$A{c}^{227}$ has a half life of 22 years. The decays follows two parallel paths 

What are the decay constants ($\lambda$) for Th and Fr respectively?

1. 0.03087, 0.00063

2. 0.00063, 0.03087

3. 0.02,0.98

4. None of these

A reaction takes place in various steps. The rate constant for first, second, third

and fifth steps are $k_1$, $k_2$, $k_3$   and $k_5$ respectively. The overall rate constant is

given by

$k<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{k_2}{k_3}{\left(\frac{k1}{k5}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

If activation energy are 40, 60, 50 and 10 kJ/mol respectively, the overall

energy of activation (kJ/mol) is : 

1. 10

2. 20

3. 25

4. None of these

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 $\to \hspace{0.17em}$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  $<mspace\; width="1em"></mspace>$                                

4. R=k[A][B]⁰[C]^0.5

For the system $A_2\left(g\right)+B_2\left(g\right)<mspace\; width="1em"></mspace>2AB\left(g\right),∆H=-80kJ$ 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

The rate constant of a first-order reaction is typically determined from a plot of:

1. Concentration of reactant vs time t

2. Log (concentration of reactant) vs time t

3. \(\frac{1}{\text { concentration of reactant }} \text { vs time } t\)
4. Concentration of reactant vs log time t

The plot of log k versus $\frac{1}{T}$ is linear with a slope of

(1) $\frac{E_a}{R}$                                                    

(2) $\frac{-E_a}{R}$

(3) $\frac{E_a}{2.303R}$                                             

(4) $\frac{-E_a}{2.303R}$

The rate constant, the activation energy, and the Arrhenius parameter of a chemical reaction at 25°C are 3.0×10^-4 s^-1, 104.4 kJ mol^-1 and 6.0×10¹⁴s^-1 respectively.
The value of the rate constant as T → ∞ will be:

1. 2.0 × 10¹⁸ s^-1                                                  

2. 6.0 × 10¹⁴ s^-1

3. $\infty$                                                                   

4. 3.6 × 10³⁰ s^-1

87.5% of a radioactive substance disintegrates in 40 minutes. What is the half life of the substance ?

(1) 13.58 min                                                   

(2) 135.8 min

(3) 1358 min                                                    

(4) None of these