The average rate of reaction between the time interval of 30 to 60 seconds in the below mentioned pseudo-first-order reaction is:

t/s	0	30	60	90
[Ester]/mol L–1	0.55	0.31	0.17	0.085

$1.$ $6.67$ $\times {10}^{-2}$ $\mathrm{mol}$ ${\mathrm{L}}^{-1}$ ${\mathrm{s}}^{-1}$
$2.$ $2.67$ $\times$ ${10}^{-4}$ $\mathrm{mol}$ ${\mathrm{L}}^{-1}$ ${\mathrm{s}}^{-1}$ $$
$3.$ $4.67$ $\times$ ${10}^{-3}$ $\mathrm{mol}$ ${\mathrm{L}}^{-1}$ ${\mathrm{s}}^{-1}$
$4.$ $4.27$ $\times$ ${10}^3$ $\mathrm{mol}$ ${\mathrm{L}}^{-1}$ ${\mathrm{s}}^{-1}$

A reaction is first-order with respect to A and second-order with respect to B. If the concentration of B is tripled while that of A remains constant, how will the rate of the reaction change?

In a reaction between A and B, the initial rate of reaction (r₀) was measured for different initial concentrations of A and B as given below:

The order of the reaction with respect to A and B would be:

For a reaction, 2A + B → C + D, the following observations were recorded:

The rate law applicable to the above mentioned reaction would be:

1. Rate = k[A]²[B]³

2. Rate = k[A][B]²

3. Rate = k[A]²[B]  

4. Rate = k[A][B]  

Given the following observations:

The reaction between A and B is first-order with respect to A and zero-order with respect to B. The values of X and Y are, respectively:

1. X = 0.2 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 08\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

2. X = 0.02 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 08\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

3. X = 0.01 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 8\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

4. X = 0.2 \(mol\) \(L^{- 1}\); Y = \(\) \(0 . 8\) \(mol\) \(L^{- 1} \left(min\right)^{- 1}\)

A radioactive substance has a rate constant of \(4 \, \text{years}^{-1}\). What is its half-life?

1. 0.05 years

2. 0.17 years

3. 0.26 ${\mathrm{years}}^{-1}$

4. 1.6 years

During a nuclear explosion, one of the products is ⁹⁰Sr with a half-life of 28.1 years. If 1µg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, the amount of ⁹⁰Sr that will remain after 10 years in the now grown up child would be -

(Given ,antilog(0.108)=1.28)

1. 0.227 µg 

2. 0.781 µg 

3. 7.81 µg 

4. 2.27 µg 

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data was obtained:

The rate constant of the above reaction would be:

For the reaction 2A + B → A₂B, the rate law is rate = k[A][B]², where k = 2.0 × 10⁻⁶ mol⁻² L² s⁻¹,
[A] = 0.1 M, and [B] = 0.2 M. What is the initial rate of the reaction?
1. \(\begin{aligned} & 0.04 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\\ \end{aligned}\)
2. \( 8 \times 10^{-8} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1} \)
3. \(8 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)
4. \( 8 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\)

What is the ratio of the time required for 99% completion to the time required for
90% completion of a first-order reaction?
1. \(t_{99 \%}=3 t_{90 \%}\)
2. \(t_{99 \%}=2 t_{90 \%}\)
3. \(t_{99 \%}=4 t_{90 \%}\)
4. \(t_{90 \%}=2 t_{99 \%}\)