2) The activation energy of a certain reaction is 75000 joules.When a catalyst is introduced into the system the activation energy decreases by 23000 joules.Calculate how many times the reaction rate increases after adding a catalyst . if we assume that both reactions occur at 25^circ C

To calculate how many times the reaction rate increases after adding a catalyst, we can use the Arrhenius equation:<br /><br />k = A * e^(-Ea/RT)<br /><br />where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.<br /><br />Given that the activation energy of the reaction is 75000 joules and the activation energy decreases by 23000 joules when a catalyst is introduced, we can calculate the new activation energy:<br /><br />New activation energy = 75000 - 23000 = 52000 joules<br /><br />Now, we can calculate the ratio of the rate constants before and after adding the catalyst:<br /><br />Ratio = k2 / k1 = e^(-Ea1/RT) / e^(-Ea2/RT)<br /><br />Since both reactions occur at the same temperature (25°C), we can simplify the equation:<br /><br />Ratio = e^(-(Ea1 - Ea2) / RT)<br /><br />Substituting the given values:<br /><br />Ratio = e^(-(75000 - 52000) / (8.314 * 298))<br /><br />Ratio ≈ e^(-0.693)<br /><br />Ratio ≈ 0.5<br /><br />Therefore, the reaction rate increases by a factor of 2 (or 2 times) after adding a catalyst.