In a catalytic reaction, involving the formation of ammonia by Haber's process $N_2+3H_2\to 2N{H}_{3,}$ the rate of appearance of NH₃. was measured as $2.5\times {10}^{-4}<mspace\; width="1em"></mspace>mol<mspace\; width="1em"></mspace>L^{-1}{s}^{-1}$. The rate of disappearance of H₂ will be- 

1.  2.5 $\times$ 10${}^{-4}$ mol L${}^{-1}$ s${}^{-1}$

2. 1.25 $\times$ 10${}^{-4}$ mol L${}^{-1}$ s${}^{-1}$ 

3. 3.75 $\times$ 10${}^{-4}$ molL${}^{-1}$ s${}^{-1}$

4. 5.00 $\times$ 10${}^{-4}$ mol L${}^{-1}$ s${}^{-1}$

Whcih of the following represents the expression for 3/4th life of a first order reaction?

1. $\frac{K}{2.303}\log \frac{4}{3}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.$<mspace\; width="1em"></mspace>\frac{2.303}{K}\log \frac{3}{4}$

3. $<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\frac{2.303}{K}\log 4<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4. $<mspace\; width="1em"></mspace>\frac{2.303}{K}\log 3$

The hydrolysis of ester is alkaline medium is a 

(1) 1st order reaction with molecularity 1 

(2) 1 st order reaction with molecularity 2 

(3) 2nd order reaction with molecularity 1 

(4) 2nd order reaction with molecularity 2 

The rate constant is given as \(K = 1.2 \times 10^3~mol^{-1} L^{-1} s^{-1}\), and the activation energy is \(E_a = 2.0 \times 10^2 ~kJ mol^{-1}\). As temperature T approaches infinity, what is the value of the pre-exponential factor (A)?

1. \(2.0 \times 10^2 \mathrm{~mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
2. \(1.2 \times 10^3 \mathrm{~mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
3. \(3.3 \times 10^3 \mathrm{~mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
4. \(2.4 \times 10^3 \mathrm{~mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)

The reate constant for a reaction $2\times {10}^{-2}{s}^{-1}$at 300K and $8\times {10}^{-2}s-1$ at 340K. The

energy of activation of the  reaction is 

1. 14.695 KJ mol${}^{-1}$

2.  29.39 KJ mol${}^{-1}$ 

3. 44 KH mol${}^{-1}$

4. 22 KJ mol${}^{-1}$ 

For an endothermic reaction, where $∆$H represents the enthalpy of the reaction in KJ/mol, the minimum value for the energy of activation will be 

1. Less the $∆$H 

2. Zero 

3. More than $∆$H 

4. Equal to $∆$H 

If the temperature coefficient of a reaction is 3, to what factor the rate of raction

increases increase when temperature is increased from 30$°$ C to 60$°$ C?

1. 3

2. 6

3. 9 

4. 27

A first-order reaction is 15 % completed in 20 minutes. The amount of time required to complete 60 % of the reaction is:

For the zero-order reaction A$\to$ B + C; initial concentration of A is 0.1 M. If A = 0.08 M after 10 minutes, then it's half-life and completion time are respectively:

1. 10 min; 20 min

2. 2x${10}^{-3}$ m; 4x${10}^{-3}$ min;

3. 25 min, 50 min

4. 250 min, 500 min

$A{c}^{227}$ 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