Activation energy of a certain reaction

In summary, using the Arrhenius Equation and the given values of the activation energy and rate constant, the temperature at which this reaction would go twice as fast can be calculated by setting k2/k1 equal to 2 and solving for T2. This can be done by rearranging the equation ln(k2/k1) = (Ea/R)(1/T1 - 1/T2) and plugging in the values for k1, Ea, and T1. The resulting value for T2 will be the desired temperature.
  • #1
sam.
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The activation energy of a certain reaction is 45.8 kJ/mol. At 20 degrees celsius, the rate constant is 0.0130 s^(-1). At what temperature would this reaction go twice as fast?

Arrhenius Equation:k = Ae^(-E_a/RT)

ln(k_2 / k_1) = (E_a /R)(1/T_1 - 1/T_2)

Okay, so I'm not quite sure how to approach this problem. I think you're supposed to solve for k_2 and then sub it into find the activation energy and then find the temperature. But I don't know how to solve for k_2 if I'm not given a second temperature. Any help is appreciated!
 
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  • #2
You are given that k2/k1=2.
 
  • #3


To find the temperature at which the reaction would go twice as fast, we can use the Arrhenius Equation and set k_2 = 2k_1 (since we want the reaction to go twice as fast). This gives us:

ln(2k_1 / k_1) = (E_a/R)(1/T_1 - 1/T_2)

Simplifying, we get:

ln(2) = (E_a/R)(1/T_1 - 1/T_2)

We know the activation energy (E_a = 45.8 kJ/mol) and the rate constant at 20 degrees celsius (k_1 = 0.0130 s^(-1)). So we can plug these values in and solve for T_2:

ln(2) = (45.8 kJ/mol / 8.314 J/molK)(1/293.15 K - 1/T_2)

Solving for T_2, we get:

T_2 = 1/(1/293.15 K - ln(2) * 8.314 J/molK / 45.8 kJ/mol)

T_2 = 352.4 K

Therefore, at a temperature of 352.4 K, the reaction would go twice as fast as it does at 20 degrees celsius.
 

FAQ: Activation energy of a certain reaction

What is activation energy?

Activation energy is the minimum amount of energy required for a chemical reaction to occur. It is the energy needed to break apart the bonds of the reactant molecules and initiate a chemical reaction.

How does activation energy affect a reaction?

The higher the activation energy, the slower the reaction will occur. This is because a higher amount of energy is needed to break the bonds of the reactant molecules, making the reaction more difficult to initiate. On the other hand, a lower activation energy means the reaction will occur more quickly.

What factors can affect the activation energy of a reaction?

The temperature, concentration of reactants, and presence of a catalyst can all affect the activation energy of a reaction. Increasing the temperature or concentration of reactants can lower the activation energy, while the use of a catalyst can decrease the activation energy even further.

How is activation energy determined experimentally?

Activation energy can be determined experimentally by measuring the reaction rate at different temperatures and using this data to calculate the activation energy using the Arrhenius equation. Alternatively, it can also be determined by using a graphical method called the Arrhenius plot.

Can the activation energy of a reaction be negative?

No, the activation energy of a reaction cannot be negative. It is always a positive value as it represents the amount of energy needed for a reaction to occur. However, a negative activation energy can be observed if the reaction is exothermic, meaning it releases energy as it occurs.

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