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?

Question

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 &#62; k2b)k1&#60;k2c)k1 = k2d)k1+k2= 0Correct answer is option 'A'. Can you explain this answer?

Answer

As the value of activation energy, Ea increases, the value of rate constant, k decreases.

So, k1 > k2 since E1 < E2

Answer

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)

Answer

Activation energy is inversely proportional to constant.so energy increase and value of constant decreases.

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