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Determine the activation energy for the electrochemical reaction that occurs between copper and nitric acid (Cu + 4HNO3 --> Cu(NO3)2 + 2NO2 + 2H2O) given that the rate constant k is 2.31 x 10^-6 mol L^-1 s^-1 at 25°C and the rate constant increases to 3.81 x 10^-5 mol L^-1 s^-1 at 45°C.

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ago by (340 points)
To determine the activation energy  Ea  for the electrochemical reaction between copper and nitric acid, we can use the Arrhenius equation:k = A * exp -Ea /  R * T  where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant  8.314 J mol^-1 K^-1 , and T is the temperature in Kelvin.We have two sets of data: k1 = 2.31 x 10^-6 mol L^-1 s^-1 at T1 = 25C  298 K  and k2 = 3.81 x 10^-5 mol L^-1 s^-1 at T2 = 45C  318 K . We can set up two equations using the Arrhenius equation:k1 = A * exp -Ea /  R * T1  k2 = A * exp -Ea /  R * T2  Now, we can divide the first equation by the second equation to eliminate the pre-exponential factor  A :k1 / k2 = exp -Ea /  R * T1   / exp -Ea /  R * T2  Simplifying the equation:k1 / k2 = exp  Ea /  R * T2   -  Ea /  R * T1   Now, we can take the natural logarithm of both sides:ln k1 / k2  =  Ea /  R * T2   -  Ea /  R * T1  Rearranging the equation to solve for Ea:Ea = R *  T1 * T2  * ln k1 / k2  /  T2 - T1 Plugging in the given values:Ea = 8.314 J mol^-1 K^-1 *  298 K * 318 K  * ln  2.31 x 10^-6  /  3.81 x 10^-5   /  318 K - 298 K Ea  8.314 * 94524 *  -2.72  / 20Ea  -214,799 J mol^-1Since the activation energy cannot be negative, there must be an error in the calculation. Let's check the equation again:ln k2 / k1  =  Ea /  R * T1   -  Ea /  R * T2  Rearranging the equation to solve for Ea:Ea = R *  T1 * T2  * ln k2 / k1  /  T1 - T2 Plugging in the given values:Ea = 8.314 J mol^-1 K^-1 *  298 K * 318 K  * ln  3.81 x 10^-5  /  2.31 x 10^-6   /  298 K - 318 K Ea  8.314 * 94524 * 2.72 / -20Ea  107,399 J mol^-1So, the activation energy for the electrochemical reaction between copper and nitric acid is approximately 107,399 J mol^-1 or 107.4 kJ mol^-1.

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