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The rate at which tree crickets chirp is $2.0 \times 10^{2}$ per minute at $27^{\circ} \mathrm{C}$ but only 39.6 per minute at $5^{\circ} \mathrm{C}$. From these data, calculate the "activation energy" for the chirping process. (Hint: The ratio of rates is equal to the ratio of rate constants.)

$$51 \mathrm{kJ} / \mathrm{mol}$$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

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Hello. So did they were going to be looking at a situation where we have crickets chirping and I told 27 degrees Celsius they chirp 200 chirps per minute in a five degree Celsius day chirp 39.6 times per minute. So how about we try to treat this as Hey, chemical reaction? So this would be the rate we'll treat. This is a first order reaction. This is the rate. This is the temperature. And how about so First, In order to calculate the activation energy, we need to know the constant. So remember that the rate so at 27 is equal to equilibrium, constant and 27 se the concentration of the crickets. That's like a first order rate law right now. Say we divide that by the rate and five degrees Celsius, which would be the rate constant five degrees Celsius in the concentration of crickets. So if we assume that there's that but there's the same amount of crickets in both scenarios, then we would simply have that the rate, at 27 degrees Celsius over the rate at five degree Celsius, is the ratio of the kulaib of the rate constant 27 to the right constant on five degrees Celsius. And if we remember to find the activation energy, it would be simply the equilibrium, the rate constant at a low temperature. My nest, the natural algal vertically, every young concert at the high temperature, one over the low temperature and one over the high. But because I've earned rules of natural logs that can also be the natural log of they call him the lower crude bream constant in the high one. So now let's start plugging involved in values really quickly. Let's convert our temperature into Calvin. So let's add 273. That would be 300 Calvin. Then for five degree Celsius, it would be 278 so could have activation. Energy over 8.314 is equal to one over 278. That s one over 300. And we want the very constant at the low temperature over rate constant of the high temperature. So that would be the rate at the low temperature over the rate after high temperatures. 27. So that would be natural long of a 39.6 want to divide that by 2.0 times, 10 to the second. So let's do some math and we will see not the negative activation energy over 8.314 is equal to negative. 6140. Now let's multiply both sides by negative 8.314 we will see that we have 51 1000 42 Jules Primal, which is basically 51 killer jewels. Permal. So that would be our activation energy if this cricket chirping was, ah first to order reaction.

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