Assertion : For a reaction $\mathrm{A}\left(\mathrm{g}\right)\to \mathrm{B}\left(\mathrm{g}\right)$

                                 $—{\mathrm{r}}_{\mathbf{e}}=2.5 {\mathrm{P}}_{\mathrm{A}} \mathrm{at} 400\mathrm{K}$

                                 $—{\mathrm{r}}_{\mathbf{e}}=2.5 {\mathrm{P}}_{\mathrm{A}} \mathrm{at} 600\mathrm{K}$

                  activation energy is 4135 J/mol.

Reason : Since for any reaction, values of rate constant at two different temp is same therefore

               activation energy of the reaction is zero.

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

If concentration are measured in mole/litre and time in minutes , the unit for the rate constant of a $3^{rd}$ order reaction are

(1) $mol li{t}^{-1} mi{n}^{-1}$                                              

(2) $li{t}^2 mo{l}^{-2}mi{n}^{-1}$

(3) $lit mo{l}^{-1}mi{n}^{-1}$                                              

(4) $mi{n}^{-1}$

The following reaction was carried out at 300 K.

2SO₂(g)  +  O₂(g) →  2SO₃(g)

The rate of formation of $S{O}_3$ is related to the rate of disappearance of $O_2$  by the following expression:

1. $-\frac{∆\left[O_2\right]}{∆t}=+\frac{1}{2}\frac{∆\left[S{O}_3\right]}{∆t}$                           

2. $-\frac{∆\left[O_2\right]}{∆t}=\frac{∆\left[S{O}_3\right]}{∆t}$

3. $-\frac{∆\left[O_2\right]}{∆t}=-\frac{1}{2}\frac{∆\left[S{O}_3\right]}{∆t}$                           

4. None of the above.

Which of the following rate laws has an over all order of 0.5 for the reaction A + B + C $\to$product ?

1. R=k[A].[B].[C]                                            

2. R=k[A]^0.5[B]^0.5[C]^0.5  

3. R=k[A]^1.5[B]^-1[C]⁰  $$                                

4. R=k[A][B]⁰[C]^0.5

For the system $A_2\left(g\right)+B_2\left(g\right) 2AB\left(g\right),∆H=-80kJ$ If the activation energy for the forward step is 100 kcal/mol.What is the ratio of temperature at which the forward and backward reaction shows the same % change of rate constant per degree rise of temperature ? (1 cal= 4.2 J)

(A) $\sqrt{0.72}$                                                    

(B) $\sqrt{0.84}$

(C) $\sqrt{0.42}$                                                    

(D) $\sqrt{1}$

For a reaction of the type 2A+B $\to$2C, the rate of the reaction is given by $k{\left[A\right]}^2\left[B\right]$. When the volume of the reaction vessel is reduced to 1/4 th of the original volume, the rate of reaction changes by a factor of

(A) 0.25                                                          

(B) 16

(C) 64                                                             

(D) 4

From the following data , the orders with respect to A, B, C , respectively, are :

1. $-1,$ $1,$ $3/2$                                     

2. $-1,$ $1,$ $1/2$

3. $1,$ $3/2,-1$                                     

4. $1,-1,$ $3/2$

The elementary reaction A + B $\to$products has k = 2 × 10^-5 M^-1 s^-1 at a temperature of $\mathrm{27 }°$C. Several experimental runs are carried out using stoichiometric proportion. The reaction has a temperature coefficient value of 2.0. At what temperature should the reaction be carried out if, in spite of halving the concentrations, the rate of reaction is desired to be 50 % higher than in the previous run?

(Given $\frac{\mathcal{l}n6}{\mathcal{l}n\mathrm{2 }}= 2.585)$

1. $\mathrm{47 }°C$                                           

2. $\mathrm{53 }°C$

3. $\mathrm{57 }°C$                                           

4. $\mathrm{37 }°C$

When the temperature of a reaction increases from 27 ^oC to 37 ^oC, the rate increases by 2.5 times. The activation energy in the temperature range will be:

1. 53.6 kJ                                             

2. 12.61 kJ

3. 7.08 kJ                                             

4. 70.8 kJ

For the reaction $R-X+OH \to ROH+$$X^{-}$ The rate is given of

Rate=$5.0\times {10}^{-5}\left[R-X\right]\left[O{H}^{-}\right]+0.20\times {10}^{-5}\left[R-X\right]$ what percentage of R-X Reaction by $S{N}^2$ mechanism when $\left[O{H}^{-}\right]=1.0\times {10}^{-2}M$

1. 96.1%                                                         

2. 3.9%

3. 80%                                                           

4. 20%