The reaction between ethyl iodide and hydroxide ion in ethanol (C 2 H 5 OH) solution, C 2 H 5 I(alc) + OH - (alc) → C 2 H 5 OH(l) + I - (alc), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 × 10 11 M -1 s -1 . (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

hi everyone for this problem, it reads ethanol can be dehydrated over alumina catalyst to yield ethylene and water. The activation energy and the frequency factor for the reaction are 26. kg per mole and three times 8 to 10 to the eighth seconds inverse, respectively, calculate the rate constant for the reaction at 75 degrees Celsius assume that the activation energy and the frequency factor do not change with temperature. Okay, so our goal here is to calculate the rate constant for the reaction At 75°C. And we can calculate the rate constant using the Iranians equation. And that equation is Ln of K is equal to A times E raise to negative activation energy over R. T. Okay, so let's just write in what we know based off of what was given in the problem. So we know what A is a is our Frequency factor and we're told it is 3.00 times 10 To the 8th seconds Inverse. Our activation energy was also given that is 26.6 killer jewels per mole. Our is our constant and it is a value. We should have memorized that is 8.314 jewels over Mul Times Kelvin. And our temperature is 75°C. So let's just take a look at our units here to make sure everything matches for our our we have our energy and jewels and our temperature in Kelvin. So that means we need to convert our activation energy to jewels and in one kill a jewel We have 1000 jewels. So that means our activation energy and jules is going to be 26, jewels per mole. And for a temperature we need to go from C to Kelvin and we can do that by adding 273.15. So that's going to give us the temperature in Kelvin of 348.15 Kelvin. Okay, so now we have everything that we need to plug into our equation above to solve for this problem. So let's go ahead and do that. So we have L N. F K is equal to a which is 3.0 times 10 to the eighth seconds, inverse times E raised to negative activation energy. So negative 26, jules Permal over our 8.314 jewels over more times kelvin times temperature 348.15 kelvin. Okay, so if we simplify this a little bit, we'll get Ln of K is equal to 3. times 10 To the 8th seconds, Inverse times E raised to the negative 9.19. Okay, so moving from here when we saw this out by raising um the E to the negative 9.19. That's going to cancel out the L N. Okay, and so this L N is going to cancel here because we have the race to Okay, so then we're going to get a final answer of K, Which is our rate constant. K is equal to 3.06 times 10 to the fourth seconds inverse. Okay, so 3.06 times 10 to the 4th, 2nd inverse is our rate constant. And that is the answer to this problem, and that is the end of this problem. I hope this was helpful.

Ch.14 - Chemical Kinetics

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Brown 14th Edition

Ch.14 - Chemical Kinetics

Problem 118d

Chapter 14, Problem 118d

The reaction between ethyl iodide and hydroxide ion in ethanol (C₂H₅OH) solution, C₂H₅I(alc) + OH^-(alc) → C₂H₅OH(l) + I^-(alc), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 × 10¹¹ M^-1 s^-1. (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

Verified step by step guidance

Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature (50 °C).

Use the Arrhenius equation: \( k = A \cdot e^{-\frac{E_a}{RT}} \), where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin.

Substitute the given values into the Arrhenius equation: \( A = 2.10 \times 10^{11} \text{ M}^{-1} \text{ s}^{-1} \), \( E_a = 86.8 \text{ kJ/mol} \) (convert this to J/mol by multiplying by 1000), and \( T \) is the temperature in Kelvin calculated in step 1.

Calculate the exponent \( -\frac{E_a}{RT} \) using the values from step 3.

Compute the rate constant \( k \) by evaluating the Arrhenius equation with the calculated exponent and the given frequency factor.

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Key Concepts

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

Arrhenius Equation

The Arrhenius equation relates the rate constant of a chemical reaction to temperature and activation energy. 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 shows how an increase in temperature can lead to an increase in the rate constant, thereby accelerating the reaction.

Activation Energy

Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. In the context of the Arrhenius equation, a higher activation energy results in a lower rate constant at a given temperature, indicating that the reaction proceeds more slowly. Understanding activation energy is crucial for predicting reaction rates and mechanisms.

Temperature Conversion

Temperature must be expressed in Kelvin when using the Arrhenius equation. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. For example, 50°C is equivalent to 323.15 K. Accurate temperature conversion is essential for correctly calculating the rate constant, as the rate constant is temperature-dependent and influences the overall reaction kinetics.