The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5⨉10 11 / s. Calculate the rate constant of the reaction at 25 °C.

Hi everyone for this problem. We're being asked to calculate the rate constant for a reaction that has an activation energy of 45. kg per mole and a frequency factor of 2. times 10 to the 10 At 38°C. Okay, so let's start off by writing out our our equation that we're going to need to solve for this problem. And that is our rate constant is equal to our frequency factor times our negative activation energy over r universal gas constant times our temperature. Okay, so this is what we're going to use to solve this. Let's take a look at what we're given. So our activation energy is 45.8 kg joules per mole. We need to convert this to jules per mole. Okay, so our activation energy Is 45.8 kg joules per mole. And to go from killer jewels, promoter joules per mole will use one. Kill a jewel Is equal to jewels. So this gives us an activation energy of 4.58 times 10 to the four jewels Permal secondly, we're given our temperature and C but we need to convert it to Kelvin. So our temperature is equal to 38°C. And to go to Kelvin we add 273.15. So we get a temperature of four. Sorry we got a temperature of .15 Kelvin. So that is all that we needed to convert. And so let's go ahead and plug in. So our Frequency factor was given, were told that it is 2.38 times 10 to the And then we have to, we have to put a negative in front of our activation energy. So we get negative 4. Times 10 to the 4th jewels per mole. And this is all over our universal gas constant, which is a value we should know. And that is 8. 314 8.314 jewels Over Mole Times Kelvin. And this is multiplied by our temperature in Kelvin 311. Kelvin. So we have everything that we need to solve four, our rate constant. And when we solve this problem, we get a final answer of K is equal to 4.90 times to the second seconds and verse. And this is our final answer. Okay, that's the end of this problem. I hope this was helpful.

Ch.14 - Chemical Kinetics

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Tro 4th Edition

Ch.14 - Chemical Kinetics

Problem 61

Chapter 14, Problem 61

The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5⨉10¹¹/ s. Calculate the rate constant of the reaction at 25 °C.

Verified step by step guidance

Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: \( T = 25 + 273.15 \).

Use the Arrhenius equation to relate the rate constant \( k \) to the activation energy \( E_a \), frequency factor \( A \), and temperature \( T \): \( k = A \cdot e^{-E_a/(RT)} \).

Convert the activation energy from kJ/mol to J/mol by multiplying by 1000: \( E_a = 56.8 \times 1000 \).

Use the gas constant \( R = 8.314 \) J/(mol·K) in the Arrhenius equation.

Substitute the values for \( A \), \( E_a \), \( R \), and \( T \) into the Arrhenius equation and solve for \( k \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. In the context of the Arrhenius equation, a higher activation energy typically results in a slower reaction rate, as fewer molecules have sufficient energy to react at a given temperature.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation highlights how temperature and energy barriers influence reaction rates.

Rate Constant

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, indicating the speed at which the reaction occurs. It is influenced by factors such as temperature and activation energy. A higher rate constant signifies a faster reaction, while a lower rate constant indicates a slower reaction, making it a crucial parameter in chemical kinetics.