Q.1. During the nuclear explosion, one of the products is ^{90}Sr with halflife of 6.93 years. If 1 µg of ^{90}Sr was absorbed in the bones of a newly bom baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically? (2020)
Ans. (23.03)
Given, halflife of ^{90}Sr = 6.93 year; amount = 1 × 10^{–6}g
From the first order kinetic
For 90% decay of ^{90}Sr,
⇒ t = 23.03 log 10
⇒ t = 23.03 years
Q.2. For the reaction
2H_{2}(g) + 2NO(g) → N_{2}(g) + 2H_{2}O(g),
the observed rate expression is, rate =. The rate expression for the reverse reaction is (2020)
(1) k_{b}[N_{2}][H_{2}O]^{2}
(2)
(3) k_{b} [N_{2}][H_{2}O]
(4)
Ans. (4)
Given, rate expression for reaction,
2H_{2} (g) + 2NO(g) → N_{2}(g) + 2H_{2}O(g)
r_{f}=k_{f}[NO]^{2}[H_{2}]
Now,
⇒
Rearranging the above equation,
=> r_{f} = r_{b}
Q.3. The rate of a certain biochemical reaction at physiological temperature (T) occurs 10^{6 }times faster with enzyme than without it. The change in the activation energy upon adding enzyme is (2020)
(1) −6(2.303)RT
(2) −6RT
(3) +6(2.303)RT
(4) +6RT
Ans. (1)
From Arrhenius equation without enzyme
(1)
With enzyme
(2)
On Dividing Eq. (1) by (2), we get
⇒ (2)
Taking log of Eq. (3), we get
E'_{a}  E_{a }=  6(2.303)RT
Q.4.Consider the following plots of rate constant versus 1/T for four different reactions. Which of the following orders is correct for the activation energies of these reactions? (2020)
(1) E_{b} > E_{a} > E_{d} > E_{c}
(2) E_{a} > E_{c} > E_{d} > E_{b}
(3) E_{c} > E_{a} > E_{d} > E_{b}
(4) E_{b} > E_{d} > E_{c} > E_{a}
Ans. (3)
From Arrhenius equation without enzyme
Taking log of Eq. (1), we get
By plotting log k against 1/T, the slope = and intercept = log A
From the graph of four different reaction,
The plot having high value of slop will have high value of activation energy. Thus, the correct order for activation energy of the reactions is: E_{c} > E_{a} > E_{d} > E_{b}.
Q.5. For the following reactions
it was found that the E_{a} is decreased by 30 kJ mol^{–1} in the presence of catalyst. If the rate remains unchanged, the activation energy for catalyzed reaction is (Assume pre exponential factor is same) (2020)
(1) 75 kJ mol^{–1}
(2) 105 kJ mol^{–1}
(3) 135 kJ mol^{–1}
(4) 198 kJ mol^{–1}
Ans. (1)
Given, E_{al} = E_{a} and E_{a2} = E_{a}  30
T_{1} = 700 K and T_{2} = 500 K
(1) [Given, Rate remains unchanged]
Substituting the values in Eq. (1), we get
⇒ 500E_{a} = 700E_{a}  2100
⇒ 2100 = 700E_{a}  500E_{a}
⇒ 2100 = 200E_{a}
⇒_{}
⇒ E_{a} = 105 KJ mol^{1}
Thus, activation energy in presence of catalyst is Ea_{2} = E_{a } 30
⇒ E_{a2} = 105  30 = 75 kJ mol^{1}
Q.6. A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ mol^{−1}) for this process is closest to ________. (2020)
Ans. (3.98)
Using Arrhenius equation at two different temperature,
(1)
Since, milk splits after 60 min. at 300 K and after 40 min. at 400 K.
