The activation energies of two reactions are ${\mathrm{E}}_{{\mathrm{a}}_1}$ and ${\mathrm{E}}_{{\mathrm{a}}_2}$ with  ${\mathrm{E}}_{{\mathrm{a}}_1}$ > ${\mathrm{E}}_{{\mathrm{a}}_2}$.
f the temperature of the reacting system is increased from T₁ to T₂ .
The correct relation is: 

1. $\frac{{\mathrm{K}}_1\text{'}}{{\mathrm{K}}_1}=\frac{{\mathrm{K}}_2\text{'}}{{\mathrm{K}}_2}$         

2. $\frac{{\mathrm{K}}_1\text{'}}{{\mathrm{K}}_1}>\frac{{\mathrm{K}}_2\text{'}}{{\mathrm{K}}_2}$

3. $\frac{{\mathrm{K}}_1\text{'}}{{\mathrm{K}}_1}<\frac{{\mathrm{K}}_2\text{'}}{{\mathrm{K}}_2}$         

4. $\frac{{\mathrm{K}}_1\text{'}}{{\mathrm{K}}_1}<2\frac{{\mathrm{K}}_2\text{'}}{{\mathrm{K}}_2}$

The units of rate constant and rate of reaction are same for :
1. First order reaction
2. Second order reaction
3. Third order reaction
4. Zero order reaction

The plot of log k vs $\frac{1}{\mathrm{T}}$ helps to calculate : 

1. Energy of activation.
2. Rate constant of reaction.
3. Order of the reaction.
4. Energy of activation as well as the frequency factor.

Rate constant K = 1.2×10³ mol^–1 L s^–1 and E_a = 2.0×10² kJ mol^–1. When T $\to \infty$ , A is equal
to
1. 2.0 × 10² kJ mol^–1
2. 1.2 × 10³ mol^–1L s^–1
3. 1.2 × 10³ mol L^–1 s^–1
4. 2.4 × 10³ kJ mol^–1L s^–1

The rate constant for a reaction 2×10^–2 s^–1 at 300 K and 8×10^–2 s^–1 at 340 K. The energy of activation of the reaction is:

1. 14.69 kJ mol^–1

2. 29.39 kJ mol^–1

3. 44.34 kJ mol^–1

4. 22.05 kJ mol^–1

The reaction 2A + B + C $\to$ D + E is found to be a first-order reaction with respect to A, second-order reaction with respect to B, and zero-order reaction with respect to C. If the concentrations of A, B, and C are doubled, the rate of the reaction will be:

1. 72 times

2. 8 times

3. 24 times

4. 36 times

$$\begin{gathered} \mathrm{For} \mathrm{first}-\mathrm{order} \mathrm{parallel} \mathrm{reaction} {\mathrm{k}}_1 \mathrm{and} {\mathrm{k}}_2 \mathrm{are} 4 \mathrm{and} 2 {\min }^{-1} \mathrm{respectively} \mathrm{at} 300 \mathrm{K}. \mathrm{If} \mathrm{the} \mathrm{activation} \mathrm{energies} \mathrm{for} \mathrm{the} \\ \mathrm{formation} \mathrm{of} \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{are} \mathrm{respectively} 30,000 \mathrm{and} 38,314 J/\mathrm{mol} \mathrm{respectively}. \\ \mathrm{The} \mathrm{temperature} \mathrm{at} \mathrm{which} \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{will} \mathrm{be} \mathrm{obtained} \mathrm{in} \mathrm{the} \mathrm{equimolar} \mathrm{ratio} \mathrm{is} : \end{gathered}$$

