Answer:
Activation energy for the reaction is 39029J/mol
Explanation:
Arrhenius equation is an useful equation that relates rate of reaction at two different temperatures as follows:
[tex]ln\frac{K_2}{K_1} = \frac{-Ea}{R} (\frac{1}{T_2} -\frac{1}{T_1} )[/tex]
Where K₁ and K₂ are rate of reaction, Ea is activation energy and R is gas constant (8.314J/molK
If the reaction at 400K is 50 times more faster than at 300K:
K₂/K₁ = 50 where T₂ = 400K and T₁ = 300K:
[tex]ln50 = \frac{-Ea}{8.314J/molK} (\frac{1}{400K} -\frac{1}{300K} )[/tex]
[tex]ln 50 = 1x10^{-4}Ea[/tex]
Ea = 39029 J/mol
The activation energy for this chemical reaction is equal to 39,029.24 J/mol.
Given the following data:
Ideal gas constant, R = 8.314 J/molK
To determine the activation energy for this chemical reaction, we would use the Arrhenius' equation:
Mathematically, Arrhenius' equation is given by the formula:
[tex]ln\frac{K_2}{K_1} = \frac{-E_a}{R} (\frac{1}{T_2} - \frac{1}{T_1})[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]ln50 = \frac{-E_a}{8.314} (\frac{1}{400} - \frac{1}{300})\\\\3.9120 = \frac{-E_a}{8.314} (\frac{-1}{1200})\\\\3.9120 = \frac{E_a}{9976.8} \\\\E_a = 9976.8 \times 3.9120\\\\E_a = 39,029.24 \;J/mol[/tex]
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