The respiration of plants is a biochemical reaction and should have a rate determined by the Arrhenius equation, k = Ae-EA/RT. Here, k is the rate, A is a constant, EA is the activation energy for the reaction, R is the gas constant, and T is the temperature in kelvins.
If the rate doubles for a 6 kelvin rise in temperature at around room temperature, what is the activation energy for the reaction?
R is about 8.31 J/K-mol. The value of e is 2.718, but you only have to know that ln(2) is about 0.693 and that you can rewrite the Arrhenius equation as ln(k) = -EA/RT. That means that the reaction rate doubles when the value of EA/RT changes by 0.693, or the value of EA/T changes by 0.693×8.31 J/K-mol = 5.76 J/K-mol.
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To find the activation energy for the reaction, we can start by using the given information:
- The rate of the reaction doubles for a 6 Kelvin rise in temperature at around room temperature.
- R is approximately 8.31 J/K-mol.
- The value of e is approximately 2.718.
According to the Arrhenius equation, ln(k) = -EA/RT.
We know that ln(2) is approximately 0.693, so when the rate doubles, the value of ln(k) increases by 0.693.
Rearranging the equation, we have EA/RT = -ln(k).
To determine the change in EA/RT, we can subtract the initial value of ln(k) from the new value when the rate doubles. In this case, the change is 0.693.
Next, we multiply the change in ln(k) by R to find the change in EA/T. So, 0.693 * 8.31 J/K-mol = 5.76 J/K-mol.
Therefore, the activation energy for the reaction is approximately 5.76 J/K-mol.