Arrhenius Equation

Q. A first order reaction has a specific reaction rate of ${10}^{-2}{s}^{-1}$. How much time will take for 20 g of the reactant to reduce to 5 g?

1. 238.6 seconds
2. 693.0 seconds
3. 138.6 seconds
4. 346.5 seconds

Q. $N_2{O}_5$ decomposes according to the equation, $N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$
This is a first order reaction. A closed container has $N_2{O}_5$ and $Ne$ gases at a total pressure of 333.8 mm of Hg. Thirty minutes after $N_2{O}_5$ starts decomposing, the total pressure is found to be 384.5 mm Hg. On complete decomposition of $N_2{O}_5,$ the total pressure is 684.5 mm Hg. What is rate constant of decomposition of $N_2{O}_5$?
(Take ln(1.169) = 0.156)

1. $2.6\times {10}^{-1}{s}^{-1}$
2. $0.312s^{-1}$
3. $5.2\times {10}^{-3}{s}^{-1}$
4. $8.67\times {10}^{-5}{s}^{-1}$

Q.

The rate of a reaction decreased by $3.555$ times when the temperature was changed from ${40}^{°}\mathrm{C}\mathrm{to}30°\mathrm{C}$. The activation energy $(\mathrm{in}\mathrm{KJ}{\mathrm{mol}}^{-1})$ of the reaction is……… $[\mathrm{Take};\mathrm{R}=8.314\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1},\mathrm{In}3.555=1.268]$

Q. According to the Arrhenius equation,

1. A high activation energy usually implies a fast reaction
2. Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
3. Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant.
4. The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.

Q. The rate constants $k_1$ and $k_2$ of two reactions are in the ratio 2:1 at some temperature and 1:1 at infinite temperature. The corresponding energies of activation of the two reactions will be related by:

1. $E_1>E_2$
2. $E_1<E_2$
3. $E_1=E_2$
4. Can't say

Q. The rate constant of a reaction becomes equal to the pre-exponential factor at temperature.

1. 0 K
2. infinite
3. 1000 K

Q. Velocity constant of a reaction at 290 K was found to $3.2\times {10}^{-3}se{c}^{-1}$. When the temperature is raised to 310 K, it will be about:

1. $6.4\times {10}^{-3}$
2. $3.2\times {10}^{-4}$
3. $9.6\times {10}^{-3}$
4. $1.28\times {10}^{-2}$

Q. Which of the following is temperature dependent?

1. Rate constant
2. $E_a$
3. Rate of the reaction
4. Both rate constant and rate of the reaction

Q.

Let’s assume I want to double the rate of a reaction. The constraint is that I can only increase the temperature by 10 K. Calculate the minimum activation energy required if the temperature is 300K.

1. $64kJmo{l}^{-1}$

2. $54kJmo{l}^{-1}$

3. $94kJmo{l}^{-1}$

4. $84kJmo{l}^{-1}$

Q.

The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be:

$(R=8.314J{K}^{-1}mo{l}^{-1}andlog2=0.301)$

(IIT-JEE-2013)

1. $48.6kJmo{l}^{-1}$

2. $58.5kJmo{l}^{-1}$

3. $60.5kJmo{l}^{-1}$
4. $53.6kJmo{l}^{-1}$

Q. A first order reaction is $50\%$ complete in $30$ minutes at $27{}^{\circ }C$ and in 10 minutes at $47{}^{\circ }C$. The energy of activation $E_a$ of the reaction is:
$(log2=0.3,log3=0.5,R=\frac{25}{3}J{K}^{-1}mo{l}^{-1})$

1. 46 $kJmo{l}^{-1}$
2. 35 $kJmo{l}^{-1}$
3. 84 $kJmo{l}^{-1}$
4. 30 $kJmo{l}^{-1}$

Q. Milk turns sour at ${40}^{\circ }$C three times as faster as $0^{\circ }$C. Hence, $E_a$ in the process of turning of milk sour is

1. $\frac{2.303\times 2\times 313\times 273}{40}log3$
2. $\frac{2.303\times 2\times 313\times 273}{40}log\left(1/3\right)cal$
3. $\frac{2.303\times 2\times 40}{273\times 313}log3cal$
4. $Noneofthese$

Q.

The $\Delta H$ and $\Delta S$ for a reaction at one atmospheric pressure are +30.558 kJ and 0.066 k J $k^{-1}$ respectively. The temperature at which the free energy change will be zero and below this temperature the nature of reaction would be:

1. 483 K, spontaneous

2. 443 K, non-spontaneous

3. 443 K, spontaneous

4. 463 K, non-spontaneous

Q. The rate constant of a reaction will be equal to the pre exponential factor when:

1. Temperature in centigrade is zero
2. The absolute temperature is zero
3. The absolute temperature is infinity
4. None of these

Q. A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be $K_1$ and $K_2$ respectively then

1. $K_2\approx 0.5K_1$
2. $K_2\approx 0.25K_1$
3. $K_2\approx 2K_1$
4. $K_2\approx 4K_1$

