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The activation energies of two reactions are given as Ea1= 40 J and Ea2= 80 J, then the relation between their rate constants can be written as:
  • a)
    k1 > k2
  • b)
    k1 < k2
  • c)
    k1 = k2
  • d)
    k1 + k2 = 0
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The activation energies of two reactions are given as Ea1= 40 J and Ea...
As the value of activation energy, Ea increases, the value of rate constant, k decreases.
 So, k1 > k2 since E1 < E2
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The activation energies of two reactions are given as Ea1= 40 J and Ea...
Explanation:

To understand the relation between the rate constants of two reactions with different activation energies, we need to refer to the Arrhenius equation. The Arrhenius equation relates the rate constant (k) of a reaction to the activation energy (Ea) and the temperature (T). The equation is given as:

k = A * e^(-Ea/RT)

Where:
- k is the rate constant
- A is the pre-exponential factor or frequency factor
- Ea is the activation energy
- R is the gas constant
- T is the temperature in Kelvin

Now, let's consider two reactions with activation energies Ea1 and Ea2. According to the Arrhenius equation, their rate constants k1 and k2 can be written as:

k1 = A1 * e^(-Ea1/RT)
k2 = A2 * e^(-Ea2/RT)

Relation between the Rate Constants:

To find the relation between k1 and k2, we can divide the two equations:

k1/k2 = (A1 * e^(-Ea1/RT)) / (A2 * e^(-Ea2/RT))

Now, let's simplify the equation. Since A1 and A2 are the pre-exponential factors and they do not depend on temperature or activation energy, we can cancel them out:

k1/k2 = e^(-Ea1/RT) / e^(-Ea2/RT)

To simplify the equation further, we can use the properties of exponents. When dividing two numbers with the same base, the exponents subtract:

k1/k2 = e^((-Ea1/RT) - (-Ea2/RT))
k1/k2 = e^(-Ea1/RT + Ea2/RT)

Now, let's simplify the exponents by combining like terms:

k1/k2 = e^((Ea2 - Ea1)/RT)

Since Ea2 > Ea1 (given in the question), the exponent (Ea2 - Ea1) is positive. Therefore, e^(positive) is always greater than 1.

Therefore, we can conclude that k1/k2 > 1, which means k1 is greater than k2. So, the correct relation between the rate constants is:

k1 > k2 (Option A)
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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

The activation energies of two reactions are given as Ea1= 40 J and Ea2= 80 J, then the relation between their rate constants can be written as:a)k1 > k2b)k1<k2c)k1 = k2d)k1+k2= 0Correct answer is option 'A'. Can you explain this answer?
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