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The Arrhenius Equation: What Is It?
The Arrhenius equation is expressed as follows: Equation of Arrhenius:
K = A[tex]e^{-Ea/RT}[/tex]
where k stands for the reaction's rate constant.
According to the collision theory, the frequency of correctly oriented collisions between the responding species is represented by the pre-exponential factor A, where e is the base of the natural logarithm (Euler's number).
Ea stands for the reaction's activation energy (in terms of energy per mole)
R stands for the global gas constant.
T stands for the reaction's related absolute temperature (in Kelvin)
The Boltzmann constant (kB) must be used in place of the universal gas constant (kG) in the Arrhenius equation if the activation energy is represented in terms of energy per reactant molecule. Svante Arrhenius, a Swedish scientist, proposed the Arrhenius equation in 1889.
What exactly are significant digits?
The critical figures of a number are the crucial or significant digits that accurately convey the meaning of that number.6.658, for instance, has four significant digits. These huge amounts give the numbers accuracy. Additionally, they are known as significant digits.
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The activation energy of this reaction is 22.87 KJ/mol.
The bare minimum additional energy needed by a reactive molecule to transform into a product is known as activation energy. It is also known as the minimal energy required to energise or activate molecules or atoms in order for them to engage in a chemical reaction or transformation.
Using the formula,
ln k₁/k₂ = - Eₐ/R (1/T₁ - 1/T₂)
where;
k₁ = Rate constant at T₁ = 4.8 X 10⁸
k₂ = Rate constant at T₂ = 2.3 X 10⁸
Eₐ = Activation energy
R = Gas constant = 8.314 X 10⁻³ KJ/k mol
T₁ = 376 ⁰C
T₂= 280 ⁰C
We need to convert T(°C) to T (K)
T(K) = T(°C) + 273.15
T₂ = (280 + 273.15)K = 553.15K
T₁ = (376 + 273.15)K = 649.15K
So,
[ln(4.8X10⁸/2.3X10⁸)] = (Eₐ/8.314X10⁻³ KJ/mol k) X (1/649.15K -1/553.15K)
Eₐ = [tex]\frac{10^{-3}X 8.314 ln(10^{8}X4.8)(10^{8} X2.3) }{\frac{-96}{359077.3225} }[/tex] KJ/mol = 22.87 KJ/mol
The activation energy of this reaction is 22.87 KJ/mol
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I understand that the question you are looking for is "The rate constant k for a certain reaction is measured at two different temperatures temperature 376.0 °c 4.8 X 10⁸ 280.0 °C 2.3 X 10⁸ Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy E for this reaction. Round your answer to 2 significant digits. kJ x10 mol"