Q. Milk turns sour at ${40}^{\circ }$C three times as faster as $0^{\circ }$C. Hence, $E_a$ in the process of turning of milk sour is

1. $\frac{2.303\times 2\times 313\times 273}{40}log3$
2. $\frac{2.303\times 2\times 313\times 273}{40}log\left(1/3\right)cal$
3. $\frac{2.303\times 2\times 40}{273\times 313}log3cal$
4. $Noneofthese$

Q. The energy of activation of a first order reaction is $187.06kJmo{l}^{-1}$ at 750 K and the value of pre-exponential factor A is $1.97\times {10}^{12}{s}^{-1}$. Calculate the half life. $(e^{-30}=9.35\times {10}^{-14})$

1. 9.76s
2. 5.76s
3. 8.76s
4. 3.76s

Q. Which of the following will increase the rate of the reaction?

1. Cooling the reaction
2. Addition of negative catalyst
3. None of the above
4. Increasing reactant concentration

Q. Which of the following is temperature dependent?

1. Rate constant
2. $E_a$
3. Rate of the reaction
4. Both rate constant and rate of the reaction

Q. Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows the Arrhenius equation is

1. 
2. 
3. 
4. 

Q. He is impressed with your work but he wants you to calculate the value of A as well. Calculate the value of A at the same conditions. (The rate constants of the reaction at 500 K and 700 K are $0.02s^{-1}$ and $0.07s^{-1}$ respectively.)

1. $1.585s^{-1}$
2. $1s^{-1}$
3. $0.5s^{-1}$
4. $0.02s^{-1}$

Q. A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the catalysed reaction if the catalyst lowers the activation energy barrier by 20 kJ/mol.

Q. A first order reaction is 50% complete in 20 minutes at $27{}^{\circ }C$ and in 5 minutes at $47{}^{\circ }C$. The energy of activation of the reaction is:

1. 43.85 kJ/mol
2. 55.14 kJ/mol
3. 11.97 kJ/mol
4. ​​​​​​6.65 kJ/mol

Q. The rate of a first order reaction gets doubled when the temperature is doubled from $T_{1}to2T_1$ (in K). $E_a$ is nearly constant activation energy at 1386 kcal. What is the value of $T_1$?
(given R=2 $cal{K}^{-1}mo{l}^{-1}$, ln2=0.693)

1. 250 K
2. 500 K
3. 1000 K
4. 750 K

Q.

For a first order reaction A ⟶ P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -2000(1/T) + 6.0. The pre-exponential factor A and the activation energy $E_a,$ respectively, are

(IIT-JEE, 2009)

1. $1.0\times {10}^6{s}^{-1}and9.2kJmo{l}^{-1}$

2. $6.0s^{-1}and16.6kJmo{l}^{-1}$

3. $1.0\times {10}^6{s}^{-1}and16.6kJmo{l}^{-1}$

4. $1.0\times {10}^6{s}^{-1}and38.3kJmo{l}^{-1}$

Q. A reversible reaction proceeds in the direction that decreases the free energy of the system. There is an important relationship between the equilibrium constant and the standard free energy of the system given by
$\text{log K}=\frac{-\Delta G^0}{2.303}\text{RT}$
This equation is applicable to all reversible processes and allows us to estimate the equilibrium constant from the standard free energy and the enthalpy change of the reaction.
Take $R=\frac{25}{3}\text{J/molK,}\frac{1}{12}\text{L atm/molk,}\ln 2=0.7,\ln 3=1.1,\ln 5=1.6,\text{log}2=0.3,\text{log 3}=0.5,log5=0.7$

The equilibrium constant for the dissociation of $N_2{O}_4$ into $N{O}_2$ is 0.125 at ${27}^{\circ }$C. What is the standard free energy change for this reaction?

1. $-5.25\text{kJ/mole}$
2. $+5.25\text{kJ/mole}$
3. $+22.50\text{kJ/mole}$
4. $-22.50\text{kJ/mole}$

Q. The specific rate for a reaction increases by a factor of 4, if the temperature is changed from $27{}^{\circ }C$ to $52{}^{\circ }C$. Find the activation energy for the reaction in $kJmo{l}^{-1}$ (Take $ln2=0.7$, R (gas const) = $\frac{25}{3}J/molK$) (Round off the answer upto two decimal places)

Q. Rate of a first order reaction becomes 4 times when temperature (in K) is doubled (assuming the initial concetration same for both cases) having almost constant activation energy of 1.386 kcal. Find the value of $T_1$ (in K)?

Q. Consider the following reversible reaction.
$A\left(g\right)+B\left(g\right)\to AB\left(g\right)$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT\left(Jmo{l}^{-1}\right)$. If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of $\Delta G^o\left(Jmo{l}^{-1}\right)$ for the reaction at $300K$ is .
$(Given:ln2=0.7;RT=2500Jmo{l}^{-1}\text{at 300 K; G is Gibbs energy})$