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Arrhenius Rate Equation

The activation energy for a process is 55,000 cal/mole. The rate of this process is known at 400^{o}C.

What is the incremental temperature needed to double the rate?

**The strings**:

S_{7}P_{5}A_{52} (Change - Chemical Change)
**The math**:

Pj Problem of Interest is of type *change* (chemical change). The rate of the chemical reaction is being changed by changing the temperature.

Temperature is a primary influencer of the rate of a chemical reaction. Concentrations of reactants is also a primary influencer of chemical reactions. In biochemical systems, enzymes are important influencer of biochemical reactions.

In 1893 A.D. Svante Arrhenius proposed an equation (now known as Arrhenius equation) that relates the rate of a chemical reaction with temperature. Arrhenius was also a pioneer in modern electrolyte theory.

Arrhenius Rate Equation

**φ = Ae ^{(-Ea/kT)}** -------------(1)

where A is a constant, e is natural logarithm,

E

k is Boltzman's constant = 3.30 x 10

T is temperature degrees Kelvin.

If the activation energy is expressed in cal/mole, k is replaced by the universal gas constant R = 1.987 (cal/

Now, 400

So, at 400

At temperature T, rate is doubled

So, 2Ae

Taking natural logarithm:

So, ln2 - E

So, ln2 = (E

so, Rln2/E

So, (1.987 x 0.693)/55000 = 0.001486 - 1/T

So, 0.0000250 = 0.0014858 - 1/T

So, 1/T = 0.0014858 - 0.0000250 = 0.001461

So, T = 684.5

So, rate at 400

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

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