1.  757.48 K

2.  378.74 K

3.  600.91 K

4.  None of the above 

$$\begin{gathered} \mathrm{For} \mathrm{reaction} \mathrm{A} \stackrel{}{\to } \mathrm{B}, \mathrm{the} \mathrm{rate} \mathrm{constant} {\mathrm{k}}_1 = {\mathrm{A}}_1 {\mathrm{e}}^{-{\mathrm{E}}_{{\mathrm{a}}_1}/\left(\mathrm{RT}\right)} \mathrm{and} \mathrm{for} \mathrm{the} \mathrm{reaction} \mathrm{X}\to \mathrm{y}, \mathrm{the} \mathrm{rate} \mathrm{constant} {\mathrm{k}}_2={\mathrm{A}}_2{\mathrm{e}}^{-{\mathrm{E}}_{{\mathrm{a}}_2}/\left(\mathrm{RT}\right)}. \\ \mathrm{If} {\mathrm{A}}_1={10}^8 {\mathrm{A}}_2={10}^{10} and {\mathrm{E}}_{{\mathrm{a}}_1}=600 \mathrm{cal}/\mathrm{mol}, {\mathrm{E}}_{{\mathrm{a}}_2} = 1800 \mathrm{cal}/\mathrm{mol}, \\ \mathrm{then} \mathrm{the} \mathrm{temperature} \mathrm{at} \mathrm{which} {\mathrm{k}}_1 = {\mathrm{k}}_2 \mathrm{is} \left( \mathrm{given} : \mathrm{R} = 2 \mathrm{cal}/\mathrm{K}-\mathrm{mol}\right) \end{gathered}$$

1.  $1600 \mathrm{K}$

2.  $1200 \mathrm{x} 4.606 \mathrm{K}$

3.  $\frac{1200}{4.606} \mathrm{K}$

4.  $\frac{600}{4.606} \mathrm{K}$

$$\begin{gathered} \mathrm{A} \mathrm{reaction} \mathrm{takes} \mathrm{place} \mathrm{in} \mathrm{various} \mathrm{steps}. \mathrm{The} \mathrm{rate} \mathrm{constant} \mathrm{for} \mathrm{first}, \mathrm{second}, \mathrm{third}, \mathrm{and} \mathrm{fifth} \mathrm{step} \mathrm{are} {\mathrm{k}}_1, {\mathrm{k}}_2, {\mathrm{k}}_3 \\ \mathrm{and} {\mathrm{k}}_5 \mathrm{respectively}. \mathrm{The} \mathrm{overall} \mathrm{rate} \mathrm{constant} \mathrm{is} \mathrm{given} \mathrm{by} \\ \mathrm{k} = \frac{{\mathrm{k}}_2}{{\mathrm{k}}_3} {\left(\frac{{\mathrm{k}}_1}{\mathrm{k}5}\right)}^{1/2} \\ \mathrm{If} \mathrm{activation} \mathrm{energy} \mathrm{are} 40, 60, 50, \mathrm{and} 10 \mathrm{kJ}/\mathrm{mol} \mathrm{respectively}, \mathrm{the} \mathrm{overall} \mathrm{energy} \mathrm{of} \mathrm{activation} \left(\mathrm{kJ}/\mathrm{mol}\right) \\ \mathrm{is}: \end{gathered}$$

1.  10

2.  20

3.  25

4.  None of the above

$\mathrm{Consider} \mathrm{the} \mathrm{reaction}.$

$$\begin{gathered} \mathrm{The} \mathrm{rate} \mathrm{constant} \mathrm{for} \mathrm{two} \mathrm{parallel} \mathrm{reactions} \mathrm{were} \mathrm{found} \mathrm{to} \mathrm{be} {10}^{-2} {\mathrm{dm}}^3 {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1} \mathrm{and} \\ 4 \mathrm{x} {10}^{-2} {\mathrm{dm}}^3 {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1}. \mathrm{If} \mathrm{the} \mathrm{corresponding} \mathrm{energies} \mathrm{of} \mathrm{activation} \mathrm{of} \mathrm{the} \mathrm{parallel} \mathrm{reaction} \\ \mathrm{are} 100 \mathrm{and} 120 KJ/ \mathrm{mol} \mathrm{respecctively}, \mathrm{the} \mathrm{net} \mathrm{energy} \mathrm{of} \mathrm{activation} \left({\mathrm{E}}_{\mathrm{a}}\right) \mathrm{of} \mathrm{A} \mathrm{is} \end{gathered}$$

1.  100 kJ/mol

2.  120 kJ/mol

3.  116 kJ/mol

4.  220 kJ/mol