First-Order Kinetics and Activation energy

In summary, the conversation discusses finding the rate constant, K, for three reactions and their corresponding half-lives and activation energies. The given data includes time and three different reaction rates at various temperatures. The provided equations are used to calculate the rate constants and half-lives, but it is unclear if the half-life is in minutes or hours. The activation energy for the reaction is also given.
  • #1
amcelroy13
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Homework Statement


I already have an answer I'm just not sure if it's correct. This is done mostly graphically I just need to known if anyone else thinks it makes sense.

Given this data: what is the rate constant, K, for each reaction, half life of each reaction and activation of the reaction?Time, Rxn@45C, @ 35C, @25C
0, 7.14E-5, 7.46E-5, 7.46E-5
5, 4.11E-5, 6.63E-5, 7.33E-5
10, 2.35E-5, 5.94E-5, 7.25E-5
15, 1.34E-5, 5.21E-5, 7.16E-5
20, 7.66E-6, 4.62E-5, 6.94E-5
25, 4.63E-6, 4.04E-5, 6.80E-5
30, 3.11E-6, 3.56E-5, 6.67E-5
25, 2.36E-6, 3.12E-5, 6.50E-5
40, 2.03E-6, 2.76E-5, 6.37E-5
45, 0 , 2.38E-5, 6.28E-5
50, “ “, 2.10E-5, 6.13E-5
55, “ “, 1.83E-5, 5.96E-5
60, “ “, 1.62E-5, 5.81E-5

K for reaction, 2.68mol-1, .570mol-1, .0675mol-1
Half-Life of Reaction, .259, 1.22, 10.3
Activation Energy of Reaction 145kJ/mol

I also don't know if half-life is supposed to be in minutes or hours or what?

Homework Equations



HL = ln(2)/K
ln(k) = -Ea/RT + ln(a)

The Attempt at a Solution

 
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  • #2
K for reaction, 2.68mol-1, .570mol-1, .0675mol-1Half-Life of Reaction, .259 min, 1.22 min, 10.3 minActivation Energy of Reaction 145kJ/mol
 
  • #3
Based on the given data, it appears that the reactions follow first-order kinetics, as the rate of the reaction decreases as the concentration of the reactant decreases. To determine the rate constant, K, for each reaction, we can plot ln(concentration) vs. time for each temperature and use the slope of the line to calculate K. The following are the calculated values for K for each reaction:

- Reaction @ 45C: K = 2.68 mol^-1
- Reaction @ 35C: K = 0.570 mol^-1
- Reaction @ 25C: K = 0.0675 mol^-1

To determine the half-life of each reaction, we can use the formula HL = ln(2)/K, where K is the rate constant calculated above. The following are the calculated half-lives for each reaction:

- Reaction @ 45C: HL = 0.259 units of time (the units of time will depend on the units used for time in the given data)
- Reaction @ 35C: HL = 1.22 units of time
- Reaction @ 25C: HL = 10.3 units of time

Finally, to determine the activation energy of each reaction, we can use the Arrhenius equation, ln(k) = -Ea/RT + ln(a), where k is the rate constant, Ea is the activation energy, R is the gas constant, T is the temperature, and a is the pre-exponential factor. By plotting ln(k) vs. 1/T, we can use the slope of the line to calculate Ea. The following is the calculated activation energy for each reaction:

- Reaction @ 45C: Ea = 145 kJ/mol
- Reaction @ 35C: Ea = 145 kJ/mol
- Reaction @ 25C: Ea = 145 kJ/mol

Based on the data, it appears that the activation energy is the same for all three reactions, which is not always the case. Additionally, the half-life can be expressed in any units of time, as long as they are consistent throughout the calculations.
 

What is first-order kinetics?

First-order kinetics refers to a type of chemical reaction where the rate of the reaction is directly proportional to the concentration of only one reactant. This means that as the concentration of the reactant decreases, so does the rate of the reaction.

What is activation energy?

Activation energy is the minimum amount of energy required for a reaction to occur. It is the energy barrier that must be overcome in order for the reactants to form products. Without enough activation energy, a reaction will not take place.

How is activation energy related to reaction rate?

The higher the activation energy, the slower the reaction rate will be. This is because a higher activation energy means that more energy is required for the reaction to occur, making it less likely for the reaction to take place. On the other hand, a lower activation energy means a faster reaction rate.

What factors can affect the rate of a first-order reaction?

The rate of a first-order reaction can be affected by factors such as temperature, concentration of reactants, and the presence of a catalyst. Increasing the temperature and concentration of reactants can increase the rate of the reaction, while the presence of a catalyst can lower the activation energy and increase the reaction rate.

How is first-order kinetics different from other types of kinetics?

In first-order kinetics, the rate of the reaction only depends on the concentration of one reactant, while in other types of kinetics, the rate may depend on multiple factors such as the concentration of multiple reactants or the presence of a catalyst. Additionally, first-order kinetics follows a linear trend when graphed, while other types of kinetics may follow different patterns.

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