Welcome to the article The rate of reaction quadruples when the temperature changes from 293 Kelvin to 313 Kelvin Calculate the activation energy. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final answer:
The student's question concerns calculating the activation energy (Ea) based on the change in reaction rate with temperature, utilizing the Arrhenius equation. Without complete information, exact calculation is not possible; however, insights can be derived by relating the given temperature change's effect on rate to known effects with activation energy.
Explanation:
To calculate the activation energy (Ea) of a reaction based on the effect of temperature on the reaction rate, we use the Arrhenius equation. This equation relates the rate constant of a reaction with its temperature and activation energy:
where k is the rate constant, A is the frequency factor, e is Euler's number (approximately equal to 2.71828), Ea is the activation energy, R is the universal gas constant (8.314 J/Kmol), and T is the temperature in Kelvin.
In this case, the reaction rate quadruples, which implies that k2/k1 = 4, when the temperature is increased from 293 K to 313 K. Using the Arrhenius equation and taking the natural logarithm of both sides, we create the following equation:
ln(k2/k1) = (-Ea/R) * (1/T2 - 1/T1)
Now, by substituting k2/k1 = 4 and the given temperatures, we can solve for Ea:
ln(4) = (-Ea/8.314) * (1/313 - 1/293)
By rearranging and solving for Ea, you would find the activation energy for the reaction at these temperatures. However, the question does not provide sufficient information to calculate the exact value of Ea without simplifying assumptions (such as the frequency factor A remaining constant). Therefore, to fully answer this question, you would need additional information or would use the information provided about how a certain activation energy (54 kJ/mol) results in a doubling of the rate to infer the activation energy for a quadrupling of the rate.
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