Calculate the time after which the concentrations of substances A and B become equal if [A₀] = 4[B₀]. Both undergo first-order decay with half-lives of 5 min and 15 min, respectively.

1.  15 minutes                                        

2.  10 minutes

3.  5 minutes                                          

4.  12 minutes

The following data were obtained during the first-order thermal decomposition of $S{O}_{2}C{l}_2$ at a constant volume.

SO₂Cl₂(g) → SO₂(g) + Cl₂(g)

The rate of the reaction when total pressure is 0.65 atm will be:

1. $7.8$ $\times$ ${10}^{-4}$ $s^{-1}$ $atm.$                                  

2. $0.8$ $\times$ ${10}^{-4}$ $s^{-1}$ $atm.$

3. $2.4$ $\times$ ${10}^{-2}$ $s^{-1}$ $atm.$                                   

4. $6.1$ $\times$ ${10}^{-8}$ $s^{-1}$ $atm.$

Assertion : A lump of coal burns at a moderate rate in air while coal dust burns explosively.

Reason : Coal dust contains very fine particles of carbon.

Assertion : Liquid bromine reacts slowly as compared to bromine vapour.

Reason : In liquid bromine, the bromine molecules are held together by a force which is much weaker than the force existing between the two molecules of bromine in the vapour phase.

Assertion : The reaction,

$N_2<mspace\; width="1em"></mspace>\left(10atm\right)<mspace\; width="1em"></mspace>3H_2<mspace\; width="1em"></mspace>\left(10atm\right)\to <mspace\; width="1em"></mspace>2N{H}_3<mspace\; width="1em"></mspace>\left(g\right)<mspace\; width="1em"></mspace>is<mspace\; width="1em"></mspace>faster.$

Reason : Catalyst lowers the activation energy of the reaction.

1.  Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
2.  Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
3.  Assertion is true, but Reason is false.
4.  Assertion is false, but Reason is true.

Assertion : For a first order reaction, the degree of dissocation is equal to $\left(1-e^{-kt}\right)$

Reason  : For a first order reaction, the pre-exponential factor in the Arrhenius equation has the dimension of $tim{e}^{-1}$

At 400 K, the energy of activation of a reaction is decreased by 0.8 kcal in the presence of a catalyst. As a result, the rate will be:

If $∆\mathrm{H}$ of a reaction is 100 kJ mol^-1, then the activation energy for the forward reaction must be :

1. Greater than 100 kJ mol^-1

2. Less than 100 kJ mol^-1

3. Equal to 100 kJ mol^-1

4. None of the above.

The half-life for radioactive decay of ${}^{14}C$ is 5730 y. An archaeological artifact containing wood had only 80 % of the ${}^{14}C$ found in a living tree. The age of the sample will be:

1. 1657.3 y                                                

2. 1845.4 y

3. 1512.4 y                                                

4. 1413.1 y