Consider the following statements in respect of zero order reaction.

I. The rate of the reaction is independent of reactant concentration.

II. The rate of the reaction is independent of temperature.

III. The rate constant of the reaction is independent of temperature.

IV. The rate constant of the reaction is independent of reactant concentration.

Choose the correct statement/s

• I only

• I and II only

• I and IV only

• I and III only

Half-lives of a first order and a zero order reactions are same. Then, the ratio of the initial rates of first order reaction to that of the zero order reaction is

• 1/0.693

• 2 ×0.693

• 0.693

• 6.93

Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of- uranium-238 with a half-life of 4.5 × 10⁹ yr. What would be the age of a rock sample originally lead free in which the molar proportion of uranium to lead is now 1 : 3?

• 1.5 × 10⁹ yr

• 2.25 × 10⁹ yr

• 4.5 × 10⁸ yr

• 9.0 × 10⁹ yr

104.

The activation energies of two reactions are E₁ and E_{2 (}E₁ > E₂). If the temperature of the system is increased from T₁ to T₂, the rate constant of the reactions changes from k₁ to k${}_1^{\text{'}}$ in the first reaction and k₂ to k${}_2^{\text{'}}$ in the second reaction. Predict which of the following expression is

• $\frac{{\mathrm{k}}_1^{\text{'}}}{{\mathrm{k}}_1} = \frac{{\mathrm{k}}_2^{\text{'}}}{{\mathrm{k}}_2}$

• $\frac{{\mathrm{k}}_1^{\text{'}}}{{\mathrm{k}}_1} > \frac{{\mathrm{k}}_2^{\text{'}}}{{\mathrm{k}}_2}$

• $\frac{{\mathrm{k}}_1^{\text{'}}}{{\mathrm{k}}_1} < \frac{{\mathrm{k}}_2^{\text{'}}}{{\mathrm{k}}_2}$

• $\frac{{\mathrm{k}}_1^{\text{'}}}{{\mathrm{k}}_1} = \frac{{\mathrm{k}}_2^{\text{'}}}{{\mathrm{k}}_2}$

A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table

Time (days)	% reactant reamianing
0	100
2	50
4	39
6	25
8	21
10	18
12	15
14	12.5
15	10

Which one of the following best describes the order and the half-life of the reaction?

• First - 2

• First - 6

• Second - 2

• Zero - 6

Two radioactive elements X and Y have half-lives of 6 min and 15 min respectively. An experiment starts with 8 times as many atoms of X as Y. How long it takes for the number of atoms of X left equals the number of atoms of Y left ?

• 6 min

• 12 min

• 48 min

• 30 min

For a zero order reaction, the plot of concentration of reactant vs time is (intercept refers to concentration axis)

• linear with +ve slope and zero intercept

• linear with -ve slope and zero intercept

• linear with-ve slope and non-zero intercept

• linear with +ve slope and non-zero intercept

For the two gaseous reactions, following data are given

           A → B;   k₁ = 10¹⁰ e^-20,000/T

           C → D;  k₂ = 10¹² e^-24,606/T

the temperature at which k₁ becomes equal to k₂

• 400 K

• 1000 K

• 800 K

• 1500 K

At 500 K, the half-life period of a gaseous reaction at an initial pressure of 80 kPa is 350 s. When the pressure is 40 kPa, the half-life period is 175 s. The order of the reaction is

• zero

• one

• two

• three

The radioactive isotope of caesium -137 of weight 8 g was collected on 1^st February, 2006 and kept in a sealed tube. On 1^st July 2006 it was found that only 0.25 g of it remained. The half-life period of the isotope is

• 37.5 day

• 30 day

• 25 day

• 50 day