The rate constants k₁ and k₂ for two different reactions are 10¹⁶. e^-2000/T and 10¹⁵. e^-1000/T, respectively. The temperature at which k₁= k₂ is:

1. $1000$ $\mathrm{K}$

2. $\frac{2000}{2.303}$ $\mathrm{K}$

3. $2000$ $\mathrm{K}$

4. $\frac{1000}{2.303}$ $\mathrm{K}$

The bromination of acetone occurring in an acid solution is represented by the equation. 
CH₃COCH₃(aq)+ Br₂(aq) → 
CH₃COCH₂Br(aq) + H⁺(aq) + Br^-(aq) 

The kinetic energy data were obtained for given reaction concentrations. 
Initial concentrations, M 
 $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$   $\left[{\mathrm{Br}}_2\right]$    $\left[{\mathrm{H}}^{+}\right]$

   0.30             0.05      0.05

   0.30             0.10      0.05

   0.30             0.10      0.10

   0.40             0.05      0.20
Initial rate, the disappearance of Br₂, Ms^-1 
5.7 $\times$ 10^-5

5.7 $\times$  10^-5

1.2 $\times$ 10^-4

3.1 $\times$ 10^-4
Based on the above data, the rate of the equation is:

1. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{H}}^{+}\right]$

2. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[\mathrm{CH}={\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$

3. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$ ${\left[{\mathrm{H}}^{+}\right]}^2$

4. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$ $\left[{\mathrm{H}}^{+}\right]$

The reaction of hydrogen and iodine monochloride is given as: 
H₂(g) + 2ICl(g) → 2HCl(g) + I₂(g) 
This reaction is of first order with respect to H₂(g) and ICl(g), for which of the following proposed mechanisms:
Mechanism A: 
H₂(g) + 2ICl(g) → 2HCl(g) + I₂(g) 
Mechanism B: 
H₂(g) + ICl(g) →HCl(g) + HI(g); slow 
HI(g) + ICl(g) →HCl(g) + I₂(g); fast

1. B Only

2. A and B both

3. Neither A nor B

4. A only

In a first order reaction A \(\overset{                         }{\rightarrow}\) B, if k is rate constant and initial concentration of the reactant A is 0.5 M then the half-life is :

(1) \(\frac{0 . 693}{0 . 5 k}\)

(2) \(\frac{log   2}{k}\)

(3) \(\frac{log   2}{k \sqrt{0 . 5}}\)

(4) \(\frac{ln   2}{k}\)

If 60% of a first-order reaction was completed in 60 min, 50% of the same reaction would be completed in approximately: 
(log 4 = 0.60, log 5 = 0.69)

For the reaction, \(2 A+B \rightarrow 3 C+D\)

An incorrect expression for the rate of reaction is:

Consider the reaction 
N₂(g) + 3H₂(g) → 2NH₃(g) 
The equality relationship between \( \frac{{d}\left[{{NH}_{3}}\right]}{dt}\) and \( {-}\frac{{d}\left[{{H}_{2}}\right]}{dt}\) is :

1. $\frac{d\left[N{H}_3\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}$

2. $+\frac{d\left[N{H}_3\right]}{dt}=-\frac{2}{3}\frac{d\left[H_2\right]}{dt}$

3. $+\frac{d\left[N{H}_3\right]}{dt}=-\frac{3}{2}\frac{d\left[H_2\right]}{dt}$

4. $+\frac{d\left[N{H}_3\right]}{dt}=-\frac{d\left[H_2\right]}{dt}$

In the reaction, 
${\mathrm{BrO}}_3^{-}\left(\mathrm{aq}\right)+5{\mathrm{Br}}^{-}\left(\mathrm{aq}\right)+6{\mathrm{H}}^{+}\to$ 3Br₂(l)+3H₂O(l) 
The rate of appearance of bromine (Br₂) is related to the rate of disappearance of bromide ions:

1. $\frac{d\left[B{r}_2\right]}{dt}=-\frac{3}{5}\frac{d\left[B{r}^{-}\right]}{dt}$

2. $\frac{d\left[B{r}_2\right]}{dt}=-\frac{5}{3}\frac{d\left[Br\right]}{dt}$

3. $\frac{d\left[B{r}_2\right]}{dt}=\frac{5}{3}\frac{d\left[B{r}^{-}\right]}{dt}$

4. $\frac{d\left[B{r}_2\right]}{dt}=\frac{3}{5}\frac{d\left[B{r}^{-}\right]}{dt}$

For the reaction, \(\mathrm{N}_2+3 \mathrm{H}_2 \rightarrow 2 \mathrm{NH}_3,\) if, \(\frac{d[NH_{3}]}{dt} \ = \ 2\times 10^{-4} \ mol \ L^{-1} \ s^{-1}\), the value of  \(\frac{-d[H_{2}]}{dt}\) would be:

For the reaction, A + B → products, it is observed that-
(1) On doubling the initial concentration of A only, the rate of reaction is also doubled and 
(2) On doubling the initial concentrations of both A and B, there is a change by a factor of 8 in the rate of the reaction. 
The rate of this reaction is given by:

1. $rate=k$ $\left[A{]}^2\right[B]$

2. $rate=k$ $\left[A\right][B{]}^2$

3. $rate=k$ $\left[A{]}^2\right[B{]}^2$

4. $rate=k$ $\left[A\right]\left[B\right]$