Values of E a = 6.3 kJ/mol and A = 6.0⨉10 8 /(M s) have been measured for the bimolecular reaction: NO(g) + F 2 (g) → NOF(g) + F(g) (a) Calculate the rate constant at 25 °C.

Hi everyone. This problem reads the activation energy is 160 kg per mole. And the frequency factor A is 4.73 times 10 to the 10th per meter. Second for the biomolecular reaction below. What is the rate constant Of the reaction at 300°C. So this is the question that we want to answer. Let's start off by writing out the equation that we're going to need to solve this problem. And that equation is the following. Okay. And what this means is K. Is rate constant A. Is the Iranians constant or frequency factor negative E. A. Is activation energy and jewels per mole. R. Is the gas constant and T. Is temperature. So by solving for the rate constant, what we're doing here is solving for K. Okay. And what we're going to need to do is plug in everything else into this equation so that we can solve for that. But the first thing that we're going to need to do is convert our activation energy which is we're told is 160 killer jewels Permal. We need to convert this from Kill the jewels, two jewels per mole. Okay, and the way that we're going to do that is by using the conversion one. Kill a jewel Is equal to 1000 jewels. Okay, so our killer jewels canceled and now we have the units of joules per mole. So our activation energy is 1.60 times 10 to the fifth jewels per mole. Okay. And another thing we're going to need to convert is the temperature. Okay, so the temperature we're told is 300°C, but we need the unit of temperature to match our gas constant. R. So let's write out our gas constant art. That is 8.314 jewels Permal kelvin. As you can see here, kelvin is the unit for temperature in r gas constant. So our temperature is going to need to go from degrees Celsius to kelvin. And the way that we do that is by adding 273.15. So temperature now becomes 573.15 kelvin. So we've converted everything that we need to convert. So now we can go ahead and plug in these values into our equation. So let's go ahead and do that. Okay, so we have K. Which is our rate constant is going to equal the Iranians constant, which is given in the problem, that is 4.73 times 10 to the 10 per meter second. And this is times E. The function E, which is a function on our calculator raised to negative activation energy. So we'll have negative one point 60 times to the five jewels per mole. So negative activation energy over R times T R is r. Gas constant 8.314 jewels per mole kelvin Times temperature in Kelvin 573.15 Kelvin. So now that we have plugged everything in, let's go ahead and simplify just a bit. So we have 4.73 times 10 to the 10th meter second, and this side becomes E. Raised to the -33.576, 9, 8, 2, 6 1. Okay, so Once we solve for this and we plug it into our calculator, what we're going to get for K, which is our rate constant is that K is going to equal 1. times 10 To the negative 4th meter seconds, and this is going to be our final answer. Okay, so this is going to be the rate constant of the reaction at 300°C. That is it for this problem? I hope this was helpful.

Ch.14 - Chemical Kinetics

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McMurry 8th Edition

Ch.14 - Chemical Kinetics

Problem 137a

Chapter 14, Problem 137a

Values of E_a = 6.3 kJ/mol and A = 6.0⨉10⁸/(M s) have been measured for the bimolecular reaction: NO(g) + F₂(g) → NOF(g) + F(g) (a) Calculate the rate constant 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 \( E_a \), the frequency factor \( A \), and the temperature \( T \): \( k = A \cdot e^{-E_a/(RT)} \).

Substitute the given values into the Arrhenius equation: \( A = 6.0 \times 10^8 \text{ M}^{-1}\text{s}^{-1} \), \( E_a = 6.3 \text{ kJ/mol} \) (convert to J/mol by multiplying by 1000), and \( R = 8.314 \text{ J/mol K} \).

Calculate the exponent in the Arrhenius equation: \( -E_a/(RT) \).

Substitute the calculated exponent back into the Arrhenius equation to find the rate constant \( k \).

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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 reaction to the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. This equation helps predict how changes in temperature affect reaction rates.

Activation Energy (Ea)

Activation energy 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 lower Ea results in a higher rate constant, indicating that the reaction can proceed more quickly at a given temperature.

Rate Constant (k)

The rate constant is a proportionality factor in the rate law of a chemical reaction, indicating the speed of the reaction. It varies with temperature and is influenced by factors such as activation energy and molecular collisions. For bimolecular reactions, the rate constant can be calculated using the Arrhenius equation, which incorporates temperature and activation energy.