Substituting the values in Eq. (1), we get
⇒ E_{a} = 3.984 kJ mol^{−1}
Q.7. The following results were obtained during kinetic studies of the reaction;
2A + B → Products
The time (in minutes) required to consume half of A is: (2019)
(1) 5
(2) 10
(3) 1
(4) 100
Ans. (1)
Q.8. For the reaction, 2A + B → products, when the concentrations of A and B both were doubled, the rate of the reaction increased from 0.3 mol L^{1}s^{1} to 2.4 mol L^{1}s^{1}. When the concentration of A alone is doubled, the rate increased from 0.3 L^{1}s^{1} to 0.6 mol L^{1}s^{1}. Which one of the following statements is correct? (2019)
(1) Total order of the reaction is 4
(2) Order of the reaction with respect to B is 2
(3) Order of the reaction with respect to B is 1
(4) Order of the reaction with respect to A is 2
Ans. (2)
∴ y = 2
Q.9. Consider the given plots for a reaction obeying Arrhenius equation (0°C < T < 300°C): (K and E_{a} are rate constant and activation energy, respectively)
Choose the correct option: (2019)
(1) I is right but II is wrong
(2) Both I and II are correct
(3) I is wrong but II is right
(4) Both I and II are wrong
Ans. (2)
From Arrhenius equation,
K= Ae^{Ea/RT}
So, as E_{a} increases, e^{Ea/RT} decreases, K decreases and as T increases, E_{a}/RT decreases, e^{Ea/RT} increases,
Q.10. For an elementary chemical reaction, the expression for d[A]/dt is: (2019)
(1) k_{1}[A_{2}]  k_{1}[A]^{2}
(2) 2k_{1}[A_{2}]  k_{1}[A]^{2}
(3) k_{1} [A_{2}] + k_{1}[A]^{2}
(4) 2k_{1}[A_{2}]  2k_{1}[A]^{2}
Ans. (4)
⇒
Q.11. If a reaction follows the Arrhenius equation, the plot lnk vs 1/(RT) gives straight line with a gradient (y) unit. The energy required to activate the reactant is: (2019)
(1) y/R unit
(2) y unit
(3) yR unit
(4)  y unit
Ans. (2)
From Arrhenius equation,
slope = y (given)
y = Ea
⇒ E_{a} = y
Q.12. The reaction 2X → B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the halflife is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be: (2019)
(1) 9.0 h
(2) 12.0 h
(3) 18.0 h
(4) 7.2 h
Ans. (3)
For zero order reaction
t=18 hrs
Q.13. Decomposition of X exhibits a rate constant of 0.05 μg/year. How many years are required for the decomposition of 5 μg of X into 2.5 μg? (2019)
(1) 50
(2) 25
(3) 20
(4) 40
Ans. (1)
Rate constant of decomposition of X= 0.05 mg/year. Unit of rate constant confirms that the decomposition of X is a zero order reaction.
For zero order kinetics,
Q.14. For a reaction, consider the plot of In k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10^{5} s^{1}, then the rate constant at 500 K is: (2019)
(1) 10^{6} s^{1}
(2) 2 x 10^{4} s^{1}
(3) 10^{4} s^{1}
(4) 4 x 10^{4} s^{2}
Ans. (3)
From Arrhenius equation,
Q.15. For the reaction 2A + B → C, the values of initial rate at different reactant concentrations are given in the table below.
The rate law for the reaction is: (2019)
(1) Rate = k[A][B]^{2}
(2) Rate = k[A]^{2}[B]^{2}
(3) Rate = k[A][B]
(4) Rate = k[A]^{2}[B]
Ans. (1)
2A + B → C
Rate = k[A]^{x} [B]^{y}
Exp1, 0.045 = k[0.05]^{x} [0.05]^{y} ...(i)
Exp2, 0.090 = k[0.1]^{x} [0.05]^{y} ...(ii)
Exp3, 0.72 = k[0.2]^{x} [0.1]^{y} ...(iii)
Divide equation (i) by equation (ii)
Divide equation (i) by equation (iii)
Rate law = k[A]^{1} [B]^{2}.
Q.16. For a reaction scheme if the rate of formation of B is set to be zero then the concentration of B is given by: (2019)
(1) (k_{1}  k_{2}) [A]
(2) k_{1}k_{2} [A]
(3) (k_{1} + k_{2}) [A]
(4) (k_{1}/k_{2}) [A]
Ans. (4)
Q.17. The given plots represents the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are: (2019)
(1) 1, 0
(2) 1, 1
(3) 0, 1
(4) 0, 2
Ans. (1)
For First order reaction
Q.18. A bacterial infection in an internal wound grows as N^{2}(t) = N_{0} exp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as dN/dt = 5N^{2}. What will be the plot of N_{0}/N vs. t after 1 hour? (2019)
(1)
(2)
(3)
(4)
Ans. (3)
When drug is administered bacterial growth is given by dN/dt = 5N^{2}
On integrating the above equation,
The above equation is similar to straight line equation with positive slope.
Thus N_{0}/N_{t} increases linearly with t.
Q.19. For the reaction of H_{2} with I_{2}, the rate constant is 2.5 x 10^{4} dm^{3} mol^{1} s^{1} at 327°C and 1.0 dm^{3} mol^{1} s^{1} at 527°C. The activation energy for the reaction, in kJ mol^{1} is: (R = 8.314J K^{1} mol^{1}) (2019)
(1) 166
(2) 150
(3) 72
(4) 59
Ans. (1)
Q.20. In the following reaction: xA → yB
‘A' and ‘B’ respectively can be: (2019)
(1) nButane and Isobutane
(2) C_{2}H_{2} and C_{6}H_{6}
(3) C_{2}H_{4} and C_{4}H_{8}
(4) N_{2}O_{4} and NO_{2}
Ans. (3)
xA → yB
Comparing this equation with the equation given in question. We get,
∴ x/y = 2
∴ The reaction is of type 2A → B.
Hence, option (3) is correct.
Q.21. NO, required for a reaction is produced by the decomposition of N_{2}O_{5} in CCl_{4} as per the equation,
2N_{2}O_{5}(g) → 4NO_{2}(g) + O_{2}(g).
