) most probable kinetic energy increases at higher temperatures
(d) most probable kinetic energy decreases at higher temperatures

Q. The R.M.S. speed of the molecules of a gas of density $4{\text{kg m}}^{-3}$ and pressure $1.2\times {10}^5{\text{N m}}^{-2}$ is:

1. $120{\text{ms}}^{-1}$
   
2. $300{\text{ms}}^{-1}$
   
3. $600{\text{ms}}^{-1}$
   
4. $900{\text{ms}}^{-1}$
   

Q.

The diagram shows the Maxwell’s speed distribution curves for a certain ideal gas at two different temperature $T_1$ and $T_2$. Pick the correct options:
Take $R=\frac{1}{12}\text{L atm/molK}$

1. At 400 K, most probable speed is 800 m/s
2. At 400 K, rms speed is 1000 m/s
3. $T_2=600K$
4. $M=5g/mol$

Q. Which of the following is/are true according to Maxwell - Boltzmann Statistics and Arrhenius Theory ?

1. When temperature is raised, the maximum of the curve moves
   to the higher energy value.
2. When temperature is raised, the maximum of the curve moves
   to the lower energy value.
3. When temperature is raised, the fraction of molecules which collide with energies greater than activation energy increases.
4. When temperature is raised, the fraction of molecules which collide with energies greater than activation energy decreases.

Q.

The diagram shows the Maxwell’s speed distribution curves for a certain ideal gas at two different temperature $T_1$ and $T_2$. Pick the correct options:
Take $R=\frac{1}{12}\text{L atm/molK}$

1. At 400 K, most probable speed is 800 m/s
2. At 400 K, rms speed is 1000 m/s
3. $T_2=600K$
4. $M=5g/mol$

Q. The ratio of $u_{\text{avg}}$ and $u_{\text{rms}}$ of a gas at a particular temperature is

1. 1.1086 : 1
2. 0.92 : 1
3. 1 : 1.1086
4. 1:0.92

Q. Analyze the generalized rate data for the reaction
$RX+N{u}^{-}⟶$ Nucleophilic Product

$\begin{array}{cccc}\text{S. No.}& \text{[RX]Substrate}& \text{[Nu] Attacking species}& \text{Rate of reaction}\left(M{s}^{-1}\right)\\ 1.& 0.10M& 0.10M& 1.2\times {10}^{-4}\\ 2.& 0.20M& 0.10M& 2.4\times {10}^{-4}\\ 3.& 0.10M& 0.20M& 2.4\times {10}^{-4}\\ 4.& 0.20M& 0.20M& 4.8\times {10}^{-4}\end{array}$
Which of the following is the most appropriate potential energy v/s reaction coordinate diagram of the reaction on the basis of above data analysis?

1. 
2. 
3. 
4. 

Q.

The diagram shows the Maxwell’s speed distribution curves for a certain ideal gas at two different temperature $T_1$ and $T_2$. Pick the correct options:
Take $R=\frac{1}{12}\text{L atm/molK}$

1. At 400 K, most probable speed is 800 m/s
2. At 400 K, rms speed is 1000 m/s
3. $T_2=600K$
4. $M=5g/mol$

Q. Analyze the generalized rate data for the reaction
$RX+N{u}^{-}⟶$ Nucleophilic Product

$\begin{array}{cccc}\text{S. No.}& \text{[RX]Substrate}& \text{[Nu] Attacking species}& \text{Rate of reaction}\left(M{s}^{-1}\right)\\ 1.& 0.10M& 0.10M& 1.2\times {10}^{-4}\\ 2.& 0.20M& 0.10M& 2.4\times {10}^{-4}\\ 3.& 0.10M& 0.20M& 2.4\times {10}^{-4}\\ 4.& 0.20M& 0.20M& 4.8\times {10}^{-4}\end{array}$
Which of the following is the most appropriate potential energy v/s reaction coordinate diagram of the reaction on the basis of above data analysis?

1. 
2. 
3. 
4.