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 At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature.
  • a)
    k1 will increase faster than k2, but always will remain less than k2.
  • b)
    k2 will increase faster than k1
  • c)
    k1 will increase faster than k2 and becomes equal to k2.
  • d)
    k1 will increase faster k2 and becomes greater than k2.
Correct answer is option 'A'. Can you explain this answer?
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Introduction:
The rate constant is a measure of the speed of a chemical reaction. It is influenced by factors such as temperature and activation energy. In this question, we are given that the first order rate constant (k1) is smaller than the second order rate constant (k2) at a certain temperature. We are also told that the energy of activation (E1) for the first order reaction is greater than the energy of activation (E2) for the second order reaction. We need to determine how these rate constants will change with an increase in temperature.

Explanation:
When the temperature is increased, the rate constant for a reaction generally increases. This is because an increase in temperature leads to an increase in the kinetic energy of the reactant molecules, which in turn increases the frequency and energy of successful collisions.

Effect of temperature on rate constants:
- As the temperature increases, the rate constant for a first order reaction (k1) will increase at a faster rate compared to the rate constant for a second order reaction (k2). This is because the increase in temperature has a greater effect on the rate of a first order reaction than on the rate of a second order reaction.
- However, even with the increase in temperature, the first order rate constant (k1) will always remain less than the second order rate constant (k2). This is because the energy of activation (E1) for the first order reaction is greater than the energy of activation (E2) for the second order reaction.
- Therefore, option 'A' is the correct answer.

Reasoning:
- The rate constant for a first order reaction is given by the Arrhenius equation: k1 = Ae^(-E1/RT), where A is the pre-exponential factor, E1 is the energy of activation, R is the gas constant, and T is the temperature.
- The rate constant for a second order reaction is given by the Arrhenius equation: k2 = Ae^(-E2/RT), where A is the pre-exponential factor, E2 is the energy of activation, R is the gas constant, and T is the temperature.
- As the temperature increases, the exponential term in both equations becomes larger, leading to an increase in the rate constants.
- However, since the energy of activation for the first order reaction is greater than the energy of activation for the second order reaction (E1 > E2), the increase in temperature has a bigger effect on the rate constant for the first order reaction (k1) compared to the rate constant for the second order reaction (k2).
- Therefore, with an increase in temperature, k1 will increase faster than k2, but it will always remain less than k2.

Conclusion:
- The rate constant for a first order reaction will increase faster than the rate constant for a second order reaction with an increase in temperature.
- However, the first order rate constant will always remain less than the second order rate constant due to the difference in energy of activation between the two reactions.
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Read the passage given below and answer the following questions:Nucleophilic substitution reaction of haloalkane can be conducted according to both SN1 and SN2 mechanisms. However, which mechanism it is based on is related to such factors as the structure of haloalkane, and properties of leaving group, nucleophilic reagent and solvent. Influences of halogen: No matter which mechanism the nucleophilic substitution reaction is based on, the leaving group always leave the central carbon atom with electron pair. This is just the opposite of the situation that nucleophilic reagent attacks the central carbon atom with electron pair. Therefore, the weaker the alkalinity of leaving group is , the more stable the anion formed is and it will be more easier for the leaving group to leave the central carbon atom; that is to say, the reactant is more easier to be substituted. The alkalinity order of halogen ion is I− < Br− < Cl− < F− and the order of their leaving tendency should be I− > Br− > Cl− > F−. Therefore, in four halides with the same alkyl and different halogens, the order of substitution reaction rate is RI > RBr > RCl > RF. In addition, if the leaving group is very easy to leave, many carbocation intermediates are generated in the reaction and the reaction is based on SN1 mechanism. If the leaving group is not easy to leave, the reaction is based on SN2 mechanism. Influences of solvent polarity: In SN1 reaction, the polarity of the system increases from the reactant to the transition state, because polar solvent has a greater stabilizing effect on the transition state than the reactant, thereby reduce activation energy and accelerate the reaction. In SN2 reaction, the polarity of the system generally does not change from the reactant to the transition state and only charge dispersion occurs. At this time, polar solvent has a great stabilizing effect on Nu than the transition state, thereby increasing activation energy and slow down the reaction rate. For example, the decomposition rate (SN1) of tertiary chlorobutane in 25° water (dielectric constant 79) is 300000 times faster than in ethanol (dielectric constant 24). The reaction rate (SN2) of 2-bromopropane and NaOH in ethanol containing 40% water is twice slower than in absolute ethanol. In a word, the level of solvent polarity has influence on both SN1 and SN2 reactions, but with different results. Generally speaking, weak polar solvent is favorable for SN2 reaction, while strong polar solvent is favorable for SN1 reaction, because only under the action of polar solvent can halogenated hydrocarbon dissociate into carbocation and halogen ion and solvents with a strong polarity is favorable for solvation of carbocation, increasing its stability. Generally speaking, the substitution reaction of tertiary haloalkane is based on SN1 mechanism in solvents with a strong polarity (for example, ethanol containing water).Q. Polar solvents make the reaction faster as they

At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature.a)k1 will increase faster than k2, but always will remain less than k2.b)k2 will increase faster than k1c)k1 will increase faster than k2 and becomes equal to k2.d)k1 will increase faster k2 and becomes greater than k2.Correct answer is option 'A'. Can you explain this answer?
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At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature.a)k1 will increase faster than k2, but always will remain less than k2.b)k2 will increase faster than k1c)k1 will increase faster than k2 and becomes equal to k2.d)k1 will increase faster k2 and becomes greater than k2.Correct answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature.a)k1 will increase faster than k2, but always will remain less than k2.b)k2 will increase faster than k1c)k1 will increase faster than k2 and becomes equal to k2.d)k1 will increase faster k2 and becomes greater than k2.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature.a)k1 will increase faster than k2, but always will remain less than k2.b)k2 will increase faster than k1c)k1 will increase faster than k2 and becomes equal to k2.d)k1 will increase faster k2 and becomes greater than k2.Correct answer is option 'A'. Can you explain this answer?.
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