The initial concentration of N_{2}O_{5} is 3.00 mol L^{1} and it is 2.75 mol L^{1} after 30 minutes. The rate of formation of NO_{2} is: (2019)
(1) 4.167 x 10^{3} mol L^{1} min^{1}
(2) 1.667 x 10^{2} mol L^{1} min^{1}
(3) 8.333 x 10^{3} mol L^{1} min^{1}
(4) 2.083 x 10^{3} mol L^{1} min^{1}
Ans. (2)
According to the question
Q.22. At 518^{0}C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.00 Torr s^{1} when 5% had reacted and 0.5 Torr s^{1} when 33% had reacted. The order of the reaction is: (2018)
(1) 2
(2) 3
(3) 1
(4) 0
Ans. (1)
Q.23. N_{2}O_{5} decomposes to NO_{2} and O_{2} and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mm Hg to 87.5 mm Hg. The pressure of the gaseous mixture after 100 minute at constant temperature will be: (2018)
(1) 106.25 mm Hg
(2) 116.25 mm Hg
(3) 136.25 mm Hg
(4) 175.0 mm Hg
Ans. (1)
2N_{2}O_{5} → 4NO_{2} + O_{2}
p − 2x 4x x
p_{t} = p − 2x + 4x + x
p_{t} = p + 3x
at t = 0, pt = p = 50 mm Hg
at t = 50 mm, p_{t} = 87.5 mm Hg
p + 3x = 87.5
p = 87.5 − 3x
50 = 87.5 − 3x
12.5 = x
p − 2x = 50 − 2(12.5) = 25
Since K will remain same
50 = 50 × 4 − 8y
50 = 200 − 8y
8y = 150
y = 18.75
pt = p + 3y
= 50 + 3 (18.73) = 106.25 mm Hg
Q.24. If 50 % of a reaction occurs in 100 second and 75 % of the reaction occurs in 200 second, the order of this reaction is: (2018)
(1) 2
(2) 3
(3) Zero
(4) 1
Ans. (4)
First order reaction as half life is constant.
Q.25. Two reactions R_{1} and R_{2} have identical pre  exponential factors. Activation energy of R_{1 }exceeds that of R_{2 }by 10 kJ mol^{–1}. If k_{1} and k_{2} are rate constants for reactions R_{1} and R_{2} respectively at 300 K, then ln (k_{1}/ k_{2}) is equal to
(R = 8.314 J mole^{–1} K^{–1}) (2017)
(1) 8
(2) 12
(3) 6
(4) 4
Ans. (4)
Q.26. The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A. (2017)
(1) 4.92 K
(2) 9.84 K
(3) 19.67 K
(4) 2.45 K
Ans. (1)
...(i)
...(ii)
= 304.92
Q.27. The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is:
(Assume activation energy and preexponential factor are independent of temperature; ln 2 = 0.693; R = 8.314 J mol^{1} K^{1}) (2017)
(1) 53.6 kJ mol^{1 }
(2) 214.4 kJ mol^{1 }
(3) 107.2 kJ mol^{1}
(4) 26.8 kJ mol^{1}
Ans. (3)
= 107165.79 J = 107.165 KJ
Q.28. Decomposition of H_{2}O_{2} follows a first order reaction. In fifty minutes the concentration of H_{2}O_{2} decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of H_{2}O_{2} reaches 0.05 M, the rate of formation of O_{2} will be: (2016)
(1) 6.93 x 10^{2} mol min^{1}
(2) 6.93 x 10^{4} mol min^{1}
(3) 2.66 L min^{1} at STP
(4) 1.34 x 10^{2} mol min^{1}
Ans. (2)
For a first order reaction
K = 2.303/t log a/(ax)
Given a = 0.5, (ax) = 0.125, t = 50 min
∴ k = 2.303/50 log 0.5/0.125
= 2.78 x 10^{2} min^{1}
r = d[H_{2}O_{2}] = 2.78 x 10^{2} x 0.05
= 1.386 x 10^{3} mol min^{1}
Now
Q.29. The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process show below:
O_{3}(g) + Cl*(g) → O_{2}(g) + ClO*(g) ...(i)
k_{i} = 5.2 × 10^{9} L mol^{1} s^{1}
ClO*(g) + O*(g) → O_{2}(g) + Cl*(g) ...(ii)
[K_{ii} = 2.6 x 10^{10} L mol^{1}s^{1}]
The closest rate constant for the overall reaction O_{3}(g) + O*(g) → 2O_{2}(g) is: (2016)
(1) 1.4 × 10^{20} L mol^{1} s^{1}
(2) 5.2 × 10^{9} L mol^{1} s^{1}
(3) 3.1 × 10^{10} L mol^{}^{1 }s^{}^{1}
(4) 2.6 × 10^{10} L mol^{1} s^{1}
Ans. (2)
The rate constant of overall reaction depends slowest step. Hence equation(i) is slowest step. Option(2) is correct.
Q.30. The rate law for the reaction below is given by the expression k [A][B]
A + B → Product
If the concentration of B is increased from 0.1 to 0.3 mole, keeping the value of A at 0.1 mole, the rate constant will be: (2016)
(1) 9 k
(2) 3 k
(3) k/3
(4) k
Ans. (4)
Rate constant is independent of concentration.